harmony in music essay

Open Music Theory

Performing a harmonic analysis.

Analyzing harmony in a piece or passage of music involves more than labeling chords. Even the most basic analysis also involves interpreting the way that specific chords and progressions function within a broader context. Ultimately, no analysis is complete until individual musical elements are interpreted in light of the work as a whole and the historical setting in which the piece occurs. But this resource simply walks through the steps of performing a basic harmonic analysis, interpreting each chord and chord progression in light of the musical phrase in which it occurs.

The first step in a harmonic analysis is to identify phrases . For the most part, that means beginning by identifying cadences . However, not every type of phrase ends with a cadence, so sensitivity to theme types is important. In classical instrumental music, that means listening for period- and sentence-like structures . In classical or romantic music with text, that means listening in particular for the ends of poetic lines and melodic phrases.

Once you have identified the musical phrases, it can be helpful to perform a harmonic reduction (thoroughbass reduction, for example) for each phrase. Below the score/thoroughbass line, write the appropriate Roman numeral, T/S/D label for each chord, and/or an uninterpreted functional bass symbol for each chord ( T1 T3 S4 etc.). This handout can help you determine the functions of chords in the thoroughbass reduction.

Next identify the general harmonic structure of each phrase. Typical phrases in classical music will do one of the following:

prolong tonic without a cadence (a classical presentation phrase, for example)
progress toward an authentic cadence (ending with V (7) I , D5 T1 in functional bass)
progress toward a half cadence (ending with V , D5 in functional bass)

If the phrase prolongs tonic (no cadence), label the entire phrase T–––.

If the phrase ends with a cadence, identify the cadential progression . This includes the last chord of the tonic zone, optionally followed by a subdominant chord or zone (most often a single chord), and a required dominant zone (most often a single chord or compound cadence formula). Half-cadence phrases end there. Authentic-cadence phrases continue on to a final tonic zone (usually a single chord).

The the (S) D T of the cadential progression should be labeled as such. Once the cadential progression is identified, everything before it is labeled as tonic prolongation. Regardless of whether it is contrapuntal prolongation, a subsidiary progression, or a combination of the two, it will be labeled T–––. (See Harmonic syntax – prolongation if those terms are unfamiliar to you.)

Thus a phrase ending with a half cadence will have a functional analysis that looks like:

T—————— (S) D

A phrase ending with an authentic cadence will have a functional analysis that looks like:

T—————— (S) D T

Following is an excerpt from the opening of Haydn’s Piano Sonata in C Major, Hob. HVI:21, I. Chords are labeled with Roman numerals and a T/S/D functional label for each chord. The tonic prolongation is shown below that with a T followed by a line for the duration of the tonic zone. The cadential progression is comprised of the last tonic chord (m. 4) through S D T to the PAC in m. 6.

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Understanding harmony in music: a beginner’s guide

Often when we think of a song, our initial thoughts gravitate towards the melody . The melody or “top-line” is the part of the music that we hum or sing, and the aspect that often lingers in our memories. But a melody seldom stands on its own. The richness and captivating dynamics of a melody largely stem from its surrounding harmonies and chords.

If we understand the definition of harmony in music we can use it to inject our melodies with life. Through clever use of harmony, we can imbue melodies with tension and resolution, complexity and depth.

You may be asking yourself if you should focus on melody or harmony in your own songs. But it isn’t really a melody vs harmony situation. They work in tandem. While melody may be the ‘star’ of the song, it’s the harmony and chords that give the melody its charisma in the first place.

Jump to these sections:

What is harmony in music.

Consonant vs. dissonant

Tonic chords

Dominant chords, predominant chords, chord progressions, key signature, types of harmonies in music.

How to use harmony to make music

Follow along with this tutorial using Komplete Start , a free bundle of standout synths, drumkits, organic instruments, creative sound design tools, professional audio processing plugins, and much more.

Get Komplete Start Free

Harmony in music refers to the sounding of two or more notes simultaneously. Because these notes are being played at the same time and are “stacked” on top of each other, people sometimes refer to harmony as being a “vertical” aspect of music.

Harmony provides richness and texture to music, and it plays a crucial role in shaping the emotional and expressive qualities of a composition.

Let’s look at a basic form of harmonization by stacking notes on top of this C major scale:

If we play the C major scale with additional notes stacked on top of it (we’re starting on E here and going all the way up the same major scale) it sounds like this:

C major scale with an upper thirds harmony

On the other hand, if we play that same scale but harmonize starting with the A below it, it sounds like this:

C Major scale with a lower thirds harmony

This shows how harmonies can affect the same melody line in very different ways.

Ultimately, harmony serves to create a “tonal center” or a “home” key that we can resolve to and rest on. It allows us to create tension, and then release.

Jacob Collier explains the idea of the home key fantastically in this video:

It is worth mentioning here that the theory explored in this article is according to Western music practice. There are many alternative approaches to harmony, including scale systems, chords, and instrument tuning. Because popular music generally employs Western harmony, we are focusing on that.

Main aspects of harmony

Now that we broadly understand the definition of harmony in music, let’s break up some essential harmonic concepts: chords, chord progressions, key signatures, and modulation.

When answering the question “What is harmony in music?” it is essential to acknowledge the fundamental significance of chords in the context of harmony.

Chords serve as the very foundation of harmony, upon which a melody builds its evocative power. They provide the context and backdrop for the melody, allowing tunes to unfold and take us on a journey. It is through chords and harmony that music finds its sense of movement.

Chords usually incorporate three or more notes that are played or sung together. Assembling different chord combinations can give vastly different sonic results.

An easy way to construct chords is to take a scale and use every alternate scale degree as a chord note. Let’s look at the C major scale again.

We can construct a chord by taking three alternate degrees of that scale (take one note, skip one note).

Let’s listen to three alternate notes – C, E, and G – that, when sounded together create the C major chord. These are called “chord tones.”

Consonant vs. dissonant chords

Consonant chords are combinations of notes that create a stable and pleasing sound. They provide a sense of resolution and rest. Consonant chords can be major:

On the other hand, dissonant chords can create a tense, unstable, and even harsh sound.

It’s important to realize that while dissonance may sound “wrong” on its own, context is key in music. As seen in the example below, a dissonant chord creates tension that is resolved in a satisfying way by the following consonant chord.

The tonic chord is the “home” chord of a musical key. It is the most stable chord in a key and is often used at the beginning or end of a phrase. It is always made from the first degree of the scale. So in C major, the tonic chord is C major, and it is made up of C-E-G. Look at the highlighted notes in the piano roll. Those are the chord tones:

The C major chord derived from the C major scale

Dominant chords create a high level of anticipation as they precede tonic resolutions. The dominant chord in a key falls on the fifth degree of the scale. So in C major, the dominant chord is G major/dominant. Its chord tones are G-B-D.

The G major chord (dominant) derived from the C major scale

These chords function to set up dominant chords, so they usually occur before the dominant in a chord progression. There are several predominant chords including the second and fourth degrees of the scale. In the case of C major those are D minor and F major. The D minor chord is made up of D-F-A.

The D minor chord derived from the C major scale

The F major chord is made up of F-A-C.

The F major chord derived from the C major scale

In Western music, chords are often strung together to convey specific harmonic movements. These groupings of chords are called chord progressions, and they provide structure and direction to musical compositions.

Certain chord progressions have become very common in pop music , and have been used countless times in songs. Let’s take the chord progression I-III-IV-iv (In C that is C major – E major – F major – F minor) as an example.

(Bear in mind that chord progressions can be played in any key – it just depends on which note/chord you start with).

So in practice – what is harmony in a song we know? Well, this particular sequence of chords has been used in countless popular tracks like Olivia Rodrigo’s “Vampire.”

“Creep” by Radiohead:

“Get Free” by Lana Del Ray:

And many others.

No one owns chord progressions, so take inspiration from the greats and use them in your own songwriting .

A key signature in music indicates the tonal center of a piece and specifies which notes to consistently raise or lower throughout the composition. It acts as a roadmap for musicians, guiding them on which notes to play as naturals, sharps, or flats.

For example, in the key of E minor we have the following notes:

E-F#-G-A-B-C-D-(E)

Since this is our key signature, both the melody and chord choices for the music will be derived from this specific set.

The key signature of a composition isn’t set in stone. In many pieces of music, we hear “modulations” or changes of key. This can provide a powerful shift of emotion in the music.

Let’s look at what is probably the most famous example of modulation in pop music – “I Will Always Love You” by Whitney Houston.

Most of the song is in the key of A major. You can listen to the chorus in this key at 1:46 . The infamous key change occurs at 3:09 where the song rapidly shifts to B major and lifts the mood of the song triumphantly.

There are many types of harmony in music. In Western music theory, three popular types of harmony are:

Diatonic harmony – which uses notes from the key signature to create melodies and chords.
Non-diatonic harmony – which utilizes notes from the key signature as well as notes from outside of the key signature.
Atonal harmony – which doesn’t use traditional tonal centers at all.

Let’s explore some of these below.

Diatonic harmony

Diatonic harmony occurs when the harmony of the song is focused on the key center, which is dictated by the key signature. In other words, the chords and melodies in diatonic harmony all derive from the key signature. This form of harmony is very common in popular music.

Non-diatonic harmony

This type of harmony uses chords and melodies that deviate from the diatonic scale. This is prevalent in jazz, classical music, and many other genres of modern music. Composers use non-diatonic harmony to “borrow” chords from different tonalities and add harmonic color to their music.

John Coltrane incorporates non-diatonic harmony in this track to add interesting and unexpected tonal colors.

Atonal harmony

Atonal harmony is an approach to music writing that totally avoids establishing a tonal center or home key. Musicians who embrace this concept typically seek to explore aspects of music that deviate from traditional harmonic relationships. Instead, they explore alternative methods of generating musical narratives.

In Jonny Greenwood’s “Future Markets,” for example, it is impossible to hear a tonal center or chordal resolution point. This piece has been composed atonally.

Start using harmony to make music

Now that you have an answer to the question “What is harmony in music?” you can incorporate these ideas into your own tracks.

If you feel like you understand the theory but need a jumpstart to help you brainstorm chords and harmony, check out Playbox – which can generate chords with single-note inputs.

To demonstrate the harmonic capabilities of Playbox, as well as the power of harmonic knowledge, let’s look at how we can transform an empty-sounding melody into something special.

Let’s start with a simple melody without harmony:

Now let’s add some chords straight out of the Curious Sun preset on Playbox. With a bit of tweaking, and some drum and bass additions, we can end up with something like this.

You can get Playbox as a standalone plugin or as part of the Komplete Now bundle for only $9.99 a month.

If you’re looking to jump in for free, you can check out Komplete Start and put your harmonic knowledge into a song right now.

Get Komplete Start free

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Harmony in Music - What harmony is and how to use it effectively

Read Time: 6 Minutes

What is Harmony in Music?

Harmony is simply when two or more different musical notes are heard at any time. When we talk about harmony in music theory, we are generally referring to chords and chord progressions.

Harmony vs Melody

There is a key difference between harmony vs melody: melody is made up of single notes, played one at a time. A melody can have harmony underneath it, but we automatically label just the top note of the harmony as a part of the melody.

How is Harmony Used in Music?

A harmony could be from the same instrument, for example, a chord on the piano, or it could be from a group of instruments or voices, such as a choir. The following could be considered an example of music harmony:

Chords on a guitar in rock music. The guitarist will strike multiple strings at once, which creates harmony.
An orchestral performance in classical music. Each instrument plays one note (violin, flute, oboe, and all the rest!) and together they create harmony.
A jazz piano solo. The pianist presses down multiple keys at once to create harmony.
Backing vocal harmonies for songs (e.g. pop or folk). The backing singers build a chord based on the main vocalist’s note.

So, what is harmony for? With harmony, we can create a wide range of colorful sounds to match the mood of our music. We can also create satisfying tension and release when harmony changes as our music progresses.

How Does Harmony Work?

When discussing harmony, we label each chord according to where its root note is in the scale. We use Roman numerals rather than numbers to represent each chord.

For example, if we were in A major, we would have:

We use upper-case numerals for major chords and lowercase for minor chords.

The 7 chords can be divided into three categories based on their function.

Tonic – I, III and VI. These chords are restful and stable, they feel like “home”.
Dominant – V and VII. These are the opposite, they are full of tension and give a feeling that we are going on a journey in the music.
Subdominant – II and IV. These are the in-between chords, they act like a bridge between the two.

You can see an example of music harmony in action by going through the chords of your favorite songs and writing down the Roman numerals. This will allow you to see how the harmony progresses through these three different functions!

Consonance and Dissonance

When writing harmonies for songs, we can use a dissonant sound to create tension at the peak point of our musical phrase and a consonant sound to create release afterwards.

These are not clear-cut categories, but generally, anything which sounds “pleasant” is considered consonant and anything “tense” or “harsh” is dissonant.

Examples of consonance include: major chords, minor chords, and perfect 5ths.

Examples of dissonance include: diminished chords, suspended chords, and minor 2nds.

Close vs. Open Harmony

We can also consider how far apart our notes are in terms of pitch, a concept also known as ‘voicing’. This is another great example of music harmony being used to create a different ‘feel’.

‘Close’ harmony refers to when the notes are close together, while in ‘open’ harmony they are more spread out.

Let’s use a Cmaj7 chord as an example. It has the notes C, E, G and B. If we stack these notes directly on top of each other, we create close harmony.

If we move the E and the B up an octave, we now have the same chord with open harmony.

An Example of Music Harmony

What is harmony like in popular music? Check out the 4 Chords Song by The Axis of Awesome – this video demonstrates how many of our favorite popular songs use the same basic chord pattern of I – V – vi – IV!

An example of music harmony from the classical world now is Debussy’s ‘Clair de Lune’. Debussy often liked to use close harmony to create a dense sound. In the first few phrases, it’s easy to hear how he switches between tonic functioning chords and dominant ones to create tension and release.

Harmony is simply when more than one note is heard at a time, and yet it is one of the most-analyzed parts of music. Important points to remember are:

Harmony vs. melody: A melody is made up of single notes, whereas harmony involves multiple.

Harmony has two purposes: to create the right ‘mood’ and ‘color’ in our music and to create tension and release.
Harmony generally refers to chords, which are labelled according to their numbered place in the scale.
Chords can have one of three different functions: tonic, dominant, and subdominant.
Harmony can be consonant (pleasant) or dissonant (harsh).
Notes in harmony can be close together or spread apart.

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Melody, Harmony, and Scales

Introduction.

Barbershop quartets, such as this U.S. Navy group, sing 4-part pieces, made up of a melody line (normally the lead) and 3 harmony parts.When you have more than one pitch sounding at the same time in music, the result is harmony. Harmony is one of the basic elements of music, but it is not as basic as some other elements, such as rhythm and melody. You can have music that is just rhythms, with no pitches at all. You can also have music that is just a single melody, or just a melody with rhythm accompaniment.

Harmony is two or more notes played together at the same time. As soon as there is more than one pitch sounding at a time, you have harmony. Even if nobody is actually playing chords, or even if the notes are part of independent contrapuntal lines, you can hear the relationship of any notes that happen at the same time, and it is this relationship that makes the harmony.

Note: Harmony does not have to be particularly “harmonious”; it may be quite dissonant, in fact. For the purpose of definitions, the important fact is the notes sounding at the same time. Harmony is the most emphasized and most highly developed element in Western music, and can be the subject of an entire course on music theory.

In music, harmony is the use of simultaneous pitches (tones, notes), or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the “vertical” aspect of music, as distinguished from melodic line, or the “horizontal” aspect.

In many types of music, notably baroque, romantic, modern and jazz, chords are often augmented with “tensions”. A tension is an additional chord member that creates a relatively dissonant interval in relation to the bass. Typically, in the classical common practice period a dissonant chord (chord with tension) “resolves” to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between “tense” and “relaxed” moments.

Etymology and Definitions

The term harmony derives from the Greek ἁρμονία ( harmonía ), meaning “joint, agreement, concord”, from the verb ἁρμόζω ( harmozo ), “to fit together, to join”. In Ancient Greece, the term defined the combination of contrasted elements: a higher and lower note.

Rameau’s ‘Traité de l’harmonie’ (Treatise on Harmony) from 172

The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the ‘replacement’ of horizontal (of contrapuntal) writing, common in the music of the Renaissance, with a new emphasis on the ‘vertical’ element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. As Carl Dahlhaus puts it,

It was not that counterpoint was supplanted by harmony (Bach’s tonal counterpoint is surely no less polyphonic than Palestrina’s modal writing) but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the (‘vertical’) structure of chords but also their (‘horizontal’) movement. Like music as a whole, harmony is a process.

Descriptions and definitions of harmony and harmonic practice may show bias towards European (or Western) musical traditions. For example, South Asian art music (Hindustani and Carnatic music) is frequently cited as placing little emphasis on what is perceived in western practice as conventional ‘harmony’; the underlying ‘harmonic’ foundation for most South Asian music is the drone, a held open fifth (or fourth) that does not alter in pitch throughout the course of a composition.

Nevertheless, emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this clearly:

In Western culture the musics that are most dependent on improvisation, such as jazz, have traditionally been regarded as inferior to art music, in which pre-composition is considered paramount. The conception of musics that live in oral traditions as something composed with the use of improvisatory techniques separates them from the higher-standing works that use notation.

Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition (which permitted the study and analysis by theorists and composers alike of individual pre-constructed works in which pitches—and to some extent rhythms—remained unchanged regardless of the nature of the performance).

Historical Rules

Some traditions of Western music performance, composition, and theory have specific rules of harmony. These rules are often described as based on natural properties such as Pythagorean tuning’s law whole number ratios (“harmoniousness” being inherent in the ratios either perceptually or in themselves) or harmonics and resonances (“harmoniousness” being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. This model provides that the minor seventh and ninth are not dissonant (i.e., are consonant). While Pythagorean ratios can provide a rough approximation of perceptual harmonicity, they cannot account for cultural factors.

Early Western religious music often features parallel perfect intervals; these intervals would preserve the clarity of the original plainsong. These works were created and performed in cathedrals, and made use of the resonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths. The English style was considered to have a sweeter sound, and was better suited to polyphony in that it offered greater linear flexibility in part-writing. Early music also forbade usage of the tritone, as its dissonance was associated with the devil, and composers often went to considerable lengths, via musica ficta, to avoid using it. In the newer triadic harmonic system, however, the tritone became permissible, as the standardization of functional dissonance made its use in dominant chords desirable.

Most harmony comes from two or more notes sounding simultaneously—but a work can imply harmony with only one melodic line by using arpeggios or hocket. Many pieces from the baroqueperiod for solo string instruments—such as Bach’s Sonatas and partitas for solo violin and cello—convey subtle harmony through inference rather than full chordal structures. These works create a sense of harmonies by using arpeggiated chords and implied basslines. The implied basslines are created with low notes of short duration that many listeners perceive as being the bass note of a chord. (See below):

Example of implied harmonies in J.S. Bach’s Cello Suite no. 1 in G, BWV 1007, bars 1-2. Play (help·info) or Play harmony (help·info)

Close position C major triad.

Open position C major triad.

Close harmony and open harmony use close position and open position chords, respectively.

Other types of harmony are based upon the intervals of the chords used in that harmony. Most chords used in western music are based on “tertian” harmony, or chords built with the interval of thirds. In the chord C Major7, C-E is a major third; E-G is a minor third; and G to B is a major third. Other types of harmony consist of quartal harmony and quintal harmony.

Unison is considered a harmonic interval, just like a fifth or a third. What’s unique about unison is that it is two identical notes being played or sung together. Most people only consider thirds and fifths and sevenths to be “harmony”. But, unison does count as harmony, and is very important in orchestration, especially. In Pop music, unison singing is usually called “doubling” which is what The Beatles used to do a lot in their early music. As a type of harmony, singing in unison or playing the same notes, often using different musical instruments, at the same time is commonly called monophonic harmonization.

Understanding Basic Music Theory. Authored by : Catherine Schmidt-Jones . Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:22/Understanding_Basic_Music_Theo . License : CC BY: Attribution . License Terms : OpenStax content can be downloaded for free at cnx.org
Harmony. Provided by : Wikipedia. Located at : http://en.wikipedia.org/wiki/Harmony . License : CC BY: Attribution

Writing music analysis for non-musicians & music majors

Whether you know music or not, you may be asked to write an essay/analysis on a piece of music. If you’re a music major or thinking about studying music in college, get used to it! This task can feel a little overwhelming, especially if it is your first time writing about music. This article is tuned for people who have very little music knowledge on up to people who have some formal music theory courses under their belts. I think the tips, suggestions, and resources I provide are useful to anyone who is tasked with this kind of writing.

Your teacher or professor gave you some direction as to what they are looking for in your work, so I’ll be addressing the topic more generally and offering my own ideas. Always refer to your specific assigned requirements.

What should music analysis include?

Before we get to the step-by-step, here’s what I think most music analysis essays should include:

Significant performances
Background of the composer(s).
Orchestration
Composition techniques
Your own ideas and conclusions

So, how do you start analyzing music? I lay out some step to get you started below.

Step 1: Get to know the music

Before writing you should listen to the music many times. Each time you listen, try listening for different things. I suggest listening at least five times in five different ways.

Listen then write what the music made you feel or imagine. Did it take you on a ride? Did it make you think of your childhood? Jot down a few notes. Then try to articulate why it had that effect on you. Was it the melody? Was there a rhythm or specific instrument that pulled you on a journey?
Listen for instrumentation. What instruments do you hear? Are they playing all the time? What combinations of instruments did you hear? Is there any significance in the instrumentation that was chosen? Are these traditional instruments or perhaps all electronic?
Listen for dynamics. You can use a line on a page to indicate the dynamic shape of the music. Did it start out quiet and stay quiet for the entire piece? Or did it go up and down?
Listen for rhythm. What kind of rhythms did you hear? Were they steady throughout the piece? Did the rhythm become more complex in some places? Polyrhythms?
Listen for meter and tempo. Were you able to identify the meter? Did the music speed up or slow down? If yes, where in the music?

Once you have listened through five times with different ears on, I like to sketch what I think the music looks like visually. I use colors, shapes, figures, words, anything to attempt to capture the music on one sheet of paper.

Finally, to get the know the music, you must get the score or written version of the music. This will help you see things in the music you may not have heard. It will also be essential if you’re going to be doing detailed music analysis (see steps 5-7). If you have a good ear, you can make your own transcription of the piece.

Step 2: Get to know the composer

Whether you’re writing about Adele or Bartok, you need to know some background information about the composer. Some key things to know are:

Date of birth
Date of death (if applicable)
About their musical background/career
Their other works
Musical “trademarks” they have
Where they live(d)

Having this knowledge before writing will help you add colorful details to your writing. Rather than simply listing these elements as facts, you’ll be able to sprinkle these facts into your paragraphs breathing a little more life into them.

Depending on the scope of the assignment, I wouldn’t recommend doing a deep dive into the composer but rather grab info from a few sources outside of Wikipedia.

Interviews on youtube can be a great place to grab quotes and get to know more about the composer in their own words.
Documentaries on youtube are great places to get a fast overview of the composer.
Composer websites is a curated experience that the composer wanted you to experience.
Fan websites
Books about the composer or by the composer (if you have the time to read an entire book about the composer, this is where you will learn the most).

Step 3: Put the music in context

Nothing exists in a bubble, so figure out where this music fits in. Here are three parameters you may explore.

Time era – When were they writing? What was the time like? Are we talking horses or Teslas? How does the time in which the composer wrote the music affect the music? Was the composer part of a particular music or art movement?
Geography – Where in the world did the composer live and where did they write the music in question? Was it in the French countryside? Or an island off of Australia? Austin, Texas? Does the geography influence the music and in what ways?
Listen to the first piece of music this composer released (or the earliest one you can find), how is it similar or different?
Listen to the last piece of music released by this composer, how is it similar or different?
Was the music written during a particular phase or episode in the composer’s life? A bad breakup? The death of a child? Just won prestigious award? Was the composer overtly trying to say something?

With this knowledge, you’ll be able to add depth to your analysis.

Step 5: The Music’s Structure

Every type/genre of music has its own musical structures. Here are a few types of structures your piece may be using:

Strophic – a specialized binary form where all verses are sung to the same music. You might see a song labeled with “A section and B section” or “verse and chorus”.
Ternary – a three-part form typically ABA.
Theme and variations
Through composed – the music does not repeat sections (Bohemian Rhapsody uses this form).
Sonata – be careful with this one, there are many variations.

In tonal music (most music form the West) we have many cues to let us know the structure of the music. If there are lyrics, then there may be lyrical patterns that inform the structure of the music. Typically, it’s a combination of melodic, rhythmic, and harmonic cues that let the listener know where the end of a section is. Here is a quick example from Adele’s Hello that exemplifies three typical signs the phrase has ended.

The melody moves downward and finishes on the tonic.
The melodic rhythm ends on a long note.
The harmony ends on the tonic.

Example of phrase ending for music analysis

The key to analyzing musical structure is to find the major sections of the music and determine how the composer fit these sections together – how are the various sections related? There is a lot that can go into this part of the analysis, but at the very least you should know the basic structure of the piece.

For an in depth look at form and structure here is a book by Leon Stein, Anthology of Musical Forms — Structure & Style: The Study and Analysis of Musical Forms

Step 6: The notes

After the structure is understood, getting a handle on the melody, harmony, articulation, and dynamics is the next step. Once again, this can go as deep or shallow as you like. I’ll go over some of the basic elements to highlight in each area.

You will want to do some basic phrasal analysis, which entails understanding the smallest units of the melody that combined together to create the full melody. You are looking for how long the phrases are. How do they relate to each other? Are the phrases transposed, inverted, retrograded, etc…? But remember to keep in mind why it matters in the first place to understand this. I look at analysis as the practice of figuring out what “works” in music. What makes music communicate so powerfully? It’s easy to get lost in the minutia of the music and then not say anything important. How are the melodic phrases and structures related and how and why do you think this contributed to the music? Here is a brief example of how I’d start a melodic analysis. This is from MINUET No 1, in G Major by Mozart. This example is by no means exhaustive of how deep you can go analyzing melody.

The pink dashed box shows the prime melodic unit – two eighth notes descending to a quarter note all slurred together.
There are two short phrases that make up the red “phrase #1”. These two phrases are a descending sequence.
The blue phrase #2 uses the prime melodic unit but shortens it by using it back to back.
Phrase #2 in measure 8 ends on the dominant five chord – a half cadence.
Phrase #1b begins with the prime melodic idea just transposed down a 6th from measure 1.
Phrase #2b begins like phrase #2a but transposed down by a perfect 5th.
The green arrows indicate a change in melodic direction at the same point in the phrase.
Phrase #2b ends on a tonic – a perfect cadence. This type of cadence completes the section before it moves onto the a B section.

If you’re a music student, you should probably go ahead and do a full roman numeral analysis. In some music, harmony will reveal many structures and patterns that hold the piece together. But be aware that many types of music place little to no importance on harmony. For example, one time I was analyzing a piece of traditional Thai music and very quickly found that there were only two harmonies used throughout the entire piece. It just went back and forth between a I (tonic) and a V (dominant). In a way the Roman numerals did their job by showing the harmony was not an element that the composer was used to hold the piece together. In most tonal music, the harmony is very important, but be careful to point out areas of harmonic interest rather than just rattle off the chords. Here are a few things to look for in harmony:

harmonic rhythm
repetitions in progressions and how the repetitions are varied
modulations
key changes
how expectations may have been played with (did the composer end on a surprising chord? and why?)

articulation

It can be useful to pay attention to some of the less structural elements in the music, like articulation. Articulation is one of those aspects of the music that is riding on the surface playing a significant role in the experience of the music.

legato: note are performed smooth and connected
staccato: notes are shorter than their written rhythmic value
tenuto: hold the note for the entire rhythmic value
marcato: louder and more forceful
accent: play the note with a little bite at the beginning of the note

Dynamics are an important way for the composer to communicate. The very quiet sections can get an audience on the edge of their seats just as much as a loud section. Here are some basic dynamics volume terms:

fortissimo = very loud
forte = loud
mezzo forte = kind of loud
mezzo piano = kind of soft
piano = quiet
pianissimo = very quiet

Here are some terms to describe changing dynamics:

crescendo = slowly get louder
decrescendo = slowly get quieter
diminuendo = slowly get quieter
subito piano = suddenly perform at the piano volume level
sforzando = suddenly loud

Step 7: Compositional techniques

Whether it’s Bon Iver or Bach, composers use compositional techniques to express themselves through the music. Every genre, composer, time period, geographic location, has their own unique set of established compositional techniques. I’m providing just the smallest sample of a few common techniques, but there are way to many to cover here.

chance: a set of rules is created and the composer plays a game to generate musical ideas and content. For example, I have some dice. Every time I roll a “1” I write the tonic of my key. I roll again to determine the rhythmic value. And I roll again to determine the articulation. And this can go on and on. If you did this, then you’d be able to generate a piece by the roll of the dice – chance.
repetition: self explanatory, just repeat a section.
sequence: take a melody or piece of the music and repeat it but alter it by transposing it up or down. Usually, do this three or more times.
pedal tones and bell tones: a pedal tone is a low pitch that is repeated over and over while the other parts change. A bell tone is a high pitch that is repeated over and over while the other parts change.
textures: think of complex vs simple.
counterpoint: layered melodic lines that follow carefully thought out rules of voice leading.
range: low vs high and everything in between.

Step 8: Outline the essay

Now that you know the music, the composer, the context, and the specific musical elements of the piece, it’s time to start outlining what you’re going to say about this music. One common method for presenting music is to start wide and zoom in with every paragraph. Think of it like an opening shot of a movie. The camera is pulled out (an establishing shot) to give the viewer context. So maybe imagine a setup with something as big as a planet, a continent, country, or city. Then the camera moves in to a neighborhood or high rise, or field. Then we get in closer to the home where we find our protagonist. We can do the same thing throughout the musical essay. Here is an example outline I did for the essay I wrote on Alfred Schnittke – Concerto Grosso no. 1.

Five-paragraph essay outline

Introduction – zoomed out look at the context of the composer, time, location, performance, etc.

Establish polystylism the compositional technique as my “protagonist.” Start zoomed out and discuss what polystylism is and other examples of this technique in use. Introduce Schnittke and his personal context. Get down to the piece and list a few of the styles that will be encountered in the music. Finally, deliver the thesis of the essay (the problem of the story), an examination of how to successfully deploy polystylism through consonance and dissonance.

Body paragraph #1- looking at polystylism across the entire piece and form

Discuss how many time styles are changed. Maybe present a chart showing the combinations of styles. Where’s the climax of the piece and what happens there?

Body paragraph #2 – zoom in a bit more and look at an entire section of a stylistic change

Give examples from a few different sections that show the stylistic writing of the various styles. For example, during a baroque section, show the counterpoint involved. Show the extended piano technique in the “contemporary” sections.

Body paragraph #3 – zoom in and look at the notes, articulations, orchestration, voice leading of the moment of change

Discuss what is happening in the music at one of the shifts from one style to another. What orchestration, textures, dynamics, and harmonic language is being used?

Conclusion – draw conclusions and say something interesting

Discuss the specific techniques Schnittke employed to transition between styles. What other contextual elements supported this music? If a composer wanted to use this as a case study, how would you distill down the polystylistic technique of Schnittke?

Brandon Alsup

A Corpus Analysis of Harmony in Country Music

Trevor de Clercq is Associate Professor at Middle Tennessee State University.

Published: 18 August 2022
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Harmony in country music is in some ways similar to that in rock music (defined broadly) while in others ways different, just as it is in some ways similar to common-practice music while in other ways different. The empirical work presented here implies that the conventions of country music lie somewhere between those found in rock music and those in common-practice music. If country music can be considered a substyle of rock defined broadly, then, presumably, we would find that harmonic practice in rock defined narrowly would be even further afield of common-practice norms. In addition, some aspects of harmony seem particularly distinctive to country music (at least in comparison to rock and common-practice styles). The strong avoidance of the minor tonic is one striking feature. We also found support for the notion that country music, more so than other styles, relies heavily on just three chords.

Introduction

As decades of scholarship have shown, harmony in contemporary Western popular music often eschews the conventions of common-practice–era European art music. 1 But while the conventions of harmony in common-practice music may be well-established, it is still unclear what the conventions of harmony might be (if any) in contemporary Western popular music. 2 Part of the difficulty arguably stems from the wide array of styles under the umbrella of “popular music.” Rock, blues, folk, R&B, rap, and reggae, for example, can all be considered popular styles, each of which likely has its own particular harmonic customs and idioms (at least to some extent). Yet each of these styles can be said, like common-practice music, to be essentially “tonal,” and so it seems reasonable to expect some shared harmonic syntax. But the question of which harmonic conventions are shared and which are idiomatic remains open.

A great deal of research in recent years has focused on harmony in rock music, although the meaning of “rock music” varies from work to work. Sometimes rock is construed in a narrow way (e.g., Biamonte 2010 ; Temperley 2011 ), distinct from styles such as folk, pop, and R&B. Other times, rock is construed more broadly (e.g., Covach and Flory 2015 ; Doll 2017 ), used instead as a catch-all term for the broad range of styles that typically top the Billboard charts—in other words, all commercially recorded Anglo-American popular music except jazz. This variability in meaning creates a thorny landscape for understanding harmony in popular music since insights gleaned from one work may or may not relate to those of another due to possible differences in the style(s) under study. Disagreements on the harmonic practice of rock may thus sometimes be more about what rock music is than anything else. It seems worthwhile, therefore, to investigate harmonic syntax in a style of popular music clearly distinct from rock, at least in its more narrow sense.

Accordingly, I present in this chapter a corpus analysis of harmony in country music. Country music seems like an appropriate style in which to investigate harmonic conventions for many reasons. First, no systematic study has yet been published of harmony in country music, even though country music constitutes a significant share of total audio consumption in the US market. 3 Second, harmony is an important feature of country music, as evidenced by the widespread use of chord charts (or “number charts”) by professional musicians playing in the style (more about this later). Third, country music is typically considered to be separate from rock, even in broader definitions of rock. 4 And, fourth, more practically, I recently published a book of harmonic transcriptions for 200 country songs ( de Clercq 2015 ), which acts as low-hanging fruit for an empirical inquiry since the work of analyzing a large set of songs has already been completed. In what follows, I describe the corpus itself, explain my method for encoding and analyzing this corpus, offer statistical results derived from this corpus, and make a few general observations.

To set the stage, it is worth reviewing extant ideas about harmony in country music as well as theories of harmony in popular and common-practice music. Generally speaking, country music is often presumed to have a fairly simple harmonic palette. For example, Harlan Howard—a prolific songwriter and author of many classic country music hits—is regularly quoted as saying that “country music is three chords and the truth.” 5 In contrast, Jocelyn Neal has expressed umbrage with this stance, arguing that harmony in country music is not as straightforward as this quote implies and that it often involves “complex harmonic sequences and unconventional chord progressions.” 6 She does not, however, offer much empirical evidence to elucidate her claim. Other than generalizations such as these, there is little documentation of expectations within the music theory community with regard to how harmonic syntax in country music compares to rock or common-practice music. One opportunity that the current study provides, therefore, is to assess the variety of chords (or lack thereof) found in country music.

There are, of course, well-documented expectations with regard to harmonic syntax in common-practice music. In general, we expect harmonic progressions to begin with a tonic sonority (e.g., I), move through optional predominant sonorities (e.g., ii and IV) to dominant sonorities (e.g., V and vii o ), and eventually conclude back on a tonic sonority. Steven Laitz refers to this order of harmonies as the “phrase model,” which—taking a Schenkerian view—can be seen to consistently account for multiple levels of the tonal hierarchy (2015). Note that a retrograde of this pattern (tonic–dominant–predominant–tonic) is traditionally seen as unstylistic if not grammatically incorrect for common-practice music. Corpus analysis (e.g., Budge 1943 ; Huron 2006 ; Temperley 2009 ; White and Quinn 2018 ) confirms that the phrase model accounts for harmony in common-practice music rather well. These statistical studies also show that, perhaps as a byproduct of the phrase model, common-practice music tends to employ an asymmetrical distribution of root motion: ascending seconds far outnumber descending seconds, descending thirds far outnumber ascending thirds, and ascending fourths (or descending fifths) far outnumber descending fourths.

For rock music, Ken Stephenson frames the standard harmonic succession scheme as directly opposite the asymmetrical root motions found in common-practice music. Specifically, Stephenson theorizes that root motions by descending second (D2), ascending third (A3), and descending fourth (D4) constitute a “rock harmonic standard,” which acts as a generative principle for typical harmonic patterns found in rock music (2002, p. 104). But Stephenson also admits that many rock songs employ common-practice root movements and that some songs blend both systems. In other words, rock music utilizes multiple cohesive yet distinct harmonic traditions, sometimes within the scope of a single song. It is worth noting that the definition of rock that Stephenson uses is relatively broad, although his examples tend to be drawn from a more narrow understanding of the term. 7

The view that rock music does not employ a monolithic, unified harmonic syntax is amplified in the work of Walter Everett. Rather than a single tonal system, Everett (2004) identifies six broad classifications of tonality found in rock music. These six tonal systems range from those in which common-practice harmonic behavior is in full effect, through modal systems in which common-practice harmonic behavior is normal but not necessary, to chromatic systems in which common-practice harmonic behavior is absent or irrelevant. Certain artists, eras, and substyles of rock music adhere primarily to a single tonal system, although some artists (such as the Beatles) employ a different tonal system from song to song. Note that Everett defines rock music in a relatively narrow way, although he admits his own definition is somewhat unclear. 8

Despite differences in details, both Everett and Stephenson posit that rock music—whether defined more narrowly or more broadly—exhibits an array of approaches to harmony ranging from strict adherence to common-practice norms to rejection or opposition to them. The implication is thus that any and all types of harmonic succession are possible. While this may be true in a trivial sense, it leaves unanswered the questions of whether certain types of harmonic motion are more probable than others and the extent to which rock (defined narrowly or broadly) adheres to common-practice harmonic standards.

To investigate these issues, David Temperley and I conducted a corpus analysis of harmony for 100 rock songs ( de Clercq and Temperley 2011 ). Since this was one of the first large-scale corpus analyses of rock, we interpreted the term broadly in order to establish a referential baseline. 9 The results of our statistical analyses on the harmony of these songs showed a number of interesting features. We found, for example, that while 1, 4, and 5 were the most common scale degrees for chord roots, ♭7 was the next most common chord root—more so than 2, 3, 6, or 7. We also found that, unlike the asymmetrical distribution of root motions observed in common-practice music, root motions in our corpus were generally symmetrical along a line of fifths (i.e., ascending and descending versions of a particular interval were equally prevalent) and frequency tended to decrease as distance on the line of fifths increased. For example, ascending and descending perfect fourths had similar frequencies and were the most common interval; root motions up or down by whole step were the next most common and roughly equal in frequency with regard to ascending and descending versions. If, as Stephenson posits, rock music blends common-practice root motion (A2, D3, A4) with its own standards (D2, A3, D4), the amalgam appears to be an equally balanced mixture of the two practices. We also found that chords with a root of scale degree 4 were especially normative before tonic, more so than chords with a root of scale degree 5, as is typical of common-practice music. Other results from our 2011 study are relevant, but I will reserve further discussion until these details can be compared with results from the current study. Note that, as reported in a later article ( Temperley and de Clercq 2013 ), Temperley and I expanded our corpus to include harmonic analyses for 200 rock songs (hereafter, the “RS 200” or “the rock corpus”). This larger corpus produced a set of statistical results very similar to those reported in our 2011 article with regard to the general distribution of harmony, so our 2013 article focused on other areas of interest, such as key-finding algorithms and song clustering.

Another corpus study of harmony in popular music, one using a larger and arguably more stylistically broad collection than the RS 200, can be found in Burgoyne (2011) . In this work, Burgoyne reports statistics on more than 500 unique songs randomly sampled from the Billboard Hot 100 charts spanning 1958 to 1991 (hereafter, “the Billboard corpus”). A number of his results echo those found in the RS 200, although some differences are worth noting. For example, while Burgoyne found that ♭7 was a common chordal root (p. 159), most other degrees of the major scale—including 2 and 6—were more common (the exception being 7). Burgoyne also found that chords with a root of 4 were especially common before tonic (p. 178), although not to the extent that Temperley and I observed in the RS 200. The Billboard corpus thus reaffirms some of the basic differences noted earlier between popular music and common-practice music, albeit with some disagreement in terms of degree.

Overall, then, a corpus analysis of harmony in country music offers an opportunity to extend and expand on existing corpus work on harmony in popular music in a few different ways. Not only does it offer the chance to learn about harmonic syntax in country music specifically, but it also offers the chance to see how well harmonic trends found in stylistically broad corpora of popular music apply to a more narrowly defined style of popular music. Whether or not country music can (or should) be considered a substyle of rock music is not an issue that will be directly addressed here. Certainly, though, the history of country music overlaps and intersects with the history of rock (both in its narrow and broad senses), and so it seems reasonable to consider the harmonic practices of one style within the context of the other.

One of the basic questions facing any corpus study is the content of the corpus itself. For this study, I chose the 200 songs in my 2015 Nashville Number System Fake Book (hereafter, the “NN 200” or “the country corpus”), not only because I had already transcribed the harmony of the songs, but—perhaps more importantly—because I originally compiled these 200 songs by aggregating fourteen separate sources of notable country songs (as detailed in Appendix A ), which ranged from Billboard sales figures to “Song of the Year” awards to music critics’ lists of “All-Time Greatest Songs,” in order to assemble a “meta-list” of famed country songs. 10 This approach was intended to balance critical acclaim with commercial success without letting the opinions of any individual critic or award panel carry undue weight. 11 All of these songs have thus been considered important exemplars of country music by multiple sources, including award agencies, chart makers, and music critics.

The 200 songs in the corpus represent a broad history of country music. The songs’ copyright dates range from 1933 (“Wabash Cannonball”) to 2014 (“Automatic”), with an average date of 1981. No attempt was made to balance the corpus by decade, although every decade from 1960 through 2000 (five decades total) includes between 28 and 38 songs. Of the 200 songs in the NN 200, only five were also members of the RS 200. 12 Despite a relatively broad definition of rock, therefore, the RS 200 appears to mostly exclude country music. Interestingly, the five overlapping songs (three of which are by Johnny Cash) all had copyright dates prior to 1963, implying that the histories of country music and rock overlapped in their early years but began to diverge by the mid-1960s. This is not to say that hybrid styles such as country rock did not exist after 1965, but these hybrids are a small fraction of what are generally considered two distinct musical traditions.

The transcriptions in my 2015 fake book follow the basic format of the Nashville number system. It is beyond the scope of this chapter to describe this system in full detail, but certain aspects of the notation are worth mentioning here. 13 At its essence, the Nashville number system is much like the system of Roman numerals traditionally used to notate harmony. Instead of using upper- and lowercase Roman numerals for triads, however, the Nashville system uses Arabic numbers followed by an indication of triad quality if other than major. An F major chord in the key of C major, for example, is thus 4 instead of IV. Similarly, an A minor chord in the key of C major (Am or A– in popular chord symbols) would be 6m or 6– in Nashville numbers instead of vi. One significant difference between Nashville numbers and Roman numerals is that chord extensions are notated separately from chord inversions. Nashville numbers do so by converting the letter-based components of standard chord symbols in popular music (see Wyatt and Schroeder 1998 ) to scale degrees. For example, a G7/B chord in the key of C major would be 5 7 /7 in Nashville numbers, as compared to V6/5 in Roman numerals. This separation of chord extensions from chord inversions allows Nashville numbers to notate a more complicated palette of harmonic entities than in the traditional Roman numeral system. A first-inversion dominant ninth chord, for instance, is represented in Nashville numbers as 5 9 /7, whereas Roman numerals typically do not allow for chord extensions above the seventh when a chord is inverted, due to potential confusion between the extensions and the intervals above the bass. The other significant difference between the two systems is that because Nashville numbers use a slash symbol (“/”) to notate inversions, applied chords cannot be notated with any second-level indication of the chord function. A V/V chord in Roman numerals, for instance, would be notated as 2 in Nashville numbers (i.e., a major chord built on scale degree 2). Similarly, V7/vi in Roman numerals would be 3 7 as a Nashville number.

The Nashville number system was developed sometime in the late 1950s ( Williams 2012 ). It is difficult to say when Nashville number charts became commonplace among professional country musicians or how deeply the system permeates the current landscape of music-making in Nashville and beyond. Nonetheless, Nashville number charts—which show only the harmonic structure of a song as organized into bars, phrases, and sections—have become a standard component of studio recording sessions and live concerts in the country music industry. That is to say, these charts provide some anthropological evidence that professional country musicians strongly conceptualize a song through its harmonic content and organization, particularly in a functional way that relates chords to a key center. In contrast, it is less clear that rock musicians necessarily think about chord function or the relationships of chords to a key center. (Undoubtedly, rock musicians think about chords and key centers, but not necessarily how these chords relate to tonic.) Country music thus provides perhaps a more culturally appropriate context in which to study harmony and harmonic function (perhaps even more so than common-practice music) because its practitioners use a chord notation system based on function when communicating with each other.

The harmonic transcriptions of the 200 songs found in my 2015 book were all done independently by myself, entirely by ear, without reference to printed lead sheets. As shown in my prior work with Temperley (2011) , harmonic analysis of popular music is a subjective process, so the reader should be aware that my transcriptions reflect only one hearing of these songs. That said, the book’s publisher (Hal Leonard) assigned an editor, Jeff Arnold (a guitarist), to play through all the charts along with the original recordings. This procedure allowed us to repair any obvious errors, of which there were only a handful. (Since the transcriptions were published under my name, I had a strong incentive to ensure their accuracy, and I thus did multiple rounds of rehearings at the keyboard or with a guitar.) After transcribing the 200 songs in the NN 200 and the 200 songs in the RS 200, my own sense is that harmony in country music is more clear-cut than in rock, and thus I would presume that any other trained musician would have a very high level of agreement with my harmonic analyses (higher than Temperley and I had in our rock corpus, which was greater than 90 percent). But without a second analyst, that can be only speculation.

Excerpt of encoded analysis for “80’s Ladies” (K. T. Oslin)

To allow for statistical analyses to be conducted on the corpus, I translated the 200 songs in my book to a set of 200 text files, with one file per song. Since the current study follows my corpus work with Temperley, I considered encoding the 200 country songs using the custom recursive format that Temperley and I developed for our studies (explained in our 2011 and 2013 articles). For the sake of easy error-checking, however, I decided to encode the country songs using a nonrecursive text-based format that mirrored the layout in the published book. Figure 22.1 shows an excerpt from my encoded analysis of “80’s Ladies.” The beginning of the file gives the song title, artist name, and copyright date. Non-chord “special” information—such as the key, meter, tempo, and “feel” (e.g., normal or swing)—is indicated in square brackets, both at the beginning of the song and anywhere a change in these parameters occurs. A new song section is indicated by text at the beginning of a line followed by a colon. Any information following this colon or after whitespace following a new line is assumed to be chord information (allowing for “special” information in square brackets). Each number or set of numbers in parentheses reflects a new bar. For each chord, the first digit represents the chord root (which may be preceded by a flat or sharp for roots outside the major scale), which is followed by quality information if not major, after which any extensions are indicated. For example, the fourth bar of the intro (“In:”) is a dominant ninth chord with a suspended fourth (“594”). Any number after a slash represents the scale degree of the bass (e.g., an inverted chord). For example, the chord in the second bar of the intro (“12/3”) is a tonic with an added ninth (indicated as “2”) in first inversion (since scale degree 3 is in the bass). Anticipations to the beat by an eighth note are notated with a left arrow (“<”), which corresponds to the “push” notation common in the Nashville number system. Two chords in parentheses are presumed to split the bar evenly, unless dots are used (where each dot corresponds to an extra beat), similar to the technique explained in de Clercq and Temperley (2011) .

Before looking at detailed results from the corpus, it is worth noting one remarkable global feature of these 200 songs: minor chords built on scale degree 1 are exceedingly rare. Specifically, only 5 of the 200 songs in the NN 200 include minor tonic chords at all, and most of these also include instances of the major tonic chord. In other words, the vast majority of the songs—about 98 percent—employ major tonic chords exclusively. 14 This strongly lopsided ratio of major to minor tonic chords contrasts significantly with statistics derived from corpora of other styles. In the RS 200, for example, about 22 percent of the songs have at least one instance of a minor tonic, and thus only about 78 percent of songs use major tonic chords exclusively. Similarly, the percentage of tonic chords in common-practice music that are major has been reported to be somewhere between 70 and 80 percent ( Budge 1943 , pp. 19–22). Thus while major tonics outweigh minor tonics in many styles, the balance in the NN 200 corpus is radically tilted, almost entirely, in favor of major.

This overwhelming tendency for songs in the NN 200 to employ major tonics is important to keep in mind when considering other aspects of the corpus. For example, Temperley and I reported that 75.8 percent of chords in our rock corpus are major, while the remaining chords (aside from a marginal number of diminished and augmented chords) are minor (2011, p. 66). In the NN 200 corpus, however, 86.5 percent of chords are major, 13.1 percent are minor, and less than 1 percent total are either diminished or augmented. The greater incidence of major chords in the country corpus is presumably a natural byproduct of the greater incidence of songs with major tonics.

Along similar lines, consider the distribution of chromatic chord roots in the NN 200, as shown in the leftmost three columns of Table 22.1 . Here we can see that chords with roots of 1, 4, and 5 are by far the most common in terms of instances. (A new chord “instance” is defined as a change of chord root or chord quality.) These are also the three most common chord roots found in the rock corpus ( de Clercq and Temperley 2011 , p. 60). But in the rock corpus, ♭7 was found to be the next most common chord root, whereas in the country corpus, chords built on scale degree 2 and 6 are considerably more prevalent than those built on ♭7. This difference in the relative frequency of ♭7 as a chordal root arguably relates to the fact that more songs in the rock corpus employ a minor tonic chord. Indeed, if we exclude those songs in the RS 200 that have a minor tonic chord (at any point in the song), the most common chord roots are, in order of frequency, 1, 4, 5, 6, 2, ♭7, and 3—results very similar to those found in the NN 200. Note that this collection of chord roots avoids the diminished sonority that naturally arises when building a triad on scale degree 7 of a major scale. As such, country and rock music distinguish themselves from common-practice norms, where triads built on ♭7 are relatively rare and are significantly outnumbered by those built on a leading-tone 7 ( Budge 1943 ; Temperley 2009 ) even when considering minor and major keys.

Despite the similarity in chord root distributions between the rock and country corpus given a major tonic, one important difference is worth highlighting. Note that the country corpus shows a greater frequency of chords built on scale degree 5 than those built on scale degree 4. This can be observed in terms of both chord instances as well as in terms of the amount of time overall spent on that chord root (as shown in the “Bars” columns in Table 22.1 ). This result contrasts with the distribution found in the RS 200, where chords built on scale degree 4 are considerably more frequent than those built on scale degree 5. 15 In this regard, the country corpus seems more similar to common-practice music, where dominant chords are much more prevalent than subdominant chords ( Budge 1943 ; Temperley 2009 ). That said, the greater frequency of chords built on scale degree 5 than 4 in the NN 200 is somewhat minimal, and thus harmonic practice in country music perhaps stands somewhere between that of common-practice music and rock. (More will be said about this later.)

With knowledge of the number of instances of a chord root and the amount of time (in bars) spent on that chord root, we can calculate the average duration of each instance of a chord root, as shown in the second-most column from the right in Table 22.1 . Overall, the average chord duration in the NN 200 is 1.27 bars, but this global average obscures some salient statistical subgroups. For example, note that the average duration of chords built on scale degree 1 is an outlier, closer to two bars than one. In fact, if we exclude chords with a tonic root, the average chord duration is 1.05 bars. These results mirror those found in the RS 200 ( de Clercq 2017 ), and so the basic harmonic rhythm found in the country corpus appears to be similar to that of rock. Note also that chromatic roots—such as ♯4/♭5, ♯2/♭3, and ♯1/♭2—have some of the shortest average durations, closer to half a bar than a full bar. Interestingly, the shortest average chord duration is scale degree 7, showing that scale degree 7 as a chordal root perhaps acts more like a chromatic scale degree in this style.

Given the distribution shown in Table 22.1 , we can assess the stereotype that country music primarily involves just three chords. Indeed, the vast majority of chordal roots are either 1, 4, or 5. Further insight can be found in Table 22.2 , which ranks triads by frequency of instances when considering both chord root and chord quality (but ignoring chord extensions and inversions). 16 As Table 22.2 shows, about 82 percent of all chord instances (11,548 of 14,090) are the major triads I, IV, or V. Moreover, about 86 percent of the time in the corpus (15,366 of 17,893 bars) is spent on these three triads alone. Based on this evidence, harmony in country music does indeed seem to be strongly predicated on just three chords. But before we discount country music as overly simplistic, we should recognize that harmony in other styles can be seen as similarly disproportionate. In the RS 200, about 73 percent of all chord instances have roots of 1, 4, or 5, which represents 82 percent of time spent; and if we limit the RS 200 corpus to only those songs with major tonics, this figure increases to about 79 percent of all chord instances and about 85 percent of the time. Similarly, the Billboard corpus shows that 76 percent of time in the corpus is spent on chords with roots of 1, 4, or 5 ( Burgoyne 2011 , p. 159). In common-practice music, the hegemony of three chords exists as well, although perhaps to a lesser extent. For example, Budge’s corpus (1943) shows that during the period from approximately 1700 to 1830, chords with roots of scale degrees 1, 4, or 5 account for about 72–76 percent of all chords, depending on the exact era. 17 Perhaps not surprisingly, this figure drops to about 62 percent for mid–nineteenth-century music (when chromatic chords become a larger portion of chords overall), although the majority share held by I, IV, and V remains nonetheless. To be sure, the NN 200 corpus shows a heavier weighting for I, IV, and V than we find in other styles, but the preference for these three chords is not endemic to country music alone. As a final comparison, note that a quarter of the songs in the NN 200 utilize the chords I, IV, and V exclusively. Similarly, a quarter of the songs in the RS 200 utilize chords with roots of 1, 4, or 5 exclusively. So while a good chunk of songs in the country corpus have a limited harmonic palette, it is not radically out of proportion with rock music taken broadly (or even certain eras of common-practice music). 18

Table 22.2 shows other interesting aspects of the corpus as well. Aside from ♭VII and i, the most frequent instances of lowered scale degrees (as compared to the major scale) are ♭VI, v, and iv. Scale degree ♭7 thus seems to be more common than ♭6 both when acting as the root of a chord and as the third. With regard to raised scale degrees, the most frequent instances are major chords built on scale degrees 2, 3, and 6 (i.e., II, III, and VI). It may be easiest to conceptualize these three chords as secondary dominants (i.e., V/V, V/vi, and V/ii, respectively). Indeed, the most common resolution in the corpus for II is V, III is vi, and VI is ii. Similarly, the most common resolution for the two most frequently used diminished chords—♯iv o and ♯v o —is via the traditional pathway, up by a half step to V and vi, respectively. It is interesting that diminished chords built on scale degrees ♯4 and ♯5 are more common than diminished chords built on scale degree 7. Perhaps it is not necessarily an avoidance of diminished chords altogether that is responsible for the lack of diminished chords on scale degree 7, but rather a particular aspect of country music’s harmonic palette (or that of popular music more broadly).

The issue of chord resolutions brings up the broader question of root motions and chord transitions overall. Table 22.3 shows root motions in the NN 200 categorized by interval size. On one hand, Table 22.3 shows a similarity in root motions between this corpus and those found in rock. In particular, the frequency of root motions in the NN 200 tends to decrease in a regular way as circle-of-fifths distance increases, similar to root motions found in the RS 200 ( de Clercq and Temperley 2011 , p. 63). For example, ascending and descending perfect fourths are the most common interval, followed by ascending and descending major seconds, with ascending and descending minor seconds being the least common interval after the tritone. Note that this pattern of root motions differs from that found in common-practice music ( Temperley 2009 ), where ascending seconds of either quality are more frequent than the descending variety. On the other hand, Table 22.3 also shows how root motions in the NN 200 are in other ways more similar to those found in common-practice music. Specifically, there is a somewhat unbalanced distribution between ascending and descending versions of the same interval type. Ascending fourths outnumber descending fourths, ascending seconds of one type outnumber descending seconds of the same type, and descending thirds of one type outnumber ascending thirds of the same type. In other words, root motions in the NN 200 tend to favor ascending fourths, descending thirds, and ascending seconds. This is the same asymmetry of root motions that authors have theorized for common-practice music (e.g., Stephenson 2002 , p. 102) and has been shown through empirical work ( Temperley 2009 ). In contrast, root motions found in my corpus of rock music with Temperley are more symmetrical, with very little statistical difference between ascending and descending versions of the same interval type (2011, p. 63). Here again, therefore, we find evidence that harmony in country music shares some characteristics with common-practice music and others with rock—as if country music were an intermediary harmonic language between the two styles.

Based on the information in Table 22.3 , it seems worthwhile to investigate these asymmetrical circle-of-fifths root motions more closely. A useful way to do so is to examine specific chord transitions. Instead of presenting a probability table of chord transitions, such as table 13.2 in Huron 2006 (p. 251) or table 3 in de Clercq and Temperley 2011 (p. 61), it will be more useful here to inspect the particular asymmetries that common chord pairs exhibit, as shown in Table 22.4 , since we can more easily see the strength of those asymmetries. Table 22.4 shows the most common two-chord progressions and their mirror-image counterparts (such as I–IV and IV–I) ranked by the extent to which the more frequent version of the chord pair (XY) outweighs its retrograde (YX). The “Interval” column lists the specific interval of the more common chord pair (XY), and the “Factor” column gives the strength of the asymmetry (e.g., a factor of 2 means the XY version is twice as frequent as the YX version). 19 With only a few exceptions, the more common version of each chord pair aligns with common-practice root motion norms: ascending seconds, descending thirds, and ascending fourths prevail. The exceptions involve two basic cases. The first is ii–IV, an ascending third that is more common than its descending dual, IV–ii. But there are not many instances of this chord pair in the corpus overall (only 232) and the asymmetry is especially weak (at a factor of 1.09), so it does not seem unreasonable to disregard this case. It is harder, however, to ignore the other case found in the first two rows of Table 22.4 , which show a strong preference for descending fourth and descending second motion (i.e., Stephenson’s “rock harmonic standard”). Interestingly, both exceptions in these first two rows involve the ♭VII chord. There thus appears to be something unique about ♭VII in the way it is employed. Not only is the sonority itself mostly foreign to common-practice music, but the root motions in which it participates do not mimic common-practice norms. Thus while most of the preferred root motions shown in Table 22.4 align with common-practice usage, the handling of ♭VII aligns more with rock.

Despite the general similarity of root motions in the NN 200 with those found in common-practice music, the strength of these asymmetries is not equivalent. Consider, for example, the chord pair IV–V and its dual, V–IV. As in common-practice music, motion from subdominant to dominant in the NN 200 is more common than the motion from dominant to subdominant; but in common-practice music, motion from IV to V heavily outweighs motion from V to IV, by some measures by a factor of around 10 to 1 ( Huron 2006 , p. 251). In contrast, motion from V to IV is not uncommon in the NN 200, even if motion from IV to V is more common. We can make similar observations about the relatively weaker asymmetries in the NN 200 of the chord pairs ii and V, I and ii, or even I and V as compared to the relatively stronger asymmetries for these same chord pairs found in common-practice music. 20 In this corpus of country music, therefore, we find further evidence of an approach that stands between the conventions of rock and common-practice music. While rock displays a fairly symmetrical distribution of root motions on a circle of fifths and common-practice music displays a strongly asymmetrical distribution of root motions, country music appears to mediate these two traditions through its weakly asymmetrical distribution.

Thus far, the statistical analyses of harmony presented here have focused almost exclusively on roots, root motions, and triad qualities. In so doing, I have ignored two important aspects of harmonic organization: chord inversions (i.e., situations when the root is not in the bass) and chord extensions (i.e., situations in which the sonority is more than just a simple triad). Generally speaking, there is limited statistical data on these two aspects for rock music or common-practice music. Nonetheless, these two aspects seem too important to overlook, and we can use some intuition and experiential knowledge to help assess the results.

Let us first examine the proportion of root position chords to non–root-position chords. In the RS 200 corpus, chord inversions are somewhat rare: about 94 percent of all chord instances are root position chords. 21 The results from the NN 200 are essentially identical, with 93.7 percent of chord instances being root-position chords. 22 Rock and country music thus seem very similar in their tendency to strongly favor root position chords. In this regard, both styles contrast with common-practice music, where previous work shows that only about 60 percent of chords are in root position ( Temperley 2009 ).

More details on the use of non–root-position chords in the NN 200 can be found in Table 22.5 . Here we can see the most common non–root-position chords, ranked by frequency, as well as the most common chords before and after these sonorities. Note that I refer to these sonorities as “non–root-position” chords instead of “inverted” chords because one of the sonorities involves a bass note that is not a member of the triad or seventh chord: a V chord with scale degree 1 in the bass (i.e., “V over 1”). 23 Other than the V over 1 chord, the most frequent non–root-position chords are those that would be typically found in common-practice music (and perhaps rock as well, although no corresponding data currently exist). Other interesting (yet perhaps not very surprising) aspects of Table 22.5 concern the means of approaching and leaving these non–root-position chords. With only one exception, every common chord before or after a non–root-position chord involves a root position chord. Moreover, most of the chords that prepare and resolve the non–root-position chords involve the bass moving by step. Both of these characteristics comport with traditional notions about how non–root-position chords are typically used (especially in common-practice music). And so many of the implied chord progressions in Table 22.5 , such as I followed by “V over 7” followed by vi, are familiar chord patterns to any music theorist.

There is one situation shown in Table 22.5 , though, that stands out as noteworthy: the approach to I over 3 from ii. In common-practice music, we would expect a supertonic chord moving to a first-inversion tonic to be unstylistic. Instead, we would expect this bass motion (scale degree 2 to 3) to be supported by a first-inversion vii o chord moving to a first-inversion tonic—as typically used, for instance, in tonic expansions involving voice exchange, parallel tenths, or soprano neighbor motion ( Laitz 2015 ). But in country music, where the use of diminished chords on scale degree 7 is extremely rare, the standard method of harmonizing ascending bass motion from scale degree 2 to 3 involves a ii chord moving to a first-inversion tonic. This occurs in the context of what could be called “tonic expansions,” such as in the songs “Always on My Mind” or “80’s Ladies” (Figure 22.1 ). Use of ii in a descending stepwise bass motion from 3 to 1 is also standard, such as in “Alcohol” or “Jesus Take the Wheel.” In many cases, the bass motion from scale degree 2 to 3 continues to scale degree 4, creating what could be called a predominant expansion, such as in “Bless the Broken Road” or “I Hope You Dance.” Similar harmonizations can be found for the bass descent from scale degree 4 to 2, such as in “The Good Stuff” or “I Saw God Today.” Country music, we might hypothesize, thus has a slightly different “Rule of the Octave” than that found in common-practice music (see Gjerdingen 2007 ), in that country music displays an overwhelming preference to harmonize scale degree 2 in the bass with a root-position chord, even in stepwise bass contexts. Finally, note that (as seen in Figure 22.1 at the beginning of the verse) the root position chord on scale degree 2 in these stepwise bass contexts often can be heard to include the chordal seventh (i.e., scale degree 1). There is often thus a sort of inner- or upper-voice pedal on tonic in these cases, which we might theorize as a voice-leading “glue” of sorts for stepwise bass motions involving scale degrees 1, 2, 3, or 4.

The fact that root-position chords on scale degree 2 in the NN 200 often contain a chordal seventh broaches not only the issue of how chordal extensions are distributed in the corpus overall but also how these extensions were analytically identified. After all, it can often be difficult to determine solely by ear the exact pitch content of a harmonic sonority from an audio recording. It was because of this inherent subjectivity that Temperley and I reported primarily root information in our 2011 article, despite our analyses of the RS 200 including upper structures. When transcribing the songs in the NN 200, I indicated chord extensions only in clear cases, such as when a scale-degree 1 is heard in the accompanimental texture during a ii chord. Note that I assessed the existence of chord extensions solely based on the instrumental parts since vocal melodies are known to often be “divorced” from the harmonic texture ( Temperley 2007 ; Nobile 2015 ).

Given these caveats, Table 22.6 presents information on chord extensions within the NN 200, showing the most common extensions for the most common triad types. The nomenclature for chordal extensions that follows is that used in my fake book (2015), which generally follows standard schemes used in jazz and pop (e.g., Wyatt and Schroeder 1998 , pp. 142–143). 24 The prevalence of seventh chords overall is not surprising, although two chords—IV and ♭VII—more commonly employ an added ninth (“2”) than a seventh. One reason why this may be the case is that, like the seventh on the ii chord, added ninths on IV and ♭VII reflect the inclusion of tonic chord members (scale degree 5 and 1, respectively). Indeed, a number of commonplace extended triads (e.g., ii 7 , IV 2 , vi 7 , ♭VII 2 , V 4 ) can be seen as deriving from a “holding over” of 1 or 5 in an inner or upper voice. Nonetheless, any differences observed in Table 22.6 from known conventions in rock or common-practice music may be as much the result of the notational system used in the transcription and encoding process as something unique to the style itself. (In the analysis of common-practice music, for example, an added ninth on a IV chord might simply be dismissed as a non-chord tone if using Roman numerals and figured bass.) Undeniably, the identification of chord extensions is one of the more subjective elements of harmonic analysis in popular music. 25

Any number of other statistical tests concerning harmony might be conducted using this corpus. For example, we might test for particularly common three- or four-chord progressions; we might investigate the change in harmonic syntax (if any) over time; or we could test for how well the existence of a particular chord in a song predicts other chords in the song (i.e., chord correlations). We could also explore the extent to which the observed trends in harmony derive from the practical performance aspects of certain instruments common to the style, such as the guitar. 26 We might further extend our research beyond harmony to see how it interacts with form, phrase structure, metric organization, or absolute time. These are all valuable modes of inquiry that, due to space limitations, will have to be reserved for future work.

What the current study shows, via a number of perspectives, is that harmony in country music is in some ways similar to rock music (defined broadly) while in others ways different, just as it is in some ways similar to common-practice music while in other ways different. Generally speaking, the work presented here implies that the conventions of country music lie somewhere in between those found in rock music and those in common-practice music. Like rock and unlike common-practice music, country music employs ♭VII much more frequently than vii o , shows a much greater use of root-position chords than inversions, has root motions that decrease in frequency along a circle of fifths, and shows numerous instances of chord transitions typically deprecated in traditional music theory (such as V–IV, V–ii, and ii–I). Yet, like common-practice music and unlike rock, country music uses more dominant chords than subdominant, has an asymmetrical distribution of root motions on a circle of fifths, and shows a preponderance of root motions that ascend by fourth, descend by third, and ascend by second. If country music can be considered a substyle of rock defined broadly, then, presumably, we would find that harmonic practice in rock defined narrowly would be even further afield of common-practice norms.

In addition, some aspects of harmony seem particularly distinctive to country music (at least in comparison to rock and common-practice styles). The strong avoidance of the minor tonic is one striking feature. We also found support for the notion that country music, more so that other styles, relies heavily on just three chords. That said, both of these aspects are more a matter of degree than of kind, and certainly many counterexamples exist. These counterexamples may be more common in certain substyles of country music than observable in such a broad sample. Jocelyn Neal, for example, notes that harmony in country music ranges from simple, such as in hillbilly and folk songs, to the complex and jazz-influenced, such as in Western swing and Countrypolitan (2013). But of course, any corpus of music can be subdivided into smaller categories, and exceptions to overall trends are rarely difficult to find. It is the overall trends, though, that allow us to recognize and appreciate the exceptions. If we take the term “rock music” in the broadest sense possible, then country music seems itself to be an exception.

What factors, we might wonder, explain the way in which country music is exceptional, at least as compared to rock? I speculate that one factor relates to the typical cultural framework of country music’s listener base, especially as it compares to the listener base for rock or popular music in general. Country music, of course, is deeply rooted in the southern region of the United States (i.e., the American South). At least as indicated by voting patterns, residents of this region generally appear to hold more conservative views on a variety of issues, from economic to political to social, than do residents in other parts of the nation. It perhaps should not be too surprising, therefore, that harmonic conventions in country music may be seen to reflect this more conservative worldview. While harmony in country music, like rock, often departs from common-practice norms, harmony in country music still adheres (if only somewhat weakly) to harmonic principles found in common-practice music that rock seems to ignore. (The preference for certain types of root motions is a particularly strong piece of evidence in this regard.) In other words, country music can be seen as a type of popular music that more strongly maintains traditional notions of harmonic syntax. This hypothesis, of course, assumes that common-practice harmonic conventions are in some way “conservative,” at least as compared to the harmonic conventions found in rock. I do not think that conflating “common-practice” with “traditional” is too far-fetched, though, nor I am the first to do so (e.g., Stephenson 2002 , p. 101), but it is an assumption that should be clarified nonetheless.

This line of reasoning also assumes that country music fans are (at least subconsciously) attuned to basic principles of harmonic organization. With that assumption acknowledged, it is not unreasonable to further hypothesize that the listener base participates in shaping the content of the music through its purchasing power and influence. As expertly detailed in monographs by Peterson (1997) and Jensen (1998) , a central concern in country music is “authenticity” (whether genuine or fabricated). Indeed, in her history of country music, Jocelyn Neal (2013) sketches the constant push and pull in the country music industry as innovations and expansions to the style are soon counteracted by a backlash and return to more traditional sounds—a cycle that has been repeating itself since the dawn of country music. After the jazz-flavored sonorities of 1940s Western swing, for example, comes the simplified harmonic language of honky-tonk; similarly, the rise of outlaw country in early 1970s, with its stripped-down instrumentation and limited chord palette, arguably arose as a reaction to the heavily produced and more harmonically sophisticated music of the Nashville sound. The tension between common-practice and rock music harmonic norms found in country music, therefore, might conceivably reflect some of the underlying back-and-forth tensions between progressive and conservative viewpoints in American culture.

Acknowledgments

The research presented in this paper was generously supported by a Faculty Research and Creative Activity Committee (FRCAC) grant from Middle Tennessee State University during the summer of 2017 (application ID 17-17-111, index number 221712).

Appendix A Sources for the “NN 200” Meta-List of Greatest Country Songs

(All links accessed May 18, 2015.)

Biamonte, Nicole. ( 2010 ). Triadic modal and pentatonic patterns in rock music. Music Theory Spectrum , 32 (2), 95–110.

Google Scholar

Budge, Helen. (1943). A study of chord frequencies based on the music of representative composers of the eighteenth and nineteenth centuries. PhD diss., Teachers College, Columbia University.

Burgoyne, John Ashley. (2011). Stochastic Processes and Database-Driven Musicology . PhD diss., McGill University.

Dansby, Andrew. ( 2002 ). Country scribe Harlan Howard dies. Rolling Stone magazine online, March 5, 2002. http://www.rollingstone.com/music/news/country-scribe-harlan-howard-dies-20020305 .

Covach, John , and Flory, Andrew. ( 2015 ). What’s That Sound? An Introduction to Rock and Its History , 4th ed. New York: W. W. Norton.

Google Preview

de Clercq, Trevor. ( 2015 ). The Nashville Number System Fake Book . Milwaukee: Hal Leonard.

de Clercq, Trevor. ( 2017 ). Interactions between harmony and form in a corpus of rock music. Journal of Music Theory , 61 (2), 143–170.

de Clercq, Trevor , and Temperley, David. ( 2011 ). A corpus analysis of rock harmony. Popular Music , 30 (1), 47–70.

Doll, Christopher. ( 2017 ). Hearing Harmony: Toward a Tonal Theory for the Rock Era . Ann Arbor: University of Michigan Press.

Everett, Walter. ( 2004 ). Making sense of rock’s tonal systems. Music Theory Online , 10 (4).

Gjerdingen, Robert. ( 2007 ). Music in the Galant Style . Oxford: Oxford University Press.

Huron, David. ( 2006 ). Sweet Anticipation: Music and the Psychology of Expectation . Cambridge, MA: MIT Press.

Jensen, Joli. ( 1998 ). The Nashville Sound: Authenticity, Commercialization, and Country Music . Nashville, TN: Vanderbilt University Press.

Laitz, Steven. ( 2015 ). The Complete Musician: An Integrated Approach to Theory, Analysis, and Listening , 4th ed. Oxford: Oxford University Press.

Matthews, Neal Jr. ( 1984 ). The Nashville Numbering System: An Aid to Playing by Ear . Milwaukee: Hal Leonard.

Moore, Allan. ( 1992 ). Patterns of harmony. Popular Music, 11(1), 73–106.

Moore, Allan. ( 1995 ). The so-called “flattened seventh” in rock. Popular Music , 14(2), 185–201.

Moore, Allan. ( 2001 ). Rock: The Primary Text: Developing a Musicology of Rock , 2nd edition. Aldershot: Ashgate.

Moore, Allan. ( 2012 ). Song Means: Analysing and Interpreting Recorded Popular Song . Surrey: Ashgate.

Neal, Jocelyn. ( 1998 ). The metric makings of a country hit. In Cecelia Tichi (Ed.), Reading Country Music: Steel Guitars, Opry Stars, and Honky-Tonk Bars (pp. 322–337). Durham, NC: Duke University Press.

Neal, Jocelyn. ( 2008 ). Country-pop formulae and craft: Shania Twain’s crossover appeal. In Walter Everett (Ed.), Expression in Pop-Rock Music: Critical and Analytical Essays , 2nd ed. (pp. 285–311). New York: Routledge.

Neal, Jocelyn. ( 2013 ). Country Music: A Cultural and Stylistic History . Oxford: Oxford University Press.

The Nielsen Company. (2017). Nielsen Music Year-End Report U.S. 2016. http://www.nielsen.com/us/en/insights/reports/2017/2016-music-us-year-end-report.html

Nobile, Drew. ( 2015 ). Counterpoint in rock music: Unpacking the “melodic-harmonic divorce. ” Music Theory Spectrum , 37 (2), 189–203.

Peterson, Richard. ( 1997 ). Creating Country Music: Fabricating Authenticity . Chicago: University of Chicago Press.

Riley, Jim. ( 2010 ). Song Charting Made Easy: A Play-Along Guide to the Nashville Number System . Milwaukee: Hal Leonard.

Spicer, Mark. ( 2017 ). Fragile, emergent, and absent tonics in pop and rock songs. Music Theory Online , 23(2).

Stephenson, Ken. ( 2002 ). What to Listen for in Rock: A Stylistic Analysis . New Haven, CT: Yale University Press.

Temperley, David. ( 2007 ). The melodic-harmonic “divorce” in rock. Popular Music , 26 (2), 323–342.

Temperley, David. (2009). A statistical analysis of tonal harmony. http://davidtemperley.com/kp-stats/

Temperley, David. ( 2011 ). The cadential IV in rock. Music Theory Online , 17 (1).

Temperley, David. ( 2018 ). The Musical Language of Rock . Oxford: Oxford University Press.

Temperley, David , and de Clercq, Trevor. ( 2013 ). Statistical analysis of harmony and melody in rock music. Journal of New Music Research , 42 (3), 187–204.

White, Christopher Wm. , and Quinn, Ian. ( 2018 ). Chord context and harmonic function in tonal music. Music Theory Spectrum , 40 (2), 314–337.

Williams, Chas. ( 2012 ). The Nashville Number System , 7th ed. Nashville, TN: Chas Williams.

Wyatt, Keith , and Schroeder, Carl. ( 1998 ). Harmony & Theory: A Comprehensive Source for All Musicians . Milwaukee: Hal Leonard.

Yim, Gary. ( 2011 ). Affordant Chord Transitions in Selected Guitar-Driven Popular Music . Master’s thesis. The Ohio State University.

To get a glimpse of existing scholarship on this issue, see the writings of Moore ( 1992 , 1995 , 2001 , 2012 ) and Stephenson (2002) .

For an overview of harmonic conventions in common-practice–era music, especially as typically taught in the modern music theory classroom, see Laitz (2015) .

According to the Nielsen Company’s 2016 year-end report ( Nielsen Company 2017 ), country music accounts for 10 percent of total audio consumption in the United States, which ranks fourth behind rock (29 percent), R&B/hip-hop (22 percent), and pop (13 percent). For comparison, jazz and classical music account for only 1 percent each.

While country music is sometimes considered to be rock in the broadest definition of rock, such as Doll (2017) , some relatively broad definitions of rock often do not include a significant amount of country music, such as Stephenson (2002) and Temperley (2018) .

I cannot find a definitive origin for this quote, although it seems to have become part of the legend of Harlan Howard, as given in his Rolling Stone magazine obituary ( Dansby 2002 ). Howard has expressed similar sentiments elsewhere, such as in his phone interview with Joli Jensen from June 27, 1979, where Howard says, “In country music, simplicity is the key” ( Jensen 1998 , p. 130).

This quote comes from her 1998 book chapter (p. 323). Earlier in the same work, Neal writes, “Musically, there is a pervading misconception that [country music] relies on three-chord harmonic progressions and repetitive structural regularity” (p. 322). In a book chapter from 2008 , she also writes, “One of the enduring clichés about country music is its primitive harmonic language …, [yet] nothing could be further from the truth” (pp. 291–292).

Stephenson writes, “In this book, the term rock refers to the mainstreams of popular music since 1954, whether they be classified as rock ‘n’ roll, rhythm and blues (R&B), soul, country rock, folk rock, hard rock, and so on.” Note that he mentions “country rock” as a style of rock, but not country. As well, very few of his examples come from music after 1990, so more modern styles like hip-hop/rap and heavy metal are not heavily represented, if at all.

Everett writes, for example, “I think we all realize that Led Zeppelin … clearly represents rock music whereas the more temperate McGuire Sisters do not, but then what of the contemplative songs of Simon and Garfunkel?” (2004, p. 4).

The corpus reported in our 2011 paper was a 100-song subset of the “500 Greatest Songs of All Time,” originally published in a 2004 issue of Rolling Stone magazine. The original 500-song list was compiled by polling 172 experts, which we believed gave a more balanced view of rock overall. Indeed, the list contains many songs that would correspond to rock defined narrowly (such as those by Led Zeppelin, the Sex Pistols, and Tom Petty) but also songs that reflect a more broad definition of rock (such as those by Johnny Cash, R. Kelly, and the Beastie Boys).

My methodology for creating the “meta-list” simply gave one point to a song for each of the 14 lists in which it appeared, irrespective of the song’s position on the original list. The final 200 songs were simply those 200 songs that had the most points, all of which earned more than a single point.

Because the publisher of my 2015 book, Hal Leonard, had to acquire copyright privileges for all 200 songs, three songs (“Desperado” by the Eagles, “Pancho and Lefty” by Townes van Zandt, and “Blown Away” by Carrie Underwood) were excluded from the final publication because rights could not be negotiated or secured. These three songs were replaced by the next three highest songs on my “meta-list” to create the final 200-song list.

The five songs included in both the NN 200 and the RS 200 are “I’m So Lonesome I Could Cry” (Hank Williams), “I Walk the Line” (Johnny Cash), “Folsom Prison Blues” (Johnny Cash), “Crazy” (Patsy Cline), and “Ring of Fire” (Johnny Cash).

For more information about the Nashville Number system, see the introduction to my 2015 book. Additional explanations can be found in Matthews (1984) , Riley (2010) , and Williams (2012) .

All songs in the NN 200 corpus were analyzed as having a tonic chord at least once in the song despite the potential for songs in popular music to have “absent” tonic chords ( Spicer 2017 ). Note also that I am hesitant to say that the vast majority of songs in this corpus are “in a major key” since traditional notions of “key” are somewhat problematic in popular music (see Doll 2017 , pp. 21–22).

The greater frequency of chords built on scale degree 4 versus 5 remains valid whether considering all the songs in the RS 200 corpus (as reported in de Clercq and Temperley 2011 , p. 60) or just those songs with major tonics.

Table 22.2 uses traditional Roman numerals to show root and chord quality, with uppercase Roman numerals representing major triads, lowercase Roman numerals representing minor triads, etc., since this chord notation style is probably more familiar to most readers than the Nashville number system and more clearly distinguishes between scale degrees (e.g., 5) and triads (e.g., V).

My estimation of these percentages is based on extrapolation from tables V, VI, and VII found on pages 19–21, using the percentages in the “Total” column to calculate the exact number of I, IV, and V chords from the diatonic totals and then dividing this number by the total number of diatonic and chromatic chord counts.

In my experience, which many readers undoubtedly share, rock songs with limited harmonic palettes are more common within specific substyles, such as blues, early rock’n’roll, and punk. Note that both the NN 200 and the RS 200 are also nearly identical in terms of the proportion of songs with four or fewer chords, which accounts for 50 percent (+/– 2 percent) of each corpus.

The reader can calculate the exact number of instances of each progression in the corpus by combining the number in the “Factor” column with the total number of “Chord Pairs.” For example, ♭VII–IV outweighs IV–♭VII by a factor of 5.52 (i.e., a ratio of 5.52:1). If we divide the number of chord pairs by the factor plus 1 (137 divided by 6.52 in this example), it will give the number of YX progressions in the corpus (21 in this case). Subtracting the number of YX progressions from the total number of chord pairs gives the number of XY progressions in the corpus (116 in this case).

See Huron 2006 (p. 251) for more statistics on chord transitions in a corpus of Baroque music.

The figure of 94 percent for root position chords holds true for both the RS 5×20 (as reported in de Clercq and Temperley 2011 , p. 66) as well as for the RS 200. Note that this figure averages the number of root-position chords in the analyses by Temperley with the number in my analyses (which both differ +/– 1.5 percent from the average).

An “instance” is counted as either a change in the chord root, chord quality, or bass note.

This sonority arises due to harmonic motion over a pedal point, which is represented somewhat differently in the Nashville number system than in traditional Roman numerals and figured bass.

For example, the number “7” indicates a minor seventh above the root, which may create a dominant seventh (or major-minor seventh) chord when used on I, IV, or V triads or a minor seventh chord when used on ii, iii, or vi triads; the number “2” indicates an added ninth (no seventh) above the root; “M7” indicates a major seventh above the root; “64” indicates an added sixth and suspended fourth (no third) above the root; and “94” indicates a dominant ninth chord (including seventh) with a suspended fourth (i.e., the “gospel” or “soul” dominant).

For more data in this regard, see Burgoyne (2011, p. 163) .

For research using the RS 200 on the role of the guitar as a compositional determinant for harmony, see Yim (2011) .

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Research (Wash D C)
v.2019; 2019

The Science of Harmony: A Psychophysical Basis for Perceptual Tensions and Resolutions in Music

Paul yaozhu chan.

1 Institute for Infocomm Research, A⁎STAR, Singapore

2 Nanyang Technological University, Singapore

Minghui Dong

3 National University of Singapore, Singapore

Associated Data

This paper attempts to establish a psychophysical basis for both stationary (tension in chord sonorities) and transitional (resolution in chord progressions) harmony. Harmony studies the phenomenon of combining notes in music to produce a pleasing effect greater than the sum of its parts. Being both aesthetic and mathematical in nature, it has baffled some of the brightest minds in physics and mathematics for centuries. With stationary harmony acoustics, traditional theories explaining consonances and dissonances that have been widely accepted are centred around two schools: rational relationships (commonly credited to Pythagoras) and Helmholtz's beating frequencies. The first is more of an attribution than a psychoacoustic explanation while electrophysiological (amongst other) discrepancies with the second still remain disputed. Transitional harmony, on the other hand, is a more complex problem that has remained largely elusive to acoustic science even today. In order to address both stationary and transitional harmony, we first propose the notion of interharmonic and subharmonic modulations to address the summation of adjacent and distant sinusoids in a chord. Based on this, earlier parts of this paper then bridges the two schools and shows how they stem from a single equation. Later parts of the paper focuses on subharmonic modulations to explain aspects of harmony that interharmonic modulations cannot. Introducing the concept of stationary and transitional subharmonic tensions, we show how it can explain perceptual concepts such as tension in stationary harmony and resolution in transitional harmony, by which we also address the five fundamental questions of psychoacoustic harmony such as why the pleasing effect of harmony is greater than that of the sum of its parts. Finally, strong correlations with traditional music theory and perception statistics affirm our theory with stationary and transitional harmony.

1. Introduction

Even though it is one of the most important components in music, and possibly the most widely studied [ 1 ], the definition of harmony differs vastly across time, genre, and individuals, reflecting how little is understood about it [ 2 , 3 ].

There are three aspects to the complete understanding of our perception of harmony, which we will, for brevity, refer to as what , why , and when . The what of harmony refers to an attribution to a defining quality. Its why goes further to explain the means by which such a quality ascribes to consonance or dissonance (or even sentiment or emotions). Finally, it should be recognized that the same harmony perceived as consonant in one context can be perceived as dissonant in another. This takes the what and why of stationary harmony (sonorities) into the context of transitional harmony (progression). We refer to this as the when of harmony and it has remained largely unaddressed by acoustic science.

1.1. Background

Early works effectively attributed the what of harmony to rational relationships [ 1 , 4 ]. This ascribes a chord's consonance to the ratio amongst its contributing string lengths (and consequently, wave periods and fundamental frequencies), being fractional with integer numerators and denominators. A fascinating number of esteemed mathematicians, physicists, and philosophers have made different contributions in this aspect. The development of the Pythagorean tuning system is commonly credited to Pythagoras in the fourth century BC [ 3 , 5 , 6 ]. Euclid wrote the earliest surviving record on the tuning of the monochord [ 7 ] and documented numerous experiments on rational tuning [ 8 ]. Aristotle and Plato made various contributions to the development of ancient Grecian (rationally scaled) music that was later integrated into the diatonic system [ 8 , 9 ]. Ptolemy developed the syntonic diatonic system as early as the second century [ 10 ]. Euler proposed a grading system of chord aesthetics based on the assertion that the notes have a least common multiple (i.e., that they are rational) [ 11 ]. Since string lengths correspond to wavelengths, which correspond to wave period, and since notes used in harmony are taken from the scale, it can be said that the Pythagorean school effectively attributes harmony to temporal features.

It was not until 1877 that Helmholtz pioneered the psychoacoustic approach [ 3 , 8 , 12 , 13 ]. Isolating adjacent harmonic sinusoids from different notes using specifically devised acoustic resonators, he was able to record how amplitude modulation that resulted from their summation grew perceptually unpleasant as their modulation frequency increased towards a certain threshold [ 8 ], thus attributing dissonance to what he called beating frequencies and addressing the questions what sounds bad and why . Numerous others [ 14 – 25 ] conducted further studies in this approach, while others raised several questions with Helmholtz's theory [ 13 , 17 , 26 ]. For example, Plomp and Levelt [ 12 ] and Schellenberg and Trehub [ 27 ] have separately shown that consonances and dissonances are still perceived in harmonies with pure tones (tones without harmonics). Itoh [ 28 ] and Bidelman [ 29 ], amongst others, also showed that electrophysiological responses to pure-tone intervals did not agree with Helmholtz. All in all, the Helmholtz school attributes harmony to frequency features and comprises a large part of what is referred to in this paper as interharmonic modulations.

In 1898, a notable but short-lived [ 3 ] attempt at what sounds good and why was seen in Stumpf's tonal fusion theory [ 30 ], which theorized that harmony was the effect the harmonics of its component notes fusing together to sound like a single note with a common fundament [ 12 , 13 , 26 , 30 ].

Because of the nonlinear relationship between tonal scale and frequency, scales derived from rational lengths of a string tended to leave certain intervals more rational than others. With this realization, Western music eventually adopted 12-tone equal temperament scale. This equally segments the octave in the log-frequency scale [ 31 ] such that each semitone interval is a factor of 2 1/12 , evenly redistributing the dissonances to accommodate to different keys. Despite its late adoption, original development of this scale predates Helmholtz to the 1500s. Vincenzo Galilei (father of Galileo Galilei) made the earliest known estimate of this in the West by approximating 2 1/12 with 18/17 [ 32 ], while Zhu was credited for perfecting it in the East by computing it to accurately to the 25 th decimal, both in the 1580s [ 12 ]. The earliest recorded estimate of this in the East was by He in the 5th century, whose estimate was already about as accurate as Galilei's [ 33 , 34 ].

In Rameau's Treatise on Harmony [ 1 ], which paved the foundations of harmony in modern music theory, notes of basic chords are derived from the division of the length of a common string [ 35 ]. However, this remains disjoint with the rest of the treatise, and modern music theory remains more of a compilation of rules and deductions from the pattern clustering of perceptual experiences [ 36 – 42 ], addressing the questions what sounds good and when without the scientific reasoning of why [ 37 ].

More recently, several studies have found high correlations between harmony and periodicity measures of the resultant signal [ 43 , 44 ]. This novel leap advances the Pythagorean school while presenting a persuasive attribute of what sounds good and why .

Several notable studies have also been conducted that relate harmony to nonacoustic attributes such as statistics and geometry. An example is Tymoczko's exploration of how multidimensional geometric patterns correlate strongly with patterns that exist in historic harmony use, addressing what sounds good and when [ 45 – 47 ]. Authors in [ 48 ] explored properties of musical scales on the Euler lattice, addressing the what of harmony. Numerous others such as [ 49 – 51 ] have worked on other mathematical relationships in harmony, addressing its what .

Yet others have looked towards a biological rationale towards our perception of harmony to address what sounds good and why . A recent example is Purves' attribution of the effect of the tonal scale to the familiarity of excited or subdued speech [ 14 , 52 – 54 ]. Other examples are the works of [ 43 , 55 , 56 ] in the neuronal mechanism of harmony perception.

In this work, we first seek a mathematical resolution across both acoustic schools by a single psychophysical theory. To start off somewhere familiar, we first describe the concept of interharmonic modulations (which adopts and encompasses Helmholtz's beating frequencies), from which we then introduce the concept of subharmonic [ 57 ] modulations and show how the two categories of modulations relate. (At some point after which, we also show how a specific case of subharmonic modulations addresses Pythagoras, thus integrating the two schools.) After explaining how perceptual tensions [ 18 , 36 , 58 , 59 ] in musical harmony may be identified in subharmonic tension in the stationary context, we continue to explain how perceptual tension resolutions [ 18 , 42 ] in transitional harmony (chord progressions) may be visualized in subharmonic trajectories. By these, we address the what , why , and when of harmony. Numerical results show strong to near-complete correlations with perception and chord-use statistics that are presented towards the end of the paper.

By applying our theory and equations, we will answer the five fundamental questions of psychoacoustic harmony. These are as follows.

(1) The phenomenon that the effect of harmony is greater than the sum of its parts [ 18 , 60 ]: ε x 1 + x 2 + x 3 ≫ ε x 1 + ε x 2 + ε x 3 (1)
where ε denotes the harmonious effect of x 1 , x 2 , and x 3 representing notes of the chord and ‘+' denotes simultaneous presentation or cumulation.
(2) There are the definition and explanation of stationary harmony, i.e., what sounds good and why , or, mathematically, to quantify ε { X n }, where X n represents chord n .
(3) There are the definition and explanation of transitional harmony, i.e., what sounds good , why , and when , or, mathematically, to quantify ε { X 1 → X 2 }, where ‘→' denotes transition from one chord to another.
(a) A chord that sounds better than another out of context can sound worse than being in context [ 42 ]. Given ε { X 2 } > ε { X 3 } this shows that ε { X 1 → X 2 } < ε { X 1 → X 3 }
(b) A chord that sounds better than another in one context can sound worse than being in another context [ 42 ]. Given ε { X 4 → X 2 } > ε { X 4 → X 3 } this shows that ε { X 1 → X 2 } < ε { X 1 → X 3 }
(5) We have the phenomenon that the transition from a low-tension chord to a high-tension one can still bring about the effect of tension release (resolution). Given ε { X 1 } < ε { X 2 } this shows that ε { X 1 → X 2 } > 0

Apart from Pythagoras [ 3 , 5 , 6 ] and Helmholtz [ 8 ], we will, in closing, also briefly explain how our theory mathematically bridges other subsidiary psychophysical theories such as Stumpf [ 30 ], Euler [ 11 ], Galilei [ 33 , 34 , 61 ], and Zhu [ 12 ].

2. A Universal Theory of Harmony

In this section, a psychophysical basis for harmony is proposed as follows.

The human perception of harmony is composed of auditory events produced by the combination of sinusoids that make up each note in the harmony. These may be classified into interharmonic and subharmonic modulations.

First-order interharmonic modulations are those produced by the interplay amongst adjacent sinusoids across differing notes. These are loosely categorized by the frequency of the resultant amplitude modulation into dissonant beating frequencies [ 8 ] and consonant low-frequency modulations, triggering a variety of emotions according to their modulation and carrier frequencies. Second-order interharmonic modulations are produced by the alignment of first-order ones. The consonance types of different intervals may be identified according to patterns cast by interharmonic modulations on the interharmonic plot.

Despite the significance of interharmonic modulations, the effect of consonances and dissonances is still experienced in the absence of harmonics with pure tone harmonies. This implies that interharmonic modulations are not exclusive in our perception of harmony [ 12 , 13 , 17 , 26 – 29 ]. From this, it may be deduced that subharmonic modulations also play a significant role.

Subharmonic modulations are produced by the interplay of sinusoids much further apart than interharmonic modulations. Unlike interharmonic modulations, which are analysed primarily in the frequency domain, subharmonic modulations are analysed primarily in the temporal domain and they are comprised of two parts. The first part is subharmonic wave formation, which occurs with the summation of component waveforms from each note to produce a waveform largely periodic to a common subharmonic frequency. The second is subharmonic wave deformation (an example is provided in Supplementary .), which is a distortion to every successive period of this composite subharmonic waveform due to the imperfect alignment of contributing wave periods. Stationary tension and transitional resolution may both be derived from subharmonic features which serve as measures of stationary and transitional harmony.

In order to explain interharmonic and subharmonic modulations in detail and how they unify the two prevailing schools of harmony, we will start from first principle by looking at the notes of a chord as the sum of their composite sinusoids.

2.1. Modulations in Sinusoidal Summation

When waveforms of two notes, x 1 ( t ) and x 2 ( t ), at amplitudes α and β , respectively, are presented together, the result may be expressed as a sum of their composite sinusoids such that

where, respectively, n and m represent the individual harmonics from each note, N and M represent the highest harmonics that need to be considered because of audible range, q n and r m represent the amplitude coefficients of each harmonic, nf 1 and mf 2 represent the frequencies of each harmonic with f 1 and f 2 representing the fundamental frequency of each note, ρ n and φ m represent the starting phases of each harmonic, and t represents monotonically increasing time.

Isolating a single pair of adjacent sinusoids from differing notes we get

where h 1 ( t ) and h 2 ( t ) are the pair of harmonics from differing notes, A = αq n , B = βr m , ω 1 = 2 πnf 1 , and ω 2 = 2 πmf 2 .

Since we are considering the modulating frequency resultant of the summation of both sinusoids spanning all phase combinations, it no longer matters which starting phase we take reference from. Hence, ρ n and φ m can both be set to zero.

In the case of A=B, the resultant amplitude modulation is trivial and, as illustrated in Figure 1 (left), is given by the sum-to-product rule

where ∆ ω /2 is the normalized modulating frequency and is given by

ω - is the normalized carrier frequency given by

and the values of A and B are normalized to 1.

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.001.jpg

Summation of sinusoids of equal (left) versus unequal (right) amplitudes. Notice the difference in modulating frequencies even though frequencies of component sinusoids remain unchanged.

However, in most cases, A ≠ B , and the problem becomes nontrivial, because of the change in modulation frequency as the modulating waveform no longer crosses zero. This can be seen in Figure 1 (right).

We approximate the summation of these sinusoids to be

where ω c is bounded by ω 1 and ω 2 and is approximated to be ω - (which denormalizes to f - ) ; ‖cos 2− A / B ⁡(∆ ω /2) t ‖ denotes the magnitude of cos 2− A / B ⁡(∆ ω /2) t signed according to the quadrant of (∆ ω /2) t . B denotes the larger of the amplitudes and A and B are normalized to A = 1.

When A = B , this simplifies to ( 4 ), where the modulating frequency is ∆ ω /2.

However, as B increases with respect to A , 2 − A / B gravitates towards 2, and

for which the modulating frequency is ∆ ω .

We can see from the plots in Supplementary that this estimation is accurate for values of B marginally larger than A to much larger than A.

For consistency, the effective modulating frequency for the case of A = B will be considered by the frequency of its rectified modulating waveform which is then, similarly, ∆ ω . In music, we are interested in this frequency in hertz. Hence, we denormalize this to be

In the next two sections, we will move on to see how this is applicable not only to the summation of adjacent harmonics in interharmonic modulations but also to distant sinusoids in subharmonic modulations.

3. Interharmonic Modulations

Interharmonic modulation refers to modulations across adjacent pairs of sinusoids from different notes that fall within a certain threshold, with modulation frequency corresponding to ∆ f in ( 9 ).

Figure 2 shows a plot of all harmonics of notes c 3 (blue) and e b 3 (red) under 3 kHz. All adjacent sinusoids less than 120 Hz apart are identified in the figure, with their centre, f - , and modulating, Δ f , frequencies labeled accordingly.

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.002.jpg

Identifying the interharmonic modulations across c 3 and e b 3 .

3.1. Beating Frequencies and Low-Frequency Modulations

Interharmonic modulations with ∆ f that increase towards a certain threshold are known to become increasingly dissonant, and, as coined by Helmholtz, are known as beating frequencies [ 8 ]. Interharmonic modulations with small ∆ f , on the other hand, contribute to the harmonious effect perceived in consonance [ 65 ]. Figure 3 illustrates this.

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Types of interharmonic modulation on the scale of Δ f .

3.2. Perceptual Responses across the ∆ f - f - Feature Space

It is known that different combinations of notes contribute to different emotive valences [ 66 ]. This too may be decomposed into a sum of its harmonics. Hence, further to the consonances and dissonances, emotive responses may also be mapped onto the interharmonic plot. Although, as one might imagine, such responses would be different for every individual, we can plot the response for an individual as an example. Figure 4 shows an example of auditory responses triggered in the mind of the (first) author when exposed to frequencies in the horizontal ( f - ) axis modulated by frequencies in the vertical ( ∆ f ) axis. The value of f - is indicated in the horizontal axis in both Hz and its corresponding note names. The degree of pleasure derived from interharmonic modulation is coded in the colored background as a reference. The green regions are perceived to be pleasing, yellow as somewhat pleasing, orange as unpleasant, but not to the point of annoying, red as dissonant, and black as beyond beating range. The black dots mark the locations of the thoughts or emotions labelled. This shows that interharmonic modulations bring about a large variety of thoughts or emotions. If several of these are triggered simultaneously when just one pair of notes sound simultaneously, one can imagine how ten fingers on a piano or all the instruments in an orchestra could combine several (thoughts or emotions) to paint stories on the interharmonic feature-space over time.

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.004.jpg

Example of auditory responses triggered by pure-tone frequencies on the horizontal axis modulated at frequencies on the vertical axis. Green, yellow, orange, red, and black indicate pleasing, somewhat pleasing, unpleasant, dissonant, and beyond beating range, respectively.

3.3. Intervals and Second-Order Modulations on the ∆ f - f - Feature Space

The interharmonic modulations of each interval within an octave are similarly plotted in Figures Figures5, 5 , ,6, 6 , and and7. 7 . However, this time, the plots are in the linear scale. Green, yellow, orange, and red, again, represent regions of different degrees of consonance or dissonance according to the same color scheme as Figure 4 . However, because this time both horizontal and vertical axes are in the linear scale, consonance-dissonance levels that populate the space on the nonlinear plot in Figure 4 now populate lower right regions of these linear plots. The remaining upper left regions are then populated with dissonance levels from [ 12 ]. These colors provide a simple background reference for the dark blue dots that each represent a modulation at their corresponding ∆ f and f - values, which results from the summation of neighboring pairs of sinusoids (at frequencies f - + ∆ f / 2 and f - - ∆ f / 2 ) of the notes specified by the indicated interval. Also, for reference, are the two white lines that run across each plot, indicating the locations where the values of ∆ f coincide with a semitone (gentler slope) and a tone (steeper slope) of the corresponding values of f - (where ∆ f = ( 2 1 / 12 - 1 ) f - and ∆ f = ( 2 2 / 12 - 1 ) f - , resp.). The semitone and the tone are regarded as the most dissonant intervals up to halfway in either direction around the cyclic chroma [ 12 , 21 , 54 ].

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.005.jpg

Interharmonic plots for all intervals within an octave regarded, in classical music theory, to be perfectly consonant with a root of g 3 . These are, namely, the Perfect 4 th (g 3 and c 4 ), Perfect 5 th (g 3 and d 4 ), and Octave (g 3 and g 4 ) intervals.

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.006.jpg

Interharmonic plots for all intervals within an octave regarded, in classical music theory, to be imperfectly consonant with a root of g 3 . These are, namely, the Minor 3 rd (g 3 and b b 3 ), Major 3 rd (g 3 and b 3 ), Minor 6 th (g 3 and e b 4 ), and Major 6 th (g 3 and e 4 ) intervals.

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.007.jpg

Interharmonic plots for all intervals within an octave regarded, in classical music theory, to be dissonant with a root of g 3 . These are, namely, the Minor 2 nd (g 3 and a b 3 ), Major 2 nd (g 3 and a 3 ), Minor 7 th (g 3 and f 4 ), Major 7 th (g 3 and f ♯ 4 ), and Diminished 5 th (g 3 and d b 4 ) intervals.

The plots of perfect consonances are presented in Figure 5 . These intervals are described with a bit of a dilemma in classical music theory [ 67 ]. They may be described as so consonant that they sound almost like one note. As such, their use contributes in a limited way to harmony [ 15 ]. For example, the use of perfect fifths is forbidden in parallel motion and octaves are regarded as the same note in a different register [ 42 ].

The interharmonic plot reveals the perceived traits of each category of intervals in a way that explains why they sound the way they do, and in a way music theory alone has never been able to. As shown in Figure 5 , the constellations formed by interharmonic modulations of perfect intervals line up almost horizontally (While the methods used in this study are applicable with any form of tuning, only equitempered tuning is assumed in the computations in this section. This is consistent throughout this paper, unless otherwise stated.). Since each point that falls on the same horizontal has the same ∆ f , this means that they modulate synchronously and may be perceived collectively as a single modulation. This may be interpreted as fewer modulating microevents taking place, making them less interesting than other consonance intervals.

Dissonant intervals are presented in Figure 7 . As can be seen in the figure, these intervals have points that fall mostly within the central dissonant region and line up along the two dissonant lines. Evenly spaced points along a line that passes through the origin also reveal that their ∆ f share a harmonic relationship. This has a similar (although this is somewhat lesser) redundant effect to that of the synchronous modulation described with perfect consonances.

Consonances that properly contribute to harmony are called imperfect consonances [ 67 ] and are presented in Figure 6 . As can be seen in the figure, imperfectly consonant intervals have points better distributed. This may be interpreted as erratic modulations that create a continuous stream of unpredictable events to stimulate aural attention, and thus, interest.

A lot of work has already been done on interharmonics since Helmholtz [ 12 , 19 – 21 , 24 , 25 ]. While the main focus of this work is not interharmonics, one purpose of this section is, nevertheless, to provide sufficient background to complete our theory of how the human experience of stationary harmony is based around modulations of both interharmonic and subharmonic nature. From the interharmonic plots in Figures Figures5 5 5 – 7 , a simple predictor of dissonance may be identified to be

where ∆ f ^ will be our shorthand for ∆ f / f - , C ( ∆ f ^ ) , or C ∆ f / f - referring to the number of interharmonic modulations that fall within the central region of dissonance region, i iterates through all interharmonic modulations on the plot, n is the total number of modulations considered, ∆ f i and f - i refer to the pair of ∆ f and f - that describe the i th interharmonic modulation, respectively, and r lower and r upper define the lower and upper boundaries of the region on the interharmonic plot, respectively.

In this section, we have seen how interharmonic modulations are significant to our perception of consonance, dissonance, and emotive response in music. When listening to a duet of instruments with no overtones such as a sinewave theremin or a very pure musical saw, we realize that consonance, dissonance, and emotion remain present even in harmony without harmonics (i.e., across a well-spaced pair of fundamental frequencies alone). This is just one amongst the several different ways [ 12 , 13 , 17 , 28 , 68 , 69 ] from which we can deduce that interharmonic modulations cannot be the only determinant of our perception of harmony, which thereby leads to our hypothesis on subharmonic modulations.

4. Subharmonic Modulations

Apart from the modulations that arise from the summation of adjacent harmonic sinusoids across differing notes, we can (as explained above) deduce that another category of modulations is significant to our perception of harmony. We call these subharmonic modulations. There are two levels of subharmonic modulations, which we dub subharmonic wave formation and subharmonic wave deformation. In this section, we will show how these are significant to our perception of not only stationary harmony, but also transitional harmony.

Figure 8 shows the waveforms of a C Major chord (C) and a C minor 7 chord (Cm 7 ) composed of the fundamental sinusoids of each composite note. We let each sinusoid start at phase zero since; for purpose of example, we are only interested in wave period. Only the fundament needs to be considered for the same reason. In both cases, the waveform resultant of this summation repeats at a frequency approximately subharmonic to all its composite waveforms. In the figure, its period is marked T sub . We call this subharmonic wave formation and say that T sub is a common subharmonic to all its composite waveforms.

An external file that holds a picture, illustration, etc.
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Subharmonic wave formation and deformation in the C and Cm 7 chords.

In the case of the C chord, as shown in the figure, each composite sinusoid crosses zero at nearly the same point around t = T sub . As marked in the figure, Δ t (which is the difference between the first and the last negative-to-positive zero-crossing around the t = T sub region) is small. However, in the case of the Cm 7 chord, Δ t is much larger. One can imagine that each successive period of the resultant waveform looks less and less like the first as it gets more and more deformed. This happens slowly for the C chord because of the small Δ t but faster for the Cm 7 because of the large Δ t . We call this subharmonic wave deformation. Supplementary compares subharmonic wave deformation in a low-tension C chord to that in a high tension Cm7 chord.

Recalling our wave equation from ( 3 ), we can rewrite A cos⁡ ω 1 t + B cos⁡ ω 2 t , or A cos⁡2 πf 1 t + B cos⁡2 πf 2 t , as

where f sub is an approximate common factor of f 1 and f 2 , k 1 and k 2 are integer multipliers, and Δ f 1 and Δ f 2 are small values that balance the equation by making up for the discrepancies that arise with finding a common factor.

In ( 11 ), two fundamental frequencies f 1 and f 2 are described as the multiple of a lower subharmonic frequency that is common to them ( f sub ). We call this their common subharmonic .

Since all harmonics are multiples of their fundamental, a subharmonic to any fundamental would inherently be subharmonic to all its harmonics. For this reason, only the fundamental of each note needs to be considered.

Since harmony in music is commonly composed of more than just two notes, we generalize this to describe fundamentals and common subharmonics from any number of notes to get

where N is the number of notes in the chord, i cycles through each of them, and A i is the amplitude coefficient of note i .

Beyond this point, it would be easier to visualize subharmonics in the time domain. With the fundamental frequency of note i given by

the fundamental period of each note i is then

where t i is the fundamental period of the note.

Hence, the period of any common subharmonic can be expressed as k i t i . We can then compensate for nonintegral discrepancies in period rather than in frequency. In doing so, we get

for all i , where T sub is the common subharmonic wave period (we will simply say common subharmonic) of the chord. What carries over as k i t i is essentially just the k th subharmonic of note i which lies in the region of T sub . Since this is true for all pairs of k i and t i across all values of i when they are each balanced by appropriate t i , i may be dropped from the left hand side of the equation.

Although the common subharmonic was introduced as the period between primary zero crossings as in Figure 8 , we shall, for computational simplicity, redefine it as the mean of k i t i across all notes of the chord. Hence,

Figure 9 shows how the period of each subharmonic in the C Major chord from Figure 8 may be plotted. The left column first shows how the period of each subharmonic of c 3 may be plotted in red. The right column then extends this to every remaining note in the chord, with orange, yellow, and blue for the notes e 3 , g 3 , and c 4 , respectively. It may be seen in the right column that a subharmonic period from every note in the chord nearly coincides at around 30 ms. Hence, we say that this is its common subharmonic, T sub , as defined in ( 16 ).

An external file that holds a picture, illustration, etc.
Object name is Research2019-2369041.009.jpg

Plotting subharmonic wave periods of the C Major chord.

Having reduced the waveform plot to subharmonic periods in the vertical axis, we can represent time spanned by each subharmonic in the horizontal axis. We will do this for a song stanza in the next section, in a subharmonic plot.

4.1. Subharmonic Modulations in Stationary Harmony

Figure 10 shows an example of a subharmonic plot. In the horizontal axis there is time in bars and in the vertical axis there is the subharmonic wave period in milliseconds. Note that the subharmonic axis runs top down to put shorter wave periods at the top because they correspond to higher frequencies. Larger wave periods, which correspond with lower frequencies sit conversely at the bottom. The tails that run horizontally represent the span of time covered by each note. Subharmonics are colored to match their corresponding notes on the music score. For example, in the first bar, all subharmonics of f # 5 are marked out in red, followed by d 5 in orange, a 4 in yellow, d 4 in green, a 3 in blue, and d 3 in purple. The musical score runs in parallel at the bottom of the plot as reference. Once again, all plots and computations in our examples assume equal temperament unless stated otherwise. This example shows the opening stanza of Pachelbel's Cannon in D [ 70 ] and focuses on stationary harmony, leaving transitional harmony to a later example.

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Subharmonic plot of the opening stanza of Pachelbel's Cannon in D with period in milliseconds on the vertical axis and time in bars on the horizontal axis. Subharmonics are colored to match the color of their corresponding notes on the music score below. The subharmonic tensions of each chord, ∆ t , are marked out on the plot with white arrows. Significant wave periods, along with common subharmonic periods, T sub , are marked against the vertical axis on the right. In the interest of visiting all common chords of the key, Em is used in the 7 th bar instead of G, which already occurs in the 5 th bar. Considering the fact that this example is not used for transitional harmony, all chords are presented in its root position at the expense of introducing parallel 5 th s in the interest of normalization for fairer comparison.

Subharmonics . For every bar, the dashes that flush with the reference point at 0 ms mark 0 × t 0 . Carrying on top down with each bar in accordance to color, we get subharmonics at 1 × t 0 , 2 × t 0 , 3 × t 0 , 4 × t 0 , etc.

Notes and Melody Line . Since the topmost dash of each color for every bar below the 0 ms reference represents 1 × t 0 , they relate to the fundamental period of each note; of these, the topmost ones of every bar across all colors mark the melody line, f # 5 -e 5 -d 5 -c # 5 -b 4 -a 4 -b 4 -c # 5 . (They are red in this particular example.) Hence, it is easy to interpret the melody line in a subharmonic plot. The periods, t i , of each note of the melody are marked against the vertical axis in milliseconds as well as their common note names.

Chords and Coincidence . Common subharmonics may be visualized in regions with the (approximate) coincidence of dashes of every color. Again, the common subharmonics ( T sub ) of each chord in the stanza are marked out against the vertical axis in both milliseconds and their respective chord names.

Key . Every note of the diatonic shares a common subharmonic. Hence, it is possible to identify the key of a song by its common subharmonic, assuming minimal deviations from its key. The common subharmonic associated with the key of this song is marked out much further down the plot. Dotted lines indicate discontinuity. (This part of the figure is plotted in just intonation to avoid the snowballing of Δ t i to better illustrate this.)

Stationary Tension . Most of the time, contributing subharmonics from different notes are not precisely coincident. Major chords have better coincidence than minor chords, and triads coincide better than sevenths and extended chords. With subharmonic modulations, perceptual tension arises with the noncoincidence of common subharmonics. Noncoincidence is measured by an overall Δ t as reflected in Figures Figures8 8 and and10. 10 . We call this its (stationary) subharmonic tension.

This Δ t is given by the difference between the largest and smallest subharmonics in the chord that coincides around T sub .

where [ k i t i ] max and [ k i t i ] min denote the largest and the smallest subharmonics in the chord that (nearly) coincides around T sub (mathematically, they are the maximum and minimum values of k i t i , resp.).

Δ t and T sub are the primary features of stationary tension. Δ t may be normalized by expressing it like a duty cycle by taking

From Figure 3 in the section on interharmonic modulation, recall that dissonances increased and decreased with interharmonic modulation frequency while consonances behaved inversely. This happens only within a certain range. When interharmonic modulation frequency shrinks to the brink of zero, it falls below musical significance.

Subharmonic tension behaves similarly. Figure 11 describes different types of harmony on the subharmonic tension scale. As can be seen in the figure, our response to subharmonic tension is likewise. Perceived dissonances increase and decrease with subharmonic tension while perceived consonances behave inversely within common range. Mathematically,

where ε {X} is the harmonious effect of chord X and Δ t ^ X is its stationary subharmonic tension (its Δ t ^ ).

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The effect of harmony, ε { X }, on the scale of subharmonic tension, ∆ t ^ .

However, as described in the figure, modulations from subharmonic tension fall below musical significance; the effect of harmony drops to zero as modulations from subharmonic tension fall below musical significance. Hence, where ∆ t ^ t h r e s h o l d is the said threshold of musical significance, as ∆ t ^ < ∆ t ^ t h r e s h o l d ,

Thus, perceptual tensions and consonances are experienced in slew-like modulations of the waveform at common subharmonic locations. (This is the effect of periodically changing phase relationships amongst the contributing waveforms, for which Δ t is a measure.) While there may be several common subharmonics for every chord within reasonable range, we theorize that our ears identify most with the shortest few. Subharmonic consonances are described by gentler modulations (small Δ t ) at the shortest common subharmonic locations (short T sub ), while subharmonic dissonances are described by more turbulent ones (associated with absence of small Δ t at short T sub ).

The sensation of a chord can be highly complex, with different tensions and consonances perceived simultaneously, an experience inadequately represented by a single term for dissonance. Attempting to rate every chord by its dissonance level alone can be compared to rating every variety of chocolate in a candy store by only how sweet or bitter it is. The advantage of ∆ t , as opposed to existing correlates of harmony [ 3 , 13 , 43 , 54 ], is the way it explains abstract notions of perceptual tensions and consonances by ascribing them to regions across the subharmonic spectrum with a strong sense of attribution or identification. While, for purpose of illustration, Figures Figures9 9 and and10 10 have shown examples where a modal T sub (shortest T sub with smallest ∆ t ) is easiest to identify, we theorize complex chords with ambiguous T sub (where it is difficult to attribute the collection of modulations experienced to a single modal); our ears often identify with several common subharmonics simultaneously. In other words indeterminate cases could possibly arise with particularly discordant harmonies without small ∆ t at short T sub . Thus, for programmatic analysis of a large number of chords, it is, nevertheless, useful to have a single term to represent the overall dissonance of each chord. For this, we use

where a single term, ∆ t ~ , represents the overall subharmonic tension, T sub , j and ∆ t j refer to individual candidates of T sub and ∆ t with j iterating through each candidate pair, c is the preemphasis (while 1/ c serves as “post de-emphasis”), and Σ n : m denotes summing over the n smallest values out of a range of m values considered. In our work, n is always chosen to be half of m unless stated otherwise. Note that T sub , j here serves as a weighting factor to weight down higher subharmonics, which, as aforementioned, are less significant. Inverting before (and rectifying after) summation mimics our hearing by allowing smaller values of ∆ t j to contribute better towards a smaller ∆ t ~ .

We will see how representative ∆ t ~ is of stationary harmony in the next section. But before that, we will first explain subharmonic modulations in transitional harmony.

4.2. Subharmonic Modulations in Transitional Harmony

While stationary harmony studies chord sonorities (how a chord sounds on its own), transitional harmony deals with chord progressions and resolutions (how chords transit from one to another). It is remarkable how a low tension (consonant) chord can transit to a high tension (dissonant) one yet still bring about the perceptual effect of tension release (resolution) [ 18 ]. From this it may be deduced that transitional harmony stands largely independent of stationary harmony, even though both are considered when assigning harmony in composition. Even though numerous studies have been conducted on stationary harmony from the psychoacoustic approach, work on transitional harmony remains primarily nonpsychophysical.

Traditional classical music theory uses the term resolution to describe the perception of tension released when a chord is suitably followed by another chord [ 18 ]. With subharmonic modulation, we theorize that these abstract perceptions of tensions released may be identified and quantified in the perceived trajectories of subharmonics as one chord progresses to the next. Figure 12 illustrates this.

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Subharmonic plot of the opening line of Beethoven's Moonlight Sonata with period in milliseconds on the vertical axis and time in bars in the horizontal axis. Subharmonics are colored to match their corresponding notes on the music score. Names of relevant notes are marked out on the left, at T sub values corresponding to their wave period. The region of each transition is numbered in white. Colored arrows follow voice leading along the notes across chord changes.

Figure 12 shows the opening line of Beethoven's Moonlight Sonata [ 71 ]. Before we begin our analysis, one should note that unlike Pachelbel's Cannon the use of arpeggios (broken chords) means that notes contributing to the harmony may not necessarily start at the same time, but, when the sustain pedal on the piano is applied, they sustain and overlap until the end of each bar. The names of the chords formed by the notes are labelled along the top of the score to aid the reader in this analysis. Another thing to note would be the fact that this piece maintains a strong sense of voice leading [ 72 ], which means that each note from a chord has strong progressive associations with a note from the previous and another from the succeeding chord. The subharmonics of all notes that are associated in this way (i.e., of the same voicing) across the song are coded with the same color to aid the reader in this analysis. For example, all notes in red on the music score represent the bass (lowest) notes throughout the song, and every subharmonic of these notes is portrayed in red.

We theorize that in chord transitions every subharmonic ( k i t i ) that (nearly) coincides around the common subharmonic ( T sub ) of a succeeding chord is perceived to transit from the nearest corresponding (i.e., of the same voicing) subharmonics in the preceding chord. These transitions are marked out by the arrows in Figure 12 , which are colored according to the notes they are associated with. Arrows are usually convergent (with the exception of, for example, a basic triad progressing onto an extended chord of the same root) because the subharmonics of the succeeding chord always identify with a common subharmonic whereas those of the preceding chord usually do not.

The central hypothesis of transitional subharmonic theory is that perceptual tension resolution, which is so often described in traditional music theory but never physically identified in acoustics, lies in the degree of convergence seen here.

Assuming transition to be abrupt (since notes do not commonly glide from one pitch to another in music) we compute a Δt for the succeeding common subharmonic and a Δt for its preceding corresponding subharmonics and simply measure this degree of convergence as the difference between the two. As such,

where ∆ t s refers to the ∆ t of the succeeding chord and ∆ t p refers to the ∆ t defined by its nearest preceding subharmonics.

This can be normalized by dividing by T sub such that

where ∆ ∆ t ^ denotes normalized ∆∆ t and T sub refers to that of its succeeding chord.

∆∆ t is, thus, a quantification of the tension; Δ t is released over the transition at the wave period of the succeeding common subharmonic.

According to our theory, tension resolution is perceived in the release of this tension across each transition. Thus, mathematically,

where ε denotes the perceptual resolving effect of tension release and ∆ ∆ t ^ X 1 → X 2 denotes the ∆ ∆ t ^ across the transition of chord X 1 to chord X 2 .

Since resolution (tension release) [ 18 , 42 ] in harmony progression is perceived in the convergence of ∆ t ^ , what we will refer to as complication (build-up of tension or negative resolution) is seen in its divergence, where ∆ ∆ t ^ < 0 and ε {X 1 → X 2 } is negative.

Three possibilities arise when looking at T sub and ∆ t from this perspective, by which we can divide transitional harmony into three classes. As illustrated in Figure 13 , these are as follows.

(1) Resolution, also called tension release: this is the most common occurrence and occurs with the convergence of Δt (i.e., ∆ t p > ∆ t s ) and a positive ∆∆ t . The larger the ∆∆ t , the larger the perceptual tension release.
(2) Complication, also called tension buildup: this is the least common occurrence and occurs with the divergence of Δ t (i.e., ∆ t p < ∆ t s ) and a negative ∆∆ t . Just as negative aesthetics may be used expressively in a painting, it may similarly be used in music [ 73 ]. The larger the magnitude of∆∆ t , the larger the perceptual tension buildup. Complications usually only occur when the preceding T sub is equal or nearly equal to the succeeding T sub . Musically speaking, it usually occurs when a simpler chord is followed by a more complex chord of the same root.
Escalation: this occurs when each [ k i t i ] shortens simultaneously, T sub shortens by a factor equivalent to 1 or 2 semitones (2 1/12 to 2 2/12 times), and f sub rises, producing the uplifting effect of melodies rising by 1 or 2 semitones.
Descent : this occurs when each [ k i t i ] lengthens simultaneously, T sub lengthens by a factor equivalent to 1 or 2 semitones (2 1/12 to 2 2/12 times), and f sub falls, producing the detrimental effect of melodies falling by 1 or 2 semitones.

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Trajectories of k i t i in different states of tension development (states of convergence).

It is fascinating to note how the perceptual development (build-up and resolution) of tension that is so often described in music [ 18 , 42 ] but never identifiable with an acoustic attribute may here be visualized in the convergence and divergence of common subharmonics. Figure 13 further illustrates how k i t i trajectories reflect the development of tension build-up and release. Additionally, trajectories for excursions are illustrated in the same figure.

Returning to Figure 12 , the transitions between each chord are labeled 1 to 7 in the figure and correspond to 1 to 7 as follows.

(1) The song starts off with a C # m chord. Hence, the common subharmonic is observed around a wave period of c # . Our ears adhere especially to the shortest one, which is at c # 2 . Large Δt is attributed to the complex tensions within a minor chord. At the region marked 1, this transits to a C # m/B chord. The tension built up with the divergence of Δt may be visualized in the divergence of the arrows in the figure (of which the dotted ones across the plot are used to indicate the continuation of subharmonics, i.e., k i t i that do not change). Both perceptually in music and acoustically, as defined above, this translates to a further complication to the existing minor tension.
(2) At region 2, there is a convergence to a momentary (half-bar) low-tension A chord. The uplifting effect of a large tension release, ∆ ∆ t ^ ≫ 0 , is counterbalanced by the detrimental effect of a falling melodic sequence (lengthening T sub ), adding to the complexity of the song.
(3) At region 3, A transits to a D/F # , which is a Neapolitan chord. The low f # bass extends over 2 octaves below the treble notes, putting a strong T sub at a nonroot period of f # 1 and creating an amount of stationary tension that is unusual for a major chord. (In such cases, there is usually another common subharmonic with lower Δ t but at a wave period corresponding to a root at a much larger T sub .)
(4) At region 4, the Neapolitan chord resolves to the Dominant 7 th , marked G #7 in the figure, with a large perceptual resolution that is signature to b II 6 -V 7 transitions in music [ 42 ]. This large tension release is visualized as a large convergence in the subharmonic plot as indicated by the arrows.
At region 5a, the transition from the G #7 progresses to what is labeled C # m. However, this C # m is functionally still a G # with a double suspension of the 3 rd (b # ) to a 4 th (c # ) and the 5 th (d # ) to a 6 th (e), respectively. The perceptual complication that arises with this transition can be visualized in the subharmonic plot as indicated by the divergence of the green and cyan arrows, respectively. The deviation of the suspended notes from the primary triad is visualized as a deviation of their k i t i from T sub .
At region 5b, the tension resolution with the 6 th being resolved back down to the 5 th can be visualized in the subharmonic plot by its k i t i resolving back to T sub as indicated by the convergent cyan arrow. The continuation of the suspended 4 th is visualized in the dotted green arrow.
At region 5c, the tension resolution with the 4 th being resolved back down to the 3 rd can be visualized in the subharmonic plot by its k i t i resolving back to T sub as indicated by the solid green arrow. In preparation for a major resolution back to the upcoming tonic, Beethoven's touch of genius combines this resolution with a simultaneous complication in the introduction of the 7 th at this point. This is visualized in the deviation of its k i t i away from T sub as indicated by the divergent solid yellow arrow.
(6) At region 6, the Dominant 7 th is resolved back to the Tonic with a tension release unique to V 7 -tonic cadences that is so immense that it is has been long established as the de facto cadence for the end of musical passages [ 42 ]. This immense perceptual release of tension, too, is identifiable in the subharmonic plot. From the figure, it may be seen that the common subharmonic, T sub , of C # m (located at the period of c # 1 this time, because of the g # 2 in purple) lies right in the middle of two common subharmonics of G #7 (located at the periods g # 1 and g # 0 ). This unique subharmonic behavior allows our ears to quite possibly identify with both k i t i for the preceding ∆ t making ∆ t ^ p significantly larger than its ∆ t ^ s . Its staggering convergence produces an immense sense of tension resolution with this transition.
(7) A final landmark that is interesting to note is at region 7, where the triad in the treble flips from the 1 st inversion to the 2 nd inversion while the chord remains unchanged. Notice that this brings about no change to both T sub and ∆ t ^ while ∆ ∆ t ^ = 0 . This, again, shows how subharmonic analysis agrees with music theory where, despite the change of notes, harmony remains the same at this point.

In this section, we have seen how, even in the context of transitional harmony, perceptual tensions and resolutions in a song may be visualized in its subharmonic modulation. We will move on to see how well numerical values computed with such modulations verify against listening tests and chord use statistics.

5. Experiment and Results

For both stationary and transitional harmony, tensions computed from our models show strong correlations with consonance rankings and historical chord use statistics. Table 1 tabulates a summary of the results of our experiment.

Summary of correlations with consonance rankings and historical chord use.

We will explain each of these results in detail in the following subsections.

5.1. Stationary Harmony

For stationary harmony, we take the overall tension of a chord to be a simple weighted sum of T ∆ f and T ∆ t

where T ∆ f ∣∆ t is overall tension, T ∆ f and T ∆ t are taken to represent the tensions contributed by interharmonic and subharmonic modulations, respectively (normalized by linearly scaling to fit between 0 and 1), and w i and w s are their weights, or summing coefficients respectively, where w i + w s = 1 and 0.61 and 0.39 are found to provide a good distribution.

We use a simple estimate of T ∆ f , taking

where C 1 ( ∆ f ^ ) and C 2 ( ∆ f ^ ) are a tally of interharmonic modulations (given by ( 10 )). By visual inspection of the interharmonic plot, regions of dissonance are defined by r lower = 0.95 and r upper = 1.1 for C 1 ( ∆ f ^ ) and r lower = 1.5 and r upper = 2.8 for C 1 ( ∆ f ^ ) .

For T ∆ t , we use ∆ t ~ 2 , where ∆ t ~ is given by ( 21 ) preemphasized with c = 2.1 across a range of m = 5. (A preemphasis of just over 2 provided the sufficient discrimination without driving data into saturation. A broad range of m -values are suitable but we settled on a smaller value of 5 for computational simplicity.)

Numerous previous authors have performed notable work for stationary harmony both within and outside the psychophysical context [ 8 , 12 , 13 , 18 , 21 – 25 , 43 , 53 , 62 – 64 ]. For dyads (intervals, or two-note chords) and triads (three-note chords), we the use precollated information in Tables 2–5 from Stolzenburg [ 43 ] for comparison. Dyads (intervals) are compared against the results of an average across 7 notable studies collated by Schwartz et al. [ 54 ] on a ranking of 12 chords. Stolzenburg adds the unison to Schwartz's list, which he reasonably assumes to be the most consonant, hence, we have appropriately included it as well. Triads are compared to results from an experiment by Johnson-Laird, Kang, and Leong [ 13 ] as cited in Stolzenburg [ 43 ]. For consistency with Stolzenburg's statistics in the comparison, these were first converted to ordinal rankings before computing the correlation as practised by Stolzenburg [ 43 ]. Table 2 lists our correlations for dyads and triads in stationary harmony against known relevant work as taken from Stolzenburg's [ 43 ]. A detailed tabulation of all available values for each chord is provided in the appendix.

Proposed and existing correlates of stationary harmony.

∗ Raw Value was used for Dyads and Degree was used for Triads.

† Fotlyn, 2012, as cited in [ 43 ]

‡ as cited in [ 43 ]

$ Dyads from [ 64 ] and Triads from Hofmann-Engl, 2004, both as cited in [ 43 ]

|| Brefeld, 2005, as cited in [ 43 ]

¶ Dyads from [ 23 ] and Triads from Hutchinson & Knopoff, 1979, both as cited in [ 43 ]

# Euler, 1739, as cited in [ 43 ]

5.2. Transitional Harmony

For transitional harmony, ∆∆ t from ( 22 ) is suitable for hand-computation of transitional harmony across individual locations of succeeding common subharmonics, ∆ t s , across the soundscape. While this is advantageous for visualizing individual complications and resolutions at multiple locations across the tensional soundscape, it requires manual identification of a modal ∆ t s for every transition which can be ambiguous for particularly discordant harmonies. For a consistent programmatic approach with larger datasets, we take the measure of overall ∆∆ t of a transition defined by

where ∆ ∆ t ~ is representative of overall tension resolved, ∆ ∆ t ^ j , ∆ t s , j , and T sub , j refer to individual candidates of ∆ ∆ t ^ , ∆ t s , and T sub , respectively, N is the range of nodes considered, j iterates through all relevant common subharmonics of the succeeding chord, ∆ T sub denotes the distance between two adjacent T sub , j , Σ j =1, ∀∆ t s , j <(1/2)∆ T sub N denotes summing across all values of 1 < j < N wherever ∆ t s , j is less than half the distance between the adjacent T sub , j on either side, n is the number of nodes summed, and c is the preemphasis as explained with ( 21 ).

This effectively computes the preemphasized, weighted, and compensated mean ∆∆ t across all eligible common subharmonics within a range of N for a given transition. T sub weights down larger subharmonics which are less significant according to the theory. (It is a reciprocal as opposed to ( 21 ) because greater pleasure is associated with larger tension released.) ∆ t s , j compensates for the fact that, apart from tension resolution alone, stationary consonance also affects one's preference for the succeeding chord. ∆ t s , j < (1/2)∆ T sub , j effectively sets the criterion for a node to be considered a common subharmonic. In our experiments, we set N = 9. (A broad range of N will work, but we choose a smaller value for computational simplicity. Larger values may be required with larger range or dataset size.) In consideration of divergent transitions in the dataset, we set c = 1 (no preemphasis) because divergent transitions have negative ∆∆ t which can be distorted by preemphasis.

With transitional harmony, conducting an accurate listening test is less straightforward. Rather than attempting to acquire a small number of fresh unproven opinions, it is reasonable to use statistics from a large number of well-esteemed premade decisions. A simple way to measure how well numerical values of subharmonic transition agree with the music theorists' school is to compare them with statistics of an expert music theorist's chord use. Capturing chord-use statistics from music score is again, however, a labor-intensive process requiring domain expertise [ 46 , 47 , 74 ]. Details such as melody-harmony discrimination, transition onset, and root ambiguity (e.g., Dm 7 /F versus F 6 ) are often not precisely defined in a song. We find the largest relevant data readily available that also meets chord-spelling precision requirements in Tymoczko's Study on the Origins of Harmonic Tonality [ 45 ]. In this study, Tymoczko interpreted and recorded the statistics of 11,000 chord transitions from Palestrina's [ 75 ] corpus. Palestrina was highly regarded for his style of harmony by Helmholtz himself [ 76 ]. He is widely considered amongst music theorists to be the pinnacle of contrapuntal harmony [ 77 ].

Table 3 lists ∆ ∆ t ~ against frequencies of occurrence for each of the 17 most frequently used chords that follow V as read-off Tymoczko [ 45 ]'s chord tendency histogram. C, D, X↑, and X↓ indicate the convergence type of the progression. Just intonation was used as being opposed to equal temperament in this case to be consistent with Palestrina.

Tabulation of ∆ ∆ t ~ for chords that most commonly follow V against Palestrina's chord tendencies as cited in [ 45 ].

∗ States of convergence:

C denotes convergence of ∆ t ^ .

D denotes divergence of ∆ t ^ .

X↑ denotes escalating excursion of ∆ t ^ .

X↓ denotes descending excursion of ∆ t ^ .

† In percent, as read off the histogram of chord tendencies from [ 45 ] computed over a dataset of 11000 chords from Palestrina.

Their correlations are listed in Table 4 . ∆ ∆ t ~ shows a significantly strong positive correlation of 0.903 with Palestrina's chord tendencies in general. It is close to perfect at 0.996 for resolutions since the programmatic version of the model was designed with resolutions in mind. Complications may be interpreted as the negative release of tension. Even though a large number of contributing ∆ ∆ t ^ j are negative, only one negative ∆ ∆ t ~ can be seen in the table due to the influence of nonnegative candidates. Nevertheless, ∆ ∆ t ~ shows a strong negative correlation of -0.761 with [ 45 ] for complications (agreeing with the fact that this resolution is negative). As earlier explained, with excursions the perception of a succeeding chord is also influenced by the rising or falling of parallel melodies. Unfortunately, descending excursions were insufficiently popular in Palestrina and only V-IV was being tallied. For escalating excursions, however, we have enough statistics to compute a correlation of 0.863. We have also computed the correlation across all other chords separately from complications (because, as explained, they correlate negatively) to be 0.970.

Tabulation of correlations between ∆ ∆ t ~ and Palestrina's chord use statistics as collated in [ 45 ]. Correlations are listed in the top row with corresponding significance in brackets below.

∗ Our model is designed to compute tension release in resolution.

† Complications in music may be interpreted as negative tension resolutions; hence, correlation seen is negative.

‡ Excursions usually encompass tension release; however, apart from resolution alone, the perception of succeeding chords are also influenced by the rising or falling of parallel melodies.

§ Apart from the descending excursions leading to IV, insufficient other descending transitions are recorded to compute its correlation.

6. Discussion

Addressing the Fundamental Questions of Psychoacoustic Harmony . At this point, let us address the fundamental questions of psychoacoustic harmony as promised at the start of this paper in the context of subharmonic modulations. We will begin with question 2 and leave the first question for the last.

(2) We discussed the definition and explanation of stationary harmony, i.e., what sounds good and why , or, mathematically, to quantify ε { X n }, where ε {} denotes the harmonious effect of and X n represents chord n .
With large subharmonic tension being perceived as dissonance while small subharmonic modulations are perceived as consonance, the aesthetics of a chord may be visualized in the subharmonic tension acting on its shortest common subharmonics. Mathematically, they are inversely related. As described by ( 19 ), ε X ∝ 1 / ∆ t ^ .
(3) We have the definition and explanation of transitional harmony, i.e., what sounds good , why , and when , or, mathematically, to quantify ε { X 1 → X 2 }, where ‘→' denotes transition from one chord to another.
The aesthetics of a chord transition may be visualized in the release of subharmonic tension at the shortest common subharmonics of the succeeding chord. As explained in ( 22 ) and indicated by the arrows in Figure 12 , this refers to the transition to the shortest common subharmonics of the succeeding chord from the nearest subharmonics of the preceding chord. Thus, resolution (tension release) in a chord transition is perceived in the convergence of ∆ t ^ (where ∆ ∆ t ^ > 0 ) while what we call complication (build-up of tension or negative resolution) is seen in its divergence (where ∆ ∆ t ^ < 0 ). Mathematically, as described by ( 24 ), ε X 1 → X 2 ∝ ∆ ∆ t ^ X 1 → X 2 .
A chord that sounds better than another out of context can sound worse than being in context [ 42 ]. Given ε { X 2 } > ε { X 3 } this shows that ε { X 1 → X 2 } < ε { X 1 → X 3 }
With reference to ( 22 ) and our answer in question 3, since our ears identify the subharmonics of preceding notes that correspond to the succeeding common subharmonic, transitional harmony is contextual. Continuing from our answer to question 4a, we take D 7 to be D 7 = { c 4 , d 4 , f # 4 , a 4 } . The transitional subharmonic resolution (tension resolution) for D 7 → G and D 7 → Am 7 may be computed by ( 22 ) to be ∆ ∆ t ^ D 7 → G = 11.421 % and ∆ ∆ t ^ D 7 → A m 7 = 4.540 % , respectively. Thus, ε { D 7 → G } > ε { D 7 → Am 7 } despite the fact that ε { E 7 → G } < ε { E 7 → Am 7 }.
(5) phenomenon that the transition from a low-tension chord to a high-tension one can still bring about the effect of tension release (resolution). Given ε { X 1 } < ε { X 2 } this shows that ε { X 1 → X 2 } > 0.
The answer to this is in the independence of stationary and transitional tension, as established in our answer to Question 4a .
Taking E = { b 3 , e 4 , g # 4 } and Am 7 = { a 3 , c 4 , e 4 , g 4 , a 4 } , the transitional subharmonic resolution (tension resolution) for E → Am 7 may be computed by ( 22 ) to be ∆ ∆ t ^ E → A m 7 = 4.323 % . The stationary subharmonic tension for E and Am 7 may be computed by ( 18 ) to be ∆ t ^ E = 0.902 % and ∆ t ^ A m 7 = 6.849 % , respectively. Hence, ε { E → Am 7 } > 0 despite the fact that ε { Am 7 } < ε { E }.
(6) There is the phenomenon that the effect of harmony is greater than the sum of its parts [ 18 , 60 ]. ε { x 1 + x 2 + x 3 } ≫ ε { x 1 } + ε { x 2 } + ε { x 3 }
Apart from certain exceptions with rational intonation and octaves, the stationary tension of any combination of unique notes is observed to be larger than zero on the subharmonic plot. Hence, ∆ t ^ x 1 + x 2 + x 3 > 0 . Likewise, the stationary tension of each note on its own is observed to be zero on the subharmonic plot. Hence, ∆ t ^ x 1 = 0 , ∆ t ^ x 2 = 0 , and ∆ t ^ x 3 = 0 for all x 1 , x 2 , and x 3 within musical range. Thus, by ( 19 ), ε { x 1 + x 2 + x 3 } ≫ 0 , whereas by ( 20 ) ε { x 1 } = 0, ε { x 2 } = 0, ε { x 3 } = 0 , and ε { x 1 } + ε { x 2 } + ε { x 3 } = 0 . Therefore, ε { x 1 + x 2 + x 3 } ≫ ε { x 1 } + ε { x 2 } + ε { x 3 }.

7. Conclusion

In this paper the notion of interharmonic and subharmonic modulations was proposed as a psychophysical basis for both stationary and transitional harmony.

In the domain of stationary harmony (tension in chord sonorities), this work presents subharmonic modulations as an integral complement to interharmonic modulations and shows how perceptual tensions [ 18 , 36 , 58 , 59 ] and consonances [ 17 , 19 , 44 ] may be visualized through which.

In the domain of transitional harmony (resolution in chord progression), it unlocks the means of physically identifying, quantizing, and, thus, verifying perceptual resolutions and complications [ 18 , 42 ] in acoustic features that have until now remained abstract and nontangible.

This work can be seen to bind prevailing psychoacoustic schools into a single theory. The Helmholtz school [ 3 , 8 , 12 – 17 , 19 , 20 , 23 ] is represented by the interharmonic ∆ f in ( 11 ). The Pythagorean school [ 5 , 6 , 11 ] generally seeks small values of integer k i in ( 15 ) and ( 16 ) while requiring Δ t i to be zero. Taking this further, if Δ t i is ignored, f sub in ( 15 ) would then correspond to the fusion tone in Stumpf's tonal fusion theory [ 3 , 30 ]. Euler's gradus suavitatis [ 11 ] graded the goodness of k i -combinations for Δ t i = 0. The adoption of 12-tone equal temperament [ 12 , 33 , 34 ] sought to evenly distribute interharmonic ∆ f in ( 11 ). Since the aforementioned conditions may be generalized by a central theory of modulations across adjacent (interharmonic) and distant (subharmonic) sinusoids which stems from ( 3 ), this effectively integrates them into a general theory.

Computed values correlate strongly with perception and harmony-use statistics for both stationary (tension) and transitional (resolution) harmony.

Finally, this paper presented a psychoacoustic solution to the five fundamental questions of harmony.

Acknowledgments

Paul would like to thank Dr. Nancy Chen for lengthy initial discussions on the manner of approach of this cross-disciplinary topic towards nonmusical readers; A/Prof. Eng Siong Chng for his tireless mentorship and motivation, as well as his review on the writing style of this paper; Prof. Dmitri Tymoczko for his kind correspondence over details of his work cited here; and Dawn Chan without whom this work would have been completed earlier, but the journey towards its completion would have had been far less meaningful.

Conflicts of Interest

The authors declare no conflicts of financial interest.

Supplementary Materials

Supplementary 1.

Supplementary Figure S1: Sinusoidal Summation across 8 Amplitude Ratios. Acos⁡ ω 1 t + Bcos⁡ ω 2 t for various values of B normalized to A=1.

Supplementary 2

Supplementary Table S1: Correlation for Intervals. There is tabulation of ordinal ranking of dyads (intervals) using T ∆f∣∆t against available rankings collated in [ 43 ].

Supplementary 3

Supplementary Table S2: Correlation for Triads. There is tabulation of ordinal ranking of triads using T ∆f∣∆t against available rankings collated in [ 43 ].

Supplementary 4

Supplementary Audio S1: Low-Frequency Modulation. There is audio example of consonant low-frequency modulation with f - = 440 H z and ∆ f = 0.5 Hz .

Supplementary 5

Supplementary Audio S2: Beating Frequency. There is audio example of dissonant high-frequency modulation with f - = 440 H z and ∆ f = 70 Hz .

Supplementary 6

Supplementary Video S1: Low versus High Subharmonic Tension. There is video example comparing subharmonic wave deformation in low tension C chord against high tension Cm 7 chord.

Supplementary 7

Supplementary Video S2: Stationary Tensions in Pachelbel's Canon. We visualize stationary harmony with subharmonic tension in Pachelbel's Canon [ 70 ].

Supplementary 8

Supplementary Video S3: Transitional Tensions in Moonlight Sonata. We visualize transitional harmony with subharmonic tension in Beethoven's Moonlight Sonata [ 71 ].

Sound, Harmony, Melody, Rhythm and Growth in Music Essay

The purpose of this paper is to reflect on the idea of categories that assist people in listening to music. It is unusual for me to use these categories in everyday life as I usually think of them as something purely theoretical. However, reading the text about these five elements showed me that being aware of them could make listening to music even more exciting than it usually is.

My approach to listening to music is mainly emotional and very subjective and using SHMRG is helpful to broaden this experience. I rarely think of what exactly I like about musical pieces or how the composer wanted the music to influence me. The questions for SHMRG categories are aimed at not only understanding the music better. They help to see the composer’s intent behind using a certain rhythm, sound texture, or form (Wilson). It is interesting to see how these SHMRG elements affect my perception of music and associations and the emotional response they provoke.

Another point to reflect on is what exactly in these categories affects my music preferences. As I said before, my experience with listening to music is based on a subjective approach. It seems reasonable to consider what exactly makes me prefer one piece of music to another. I wonder how much my selection of music depends on dynamics, tonality, shape, and motion. Understanding these categories will help me find more music to my taste.

In conclusion, reading the text about SHMRG categories made me realize that learning these elements helps me enjoy listening to music more. This knowledge is useful for understanding the composer’s message more clearly. It provokes a certain level of self-awareness in experience with music as well. Knowing how these categories affect me helps me learn more about my own music preferences.

Wilson, Frances. “ The Composer’s Intentions? ” Interlude , Web.

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"Sound, Harmony, Melody, Rhythm and Growth in Music." IvyPanda , 15 Feb. 2024, ivypanda.com/essays/sound-harmony-melody-rhythm-and-growth-in-music/.

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IvyPanda . 2024. "Sound, Harmony, Melody, Rhythm and Growth in Music." February 15, 2024. https://ivypanda.com/essays/sound-harmony-melody-rhythm-and-growth-in-music/.

1. IvyPanda . "Sound, Harmony, Melody, Rhythm and Growth in Music." February 15, 2024. https://ivypanda.com/essays/sound-harmony-melody-rhythm-and-growth-in-music/.

Bibliography

IvyPanda . "Sound, Harmony, Melody, Rhythm and Growth in Music." February 15, 2024. https://ivypanda.com/essays/sound-harmony-melody-rhythm-and-growth-in-music/.

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Harmony in Music

Updated 25 October 2023

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Category Music

The Harmony and Cultural Values of Classical Music

The harmony created by musical instruments is fundamental to shifting the preference of the listener positively or negatively. The musical sounds and words used in developing the music form the culture relied upon by the artists dealing in the practice. Classical music, my choice of culture, originated from the traditional art practiced by people of western descent. Despite the passage of time from the time of invention to the current times, classical music retained a culture of moral and ethical representation of ideas throughout the tune. A comparison between the culture and others in society today, such as the hip-hop culture, reveals two distinct ideologies with one marred with violence and promotion of aggressive practices. Such cultures tend to mislead the traits of the young generation, which copies most of the attributes seen in the media. I identify with the classical music culture due to the promotion of moral and ethical ideologies, which are imperative in the current generation.

The Focus on Message Delivery in Classical Music

In classical music culture, the focus is on message delivery in the most audible format possible. For example, classical music does not incorporate noisy sounds from the instruments (Holmes 56). The voice of the singer is always at the top with the accompanying tools reinforcing the smooth harmony of the singer. The music is slow and audible, hence fit for a variety of audience. My preference of the culture emanates from the clarity of the messages presented in the artistic works. For example, some of the cultures in the music industry tend to use vulgar language that is not fit for all persons. In the song, Old Money by Lana Del Rey, the coordination of the instruments is eloquent, and the diction is clear (Alaa). Therefore, the culture upholds the cultural values by using ethical words that are acceptable to the entire community. I support cultures that motivate the young generation to moral values instead of wrong words and actions as evident in cultures such as hip-hop.

The Use of Sonata Form in Classical Music

The classical music culture uses the sonata form in the implementation of the design. The sonata incorporates a single soloist with the reinforcement of the piano. The plan is unique to the western culture without influence from other cultures with different backgrounds. The maintenance of the discipline over the years communicates the value of maintaining the lifestyle without changes that might dilute the practice. For example, the song by Lana Del Rey hit the airwaves in the year 2014. However, the song uses the same sonata as the original version of the song played in 1968. Therefore, the discipline of the song applies in both the message communicated as well as the maintenance of the traditional aspects of the culture. The concept captivates my mind intensely from the fact that the music appreciates the traditional values behind the invention of the music. Currently, modernization is the primary reason behind the loss of cultural values (Zonggui 202). My appreciation of the culture is through the maintenance of the original values making the music very entertaining to listen.

The Importance of Homophonic Culture in Classical Music

Homophonic culture in classical music allows the audience to relate well with the rising and falling intonations (Hoffer 110). At one point, the tone in the music is high while the other moments characterize low tones. Accurately, the rising and falling intonation appear in successive intervals creating a rhythmical tune. Without the high and low tones, the music would fall short of the expectation of the crowd. The song, Old Money by Lana Del Rey, starts on a low sound that rises as the music progresses. The change in tone communicates to the audience that summary of life. I can relate to the fact that life is full of challenges, which represent the low tone. The solution to the problems present the high tones characterized as happy moments. However, the culture reminds the audience that the challenges and successes make life worth living. Some cultures fail to observe tonal variation leading to the composition of songs with a constant tone, which tends to be boring.

The Coordination and Unity in Classical Music Culture

Every culture possesses a distinct quality that differentiates it from the others. However, some cultures end up borrowing tips from other regions diluting the originality. The amount of coordination in classical music requires professional usage of instruments such as symphony and serenade for quality output (Sly 157). Despite the invention of modern musical instruments that can produce similar sounds, such as the piano, the artists invest in the original instruments. Coordinating the entire group is tiresome. However, the output is worth the product. The classical culture seeks to communicate the value of working in unity. As much as the artists can produce the song with a limited number of artists, the songs sound better with many performers in the instruments section. Lana Del Rey is a soloist; however, many artists boost the song from the instruments section. I enjoy the coordination of the team from the perception that unity produces better results as opposed to working individually. The classical musical culture promotes integration in society and discourages negative attributes such as jealousy and hatred.

The Moral and Ethical Aspects of Classical Music

The society today faces so many challenges especially in bringing up the young children. The youngsters tend to copy attributes seen in the media through dress codes, languages spoken, and lifestyles. Desirable cultures in these generations are those that instill positive behaviors in the young people. Such practices include the use of decent language, proper dressing, and respect for the elderly. The classical music culture possesses such attributes making it my best. For example, the song uses a smooth rhythm with a clear message as demonstrated by the audible words. Despite the technological invention of musical instruments, the culture retains originality through the instrumentation part. Therefore, the culture holds a firm stand in maintaining the values and ensuring that the modernization processes do not alter the originality of the art. Thus, the ethical and moral aspects promoted by the culture in classical music are highly desirable. The entire generation would enjoy the art and learn many values that are important for a moral population.

Works Cited

Alaa, Mahmoud. "Lana Del Rey - Old Money [Ultraviolence Album]." YouTube, 17 June 2014, www.youtube.com/watch?v=0MaAPzg_YbQ.

Hoffer, Charles R. Music listening today. Belmont, CA: Thomson/Schirmer, 2009. Print.

Holmes, Thom. The Routledge Guide to Music Technology. Hoboken: Taylor and Francis, 2013. Print.

Sly, Gordon Cameron, ed. Keys to the drama: nine perspectives on sonata forms. Ashgate Publishing, Ltd., 2009.

Zonggui, Li. Between tradition and modernity : philosophical reflections on the modernization of Chinese culture. Oxford: Chartridge Books Oxford, 2014. Print.

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Harmony in Popular Music: the Lyrics of ‘Soul Meets Body’

This essay about “Soul Meets Body” by Death Cab for Cutie explores the song’s lyrical themes of love, connection, and the intertwining of the spiritual and physical realms. It examines the longing expressed in the lyrics for a place where soul and body unite, reflecting on the human desire for harmony within oneself and in relationships. The piece also touches on the imagery used in the song to convey hope that love can transcend the mundane, and it considers the contemplation of mortality and life’s impermanence. Highlighting the song’s exploration of complex emotional landscapes, the essay underscores the power of music to articulate the depths of human experience, making “Soul Meets Body” a poignant meditation on the essence of being human and the search for meaning and beauty in a transient world.

How it works

In the landscape of modern music, few songs capture the intricate dance between the ethereal and the tangible as poignantly as “Soul Meets Body” by Death Cab for Cutie. This piece delves into the lyrical content of the song, exploring its themes of connection, love, and transcendence, which have resonated with audiences worldwide. The song, with its haunting melody and introspective lyrics, invites listeners into a reflective journey on the nature of the soul’s relationship with the physical world.

At the heart of “Soul Meets Body,” there’s a profound inquiry into what it means to truly connect with another being.

The lyrics, “I want to live where soul meets body,” speak to a longing for a place where the spiritual and physical realms intertwine seamlessly. This line serves as a metaphorical crossroads, suggesting a yearning for unity not just within the context of a relationship but also within oneself. It evokes the universal quest for harmony between our inner and outer worlds, a theme that’s both timeless and deeply personal.

Moreover, the song navigates the complexities of love and existence through its poetic narrative. The imagery of “a city by the sea” and the desire to “lay my skin beside the sea” taps into the human inclination to seek solace in nature and in one another. These lyrics reflect a deep-seated hope that love can transcend the mundane, offering a glimpse into a realm where the soul can find peace and fulfillment. It’s this exploration of love as a force that can elevate and transform that lends the song its emotional depth and resonance.

Another layer of “Soul Meets Body” is its contemplation on mortality and the impermanence of life. The acknowledgment that “I do believe it’s true that there are roads left in both of our shoes” is a poetic acceptance of life’s journey, with its inherent uncertainties and undiscovered paths. This recognition of life’s fleeting nature and the finite time we have to forge meaningful connections adds a poignant undercurrent to the song’s narrative. It challenges listeners to consider the legacy of love and intention we leave behind, urging a conscious engagement with the world and the people in it.

The enduring appeal of “Soul Meets Body” lies in its ability to articulate complex emotional landscapes with eloquence and authenticity. Its lyrics serve as a canvas for reflection, offering insights into the human condition and the myriad ways in which our souls seek connection, meaning, and beauty in a transient world. The song stands as a testament to the power of music to explore and express the depths of human experience, resonating with listeners who find echoes of their own stories within its verses.

In conclusion, “Soul Meets Body” is more than a song; it’s a lyrical meditation on the profound intersections between the soul and the physical world. Through its exploration of love, connection, and the quest for harmony, it captures the essence of what it means to be human. The song’s enduring popularity underscores its relevance and its ability to touch the hearts of those who listen, inviting them on a journey of introspection and discovery. In a world where the noise of existence can often drown out the whispers of the soul, “Soul Meets Body” offers a moment of clarity and connection, reminding us of the beauty that arises when soul indeed meets body.

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Essay on Music for Students and Children

500+ words essay on music.

Music is a vital part of different moments of human life. It spreads happiness and joy in a person’s life. Music is the soul of life and gives immense peace to us. In the words of William Shakespeare, “If music is the food of love, play on, Give me excess of it; that surfeiting, The appetite may sicken, and so die.” Thus, Music helps us in connecting with our souls or real self.

What is Music?

Music is a pleasant sound which is a combination of melodies and harmony and which soothes you. Music may also refer to the art of composing such pleasant sounds with the help of the various musical instruments. A person who knows music is a Musician.

The music consists of Sargam, Ragas, Taals, etc. Music is not only what is composed of men but also which exists in nature. Have you ever heard the sound of a waterfall or a flowing river ? Could you hear music there? Thus, everything in harmony has music. Here, I would like to quote a line by Wolfgang Amadeus Mozart, one of the greatest musicians, “The music is not in the notes, but in the silence between.”

Importance of Music:

Music has great qualities of healing a person emotionally and mentally. Music is a form of meditation. While composing or listening music ones tends to forget all his worries, sorrows and pains. But, in order to appreciate good music, we need to cultivate our musical taste. It can be cited that in the Dwapar Yug, the Gopis would get mesmerized with the music that flowed from Lord Krishna’s flute. They would surrender themselves to Him. Also, the research has proved that the plants which hear the Music grow at a faster rate in comparison to the others.

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Magical Powers of Music:

It has the power to cure diseases such as anxiety, depression, insomnia, etc. The power of Music can be testified by the legends about Tansen of his bringing the rains by singing Raag Megh Malhar and lighting lamps by Raga Deepak. It also helps in improving the concentration and is thus of great help to the students.

Conclusion:

Music is the essence of life. Everything that has rhythm has music. Our breathing also has a rhythm. Thus, we can say that there is music in every human being or a living creature. Music has the ability to convey all sorts of emotions to people. Music is also a very powerful means to connect with God. We can conclude that Music is the purest form of worship of God and to connect with our soul.

FAQs on Essay on Music:

Q.1. Why is Music known as the Universal Language?

Ans.1. Music is known as the Universal language because it knows no boundaries. It flows freely beyond the barriers of language, religion, country, etc. Anybody can enjoy music irrespective of his age.

Q.2. What are the various styles of Music in India?

Ans.2. India is a country of diversities. Thus, it has numerous styles of music. Some of them are Classical, Pop, Ghazals, Bhajans, Carnatic, Folk, Khyal, Thumri, Qawwali, Bhangra, Drupad, Dadra, Dhamar, Bandish, Baithak Gana, Sufi, Indo Jazz, Odissi, Tarana, Sugama Sangeet, Bhavageet, etc.

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What Is Harmony In Music? Complete Guide
The Definition of Harmony. In simple terms, harmony is what occurs when more than one note is played or sung at the same time. This can be as an interval (two notes, also called a dyad), or chords of three or more notes. Check out our posts on intervals and chords if you want to learn more about them.. One way to think about harmony is that it deals with the 'vertical' aspects of music ...
Music Harmony Studying
Introduction. Music harmony is the art of simultaneously employing pitches and chords in the enrichment of sound. The study of music harmony, therefore, entails unveiling the intricate characteristics of chords, the way they are built and the principles of their connection. We will write a custom essay on your topic. 809 writers online.
Music 101: What Is Harmony and How Is It Used in Music?
Music consists of three main elements—melody, rhythm, and harmony. While the first two are typically accountable for making a piece of music memorable—think of the opening motif of Beethoven's Symphony No. 5, or Timbaland's synth lick on the Jay-Z song "Dirt Off Your Shoulder"—it's the third element, harmony, that can elevate a piece from common and predictable to challenging ...
Performing a harmonic analysis
Performing a harmonic analysis. Analyzing harmony in a piece or passage of music involves more than labeling chords. Even the most basic analysis also involves interpreting the way that specific chords and progressions function within a broader context. Ultimately, no analysis is complete until individual musical elements are interpreted in light of the work as a whole and the historical ...
Harmony
harmony, in music, the sound of two or more notes heard simultaneously.In practice, this broad definition can also include some instances of notes sounded one after the other. If the consecutively sounded notes call to mind the notes of a familiar chord (a group of notes sounded together), the ear creates its own simultaneity in the same way that the eye perceives movement in a motion picture.
Understanding harmony in music: a beginner's guide
Harmony provides richness and texture to music, and it plays a crucial role in shaping the emotional and expressive qualities of a composition. Let's look at a basic form of harmonization by stacking notes on top of this C major scale: NativeInstruments · 01 C-major Scale. C major scale.
Harmonic Analysis
Harmonic Analysis with Decoration. When we analyse chromatic music, we need to begin by separating the layers of music (bass, melody and any middle parts), to work out a functional harmonic structure.We can then determine what sort of decoration, chromatic or otherwise, has been used.+ In most music, the lower parts form the harmony and the upper parts contain the melody and decoration notes.
What is Harmony in Music? Our Beginner's Guide
A harmony could be from the same instrument, for example, a chord on the piano, or it could be from a group of instruments or voices, such as a choir. The following could be considered an example of music harmony: Chords on a guitar in rock music. The guitarist will strike multiple strings at once, which creates harmony.
Harmony
Harmony is the most emphasized and most highly developed element in Western music, and can be the subject of an entire course on music theory. In music, harmony is the use of simultaneous pitches (tones, notes), or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that ...
Harmony in Music
What is Harmony? Harmony, in music, consists of two or more notes being heard in unison and usually have a pleasing effect on the listener. These notes can be played by an instrument or sung by ...
Harmony in Chopin
The Enigmatic Narrative of Chopin's C-Sharp Minor Prelude," in Engaging Music: Essays in Music Analysis, ed. Stein, D., Oxford University Press, 2005, pp. 236 - 252 Spicer , M. J. , " Root Versus Linear Analysis of Chromaticism: A Comparative Study of Selected Excerpts from the Oeuvres of Chopin ," College Music Symposium 36 ( 1996 ...
Writing music analysis for non-musicians & music majors
Step 8: Outline the essay. Now that you know the music, the composer, the context, and the specific musical elements of the piece, it's time to start outlining what you're going to say about this music. One common method for presenting music is to start wide and zoom in with every paragraph.
How to Analyze Harmony in Music
How to undertake a roman numeral chord analysis of a piece of music. Using a short movement by Schumann this music theory lesson explains how to read the key...
Music And Harmony In Music
Harmony is a magic compare to other elements of music. The tonal-gravitational forces for harmony are more complex and powerful than the melody. It contributes to the effect of the motion in music and it allows the component to manipulate the human emotion. Besides, harmony is music coming together with two or more sound to make effect and all ...
A Corpus Analysis of Harmony in Country Music
As decades of scholarship have shown, harmony in contemporary Western popular music often eschews the conventions of common-practice-era European art music. 1 But while the conventions of harmony in common-practice music may be well-established, it is still unclear what the conventions of harmony might be (if any) in contemporary Western popular music. 2 Part of the difficulty arguably stems ...
The Science of Harmony: A Psychophysical Basis for Perceptual Tensions
1. Introduction. Even though it is one of the most important components in music, and possibly the most widely studied [], the definition of harmony differs vastly across time, genre, and individuals, reflecting how little is understood about it [2, 3].There are three aspects to the complete understanding of our perception of harmony, which we will, for brevity, refer to as what, why, and when.
Sound, Harmony, Melody, Rhythm and Growth in Music Essay
Need an custom research paper on Sound, Harmony, Melody, Rhythm and Growth in Music written from scratch by a professional specifically for you? 808 writers online Get Writing Help
The Importance Of Harmony In Music
The Importance Of Harmony In Music. 814 Words4 Pages. 2. Harmony-When two or more different notes are played together so as to produce a chord, it is known as harmony. The movement through the harmony is known as the progression of chords. Melody is horizontal since it is linear succession of musical notes, whereas harmony is vertical in structure.
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Understanding harmony in music: a beginner’s guide

Jump to these sections:

Tonic chords

Main aspects of harmony

Consonant vs. dissonant chords

Diatonic harmony

Non-diatonic harmony

Atonal harmony

Start using harmony to make music

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Harmony in Music - What harmony is and how to use it effectively

What is Harmony in Music?

Harmony vs Melody

How is Harmony Used in Music?

How Does Harmony Work?

Consonance and Dissonance

Close vs. Open Harmony

An Example of Music Harmony

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Melody, Harmony, and Scales

Etymology and Definitions

Historical Rules

Writing music analysis for non-musicians & music majors

What should music analysis include?

Step 1: Get to know the music

Step 2: Get to know the composer

Step 3: Put the music in context

Step 5: The Music’s Structure

Step 6: The notes

articulation

Step 7: Compositional techniques

Step 8: Outline the essay

Five-paragraph essay outline

Body paragraph #1- looking at polystylism across the entire piece and form

Body paragraph #2 – zoom in a bit more and look at an entire section of a stylistic change

Body paragraph #3 – zoom in and look at the notes, articulations, orchestration, voice leading of the moment of change

Conclusion – draw conclusions and say something interesting

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A Corpus Analysis of Harmony in Country Music

Introduction

Acknowledgments

Appendix A Sources for the “NN 200” Meta-List of Greatest Country Songs

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The Science of Harmony: A Psychophysical Basis for Perceptual Tensions and Resolutions in Music

Minghui Dong

Associated Data

1. Introduction

1.1. Background

2. A Universal Theory of Harmony

2.1. Modulations in Sinusoidal Summation

3. Interharmonic Modulations

3.1. Beating Frequencies and Low-Frequency Modulations

3.2. Perceptual Responses across the ∆ f - f - Feature Space

3.3. Intervals and Second-Order Modulations on the ∆ f - f - Feature Space

4. Subharmonic Modulations

4.1. Subharmonic Modulations in Stationary Harmony

4.2. Subharmonic Modulations in Transitional Harmony

5. Experiment and Results

5.1. Stationary Harmony

5.2. Transitional Harmony

6. Discussion

7. Conclusion