Category Archives: Music Theories

What Musicians Do

Choosing small groups of sounds and placing them in time is the simplest description I can think of for what musicians do.

Every sound has a set of pitches (very rarely a set of one).

The total number of perceptible pitch steps in the average (very subjective) range of human hearing, 16-16,000 Hz, is about 1,400 (the total number of notes in the equal-tempered scale over the same range is 120 (a piano has 88 -the range of the piano is 27.5 to 4186 Hz)), so even a musician “playing every note” is using a small group of perceptible pitches).

Every sound has what is generally called timbre (which despite rigorous work by numerous highly intelligent people remains “the psychoacoustician’s multidimensional wastebasket category for everything that cannot be labeled pitch or loudness” (W. Dixon Ward, Psychoacoustics, 1965)

Every sound has loudness (amplitude).  Loudness is variable, subject to the duration of the sound and relative to its proximity.

Every sound occurs in time: attacks, has duration, and decays.

Sounds interact with other sounds and with the spaces in which they occur forming localized soundworlds.  Once a sound enters the soundworld, it is subject to and integrated with the influences of its environment.  Except under rigorously controlled laboratory conditions, no sound has a separate identity, from the instant it is made it is a component of the soundworld.

A musician participates in and influences a localized soundworld by choosing small groups of sounds and placing them in time (so does a passing driver —makers of music are just being more deliberate about it).


Origins of western “music theory”

There is no theory, you just have to listen.  –Claude Debussy

There is a long history in the westworld of authoritarians fearing music and imposing constraints on it in the interests of controlling our behavior. Here is some of what Plato (in The Republic) had to say about music at the dawn of western civilization (c.400 BC).

These two harmonies I ask you to leave; the strain of necessity and the strain of freedom, the strain of the unfortunate and the strain of the fortunate, the strain of courage, and the strain of temperance; these, I say, leave. . . 

Then, I said, if these and these only are to be used in our songs and melodies, we shall not want multiplicity of strings or a panharmonic scale?

I suppose not.

Then we shall not maintain the artificers of lyres with three corners and complex scales, or the makers of any other many-stringed, curiously harmonized instruments?

Certainly not.

But what do you say to flute-makers and flute-players? Would you admit them into our State when you reflect that in this composite use of harmony the flute is worse than any stringed instrument; even the panharmonic music is only imitation of the flute?

Clearly not.

Then let us now finish the purgation, I said. Next in order to harmonies, rhythms will naturally follow, and they should be subject to the same rules, for we ought not to seek out complex systems of metre, and a variety of feet, but rather to discover what rhythms are the expressions of a courageous and harmonious life; and when we have found them, we shall adapt the foot and the melody to words having a like spirit, not the words to the foot and melody.  Any musical innovation is full of danger to the whole state, and ought to be prohibited. When modes of music change, the fundamental laws of the state always change with them.

This mentality has persisted among ruling elites ever since.

The medieval catholic church set up the first system of common musical practice in Europe with sets of allowable (and forbidden) intervals, modes (those used in plainsong) and meters (everything had to be in 3 to represent the trinity). More recently Nazi germany banned the performance of modern “degenerate” music (approving primarily of Beethoven, Wagner, and Bruckner) and the USSR banned everything that didn’t glorify the state and the communist party.  Until fairly recently, women were essentially excluded from having any part in it –for a while they even castrated males to avoid having women sing women’s roles.

As ludicrous and pathetic as these attempts to mold culture seem in retrospect, they haven’t been completely unsuccessful (nor were they ludicrous and pathetic to those who had to live under those regimes).  Almost all of us who consider ourselves musical are unconscious inheritors and perpetuators of ways of musical practice that have their origins in the chain of suppressive thinking running from Plato, through the Church and the 20th century totalitarians, to Richard Taruskin’s Oxford History of Western Music (pub. 2009).

Our western system of equal temperament and the major/minor system that it enables is the descendant of those two harmonies Plato was willing to allow in his republic.  Our two commonly accepted meters, the simplest possible, are almost universal in the music we hear and make.  The codification of the instruments has occurred as well (generally speaking, the instruments included in the philharmonic and taught in conservatories are they same as they were in the 19th century).

This system (which most western people think of as simply music) did not evolve naturally, it was deliberately imposed on the soundworld by generations of oligarchs with the expressed purpose of limiting our thoughts and behaviors.  Wonderful music has and will be made with it, but it’s worth remembering that, to a large extent, it was and will be made in spite of the system, not because of it.

‘Music is born free; and to win freedom is its destiny.’  -Ferruccio Busoni

a society of voices

A piece of music is a society of voices (sounds made by instruments) generally involved in working together toward the goal of delivering the immediate moment from the boredom of silence and/or ambience.


One might picture a piece of music as a room or a field or a subway car with a group of people in it each affecting the general ambience in their own way.


One might think of a piece of music as a pot on a stove in which assorted ingredients, ranging from stocks to garnishes, contribute to an aggregate unity perceptible as soup.

A society of voices expresses (metaphorically) a sociopolitical worldview.

I find it instructive to listen to music with this in mind, to imagine / project the relationships between the individual voices within the generated soundscape to one another and the whole.

Some pieces of music express obvious hierarchies with clearly defined leaders and followers.  Others express the interactions of groups of equals, sometimes in contest, sometimes in cooperation.

Every piece of music is system unto itself: metaphorically, a unique social interaction among whatever voices have gathered at a particular time under particular circumstances.

where does music come from?

Obviously, for humans, it starts with singing.  Babies sing long before they start trying to talk.

Having a sense of relationships between different pitches is as basic to us as having a sense of relationships between loud and quiet, light and dark, cold and hot, sour and sweet, hard and soft, rough and smooth, flowers and farts.

Every sound has pitch (generally several at once).  There are an infinite number of pitches. Our voices tend to make one predominant pitch at a time.  When we sing, we choose a small group of pitches and explore the relationships between them.  We make pitch shapes in time.

Choosing small groups of pitches and arranging them in time is making music.

When those babies begin talking, a disparity arises over the dominant function of the shared tool (the voice).  Language does most of its work in the left hemisphere of the brain and music does most of its work in the right hemisphere.  The relationships of pitches in time tends to become subservient to semantics, affecting the meanings of words, but not defining them.

(Here we enter Borges’ Garden of the Forking Paths about where singing stands in terms of semantics and pitch relationships: there are an infinite numbers of possibilities, all of them worthy of interest.)

Owing to that, a lot of our non-semantic musical impulses (arranging small groups of pitches in time) get transferred to our hands, detached from providing context for verbal expressions.  We choose small groups of pitches to arrange with our hands and fingers (even feet sometimes).

Very likely, this began with clapping as we sang and developed by substituting rocks or sticks for palms and recognizing that the objects had pitches and that there were sonic possibilities beyond the range of the voice alone.

There were practical reasons to make non-vocal sounds as well: drums, horns, and whistles allowed people to communicate over distance; certain sounds attracted or repelled animals.

And, most of all, we are curious and playful and have been fascinated by sounds and their relationships from the moment we were born.

Learning that we could arrange pitches in time with objects got our tool making species started on building instruments.

Using objects to generate pitched sounds sets specific limits on the sizes of pitch sets available: on flute-like instruments, there can only be as many toneholes as fingers are able to cover; on xylophone-like or dulcimer-like or instruments there are limits of arm reach; stringed instruments with necks are effectively confined to the reach of the fingers and wrists .

Whenever we build an instrument we are compelled to choose a small group of pitches for it to provide us with.  Whether our choices are based on complex fractions, religious/cosmological suppositions, acceptance of standard academic practice, the desire to replicate what we hear around us, pure accident, or simply “that sounds cool”, we are generating theories of music —none of which are intrinsically any more or less “valid” than any other one.

Small groups of pitches are called scales (or rows, or sets, or modes, or fields, or sieves, or Ragas, or Maqams, or Dastgahs, or whatever else anybody chooses to call them).

A group of four pitches is enough to sing/play “Mary Had a Little Lamb”.  Five pitches (or six. one of them is used an octave* higher) is enough for “Amazing Grace”. Five pitches (or six, the octave in use again) in a different configuration is enough for “Row, Row, Row Your Boat”.  Six pitches is enough for “Twinkle, Twinkle, Little Star”.  Six (or seven, the octave again) is enough for “Frere Jacques”.

*(An octave is the name used in the west for a pitch that is the same as another pitch, but in a different register, as when an adult sings with a child, they sing the same song at the same time, but the child’s voice is higher.  Physically speaking it is a pair of waves that have a 2-to-1 frequency relationship.)

In the western traditions from which these songs come, the small groups of pitches are sung specifically, but in many other traditions (middle eastern, asian, african, etc.) pitches are variable and the subtleties of pitch inflection are a desirable and essential musical quality.  In Javanese music, every group –Gamelan– is expected to have its own tunings which also purposefully include what western tradition would call detuning.

From the time of Pythagoras, western musical culture (seeking what it considers tonal purity) has always looked at pitch as specific and limited and from that time it has evolved a system with a single set of twelve equally spaced pitches within an octave that are used for (almost) all of its music.  There are 120 notes in the equal-tempered scale from 16 to 16,000 Hz (the approximate range of human hearing –the range of the piano is 27.5 to 4186 Hz), the total number of perceptible pitch steps by an average human from 16 to 16,000 Hz is about 1,400.

This tradition (equal temperament) does have its discontents (microtonalists) and they have evolved larger sets (19, 31, 43, et al. per octave) of precise tones (doubling down on the concept of tonal purity and expanding it to be even purer).  Technically, microtonality is defined as music using intervals smaller than those of equal temperament including those found in nonwestern musics, but it is most commonly applied to comprehensive tonal systems similar in scope but different in practice from equal temperament.

Aside from the microtonalists, another group of western discontents diverged from equal temperament.  African-americans, using the same instruments and a lot of the same theoretical elements found ways of adapting them to suit a more flexible concept of pitch in blues and jazz.

“You can play sharp on a tune, or you can play flat on a tune.”

—Ornette Coleman

To a lot of “trained” musicians that statement would express a fundamental disrespect for the idea of pitch, but to a lot of others it would express a healthy lack of acceptance of equal temperament as a comprehensive system of pitch selection.

Non-european cultures tend to treat pitch as situational and none of them developed a single set for universal use.  In indian musical tradition, for example, there are scales (ragas) considered appropriate for certain times of day and the beginning (alap) of each piece is given over to determining the pitch set used for the rest of the piece.  In some middle-eastern traditions, different pitch sets (maqams) are believed to convey or evoke different emotions.  In these traditions (and others like them), musicians develop individualized senses of pitch relations (often influenced by a particular teacher or locality) and these selections are absolutely particular to the circumstances in which they are made.

In the western tradition, pitch is pre-determined and arbitrary —a musician is either “in tune” or “out of tune” and aside from accomplishing “in-tunedness” no further thought is given to individual pitches.

That sounds terrible and foolish (and in many respects, it is —it’s like saying all sports have to be basketball, all food has to be Italian, or every car has to be a sedan), but it does have some advantages, mostly relating to efficiency:  a western flutist needs only one flute while an Iranian player of the nez will have several of them: a western band will tune up quickly (electronically most of the time) and jump right into playing while a sitarist, tambourist, and tabla player will spend several minutes establishing the pitches they’ll be using; the music of the nonwestern traditions will generally have a single set of pitches with inherent relationships that remain essentially constant throughout a piece while the music of the west has the capacity to extract and use numerous sets and a variety of relationships within a piece; nonwestern music tends (except for greatly simplified ceremonial applications) to be played by small groups of musicians while western music functions well in large orchestras and can produce thunderous crescendos; nonwestern music has different instruments, different ways of constructing pitch sets, and different names for the elements of music in different places while in western music they are all the same everywhere.

There’s nothing “wrong” with what the equal temperament system includes.  A lot of wonderful music of great diversity has been made with it.  As one system out of many, it has much to recommend it.  An enormous amount of intelligence and imagination has gone into finding a multitude of ways of using it.  But we cheat ourselves at a very basic human level when we narrow our choices of available pitch relationships to its confines.  The problem isn’t with what it includes, but what it excludes and that it excludes in the first place.

It isn’t the music we’ve made, loved, and understood that’s the problem, it’s all the music our limited methodologies have prevented us from making.

As tonally limited as the equal temperament system is, perhaps the worst thing about it is its nomenclature (see * below), a collection of unintuitive complex terms for very simple relationships.

If there were some great acoustical truth embedded in the western system, it’s universality would be greatly welcome, but what’s embedded in it is a ‘one size fits all’ pitch selection mechanism that approximates many musics while it ignores and dismisses the simplest and most basic qualities that make them expressive, personal, and intimate.  It is a compromise that, depending on circumstances, is sometimes functional and other times not.

Many musicians trained in the western system argue that many of the pitch sets used in nonwestern music are nearly identical to those used in western music (which is kinda like saying most adult people are between 5 and 6 feet tall), they tend to dismiss nonwestern music as less organized and/or less precise (when in actuality it is the very precision of nonwestern pitch classes that makes them too numerous to be integrated into a single, elegant, system).

Rhythm (the ways in which sounds are arranged in time) has two basic components: there is always a heartbeat, a pulse (tempo), and there is always a breathing, a cycle (meter).

As with pitch, the standard western tradition stresses the concept that beats are exactly divided and precisely disposed.  Musicians from the blues/jazz traditions (among others) have a more flexible sense of this, abstractly considering the beats equally spaced, but free (and even expected) to inflect (displace) them in practice.  This opens the music up to small scale tensions and releases allowing the sense of momentum to vary while maintaining a stable tempo.

With rare exceptions, the music we hear goes “oom pa oom pa” or “oom pa pa oom pa pa”.

These are the time signatures (meters) of 4/4 and 3/4 (and all of their obvious permutations, 2/4, 4/8, 6/8, 12/8, etc.).  They can be sliced, diced, etc. in a multitude of ways ranging from the mechanical precision of a Bach fugue to the fluid improvisations of Charlie Parker.

Their rootedness in our bodies is obvious: 4 is left-right-left-right, 3 is how our hearts beat when healthy.

They are easy and intuitive to play in (almost any four year old can manage them), but they confine us to making all of our musical ideas fit either into metrical squares or metrical triangles.  If we want music to conform to expectations we can’t go wrong using them.

In the standard western tradition tempo tends to be fixed, occasionally varying, but generally expected to be the same throughout a piece or a section of a piece.  In other traditions (Korean drumming for example) the variability of tempo (and even meter) is an essential musical element.

In the standard western conception a measure (3/4 or 4/4, etc.) is divided into beats and the beats are then divided into parts (halves of beats, halves of halves of beats etc.) and the measures are strung together (usually in groups of four) to make phrases.  These phrases structures tend to repeat for the duration of the piece or section of a piece.   In other traditions beats are added to beats to generate units and cycles (which may or not repeat).

In brief: for all its genuinely glorious achievements, the western musical tradition (euromusic) accomplishes its ease of use by essentially ignoring (through codification) the most basic elements of making music.

*The traditional system of nomenclature used in western music is idiotic and has been obsolete for centuries.

For my own convenience I use a system adopted by many serialists in the 1950-70’s.

It’s very simple.  It uses the same twelve tones

In place of C it uses 0, in place of C-sharp/Dflat it uses 1, in place of D it uses 2, etc.

Instead of the intervals themselves having unintuitive names (major or minor 2nds, 3rds, 6ths, and 7ths, perfect or augmented 4ths, perfect or diminished 5ths, and various species of 10ths, 11ths, 13ths, etc., they have simple integer relationships.  In microtonalities (in which the tones don’t conform to equal temperament) the pitches can be located by decimal points if desired.

No more whole steps and half steps, no more flats and sharps, no more confusing transpositions.  Just common sense any kid (of any calendrical age) can master in a single sitting.

The C-Major scale (“but why doesn’t it start with A?” they tend to ask) is 0 2 4 5 7 9 11.

Anyone who has taught (or tried to teach) music to someone (particularly without a piano) will have run into their fair share of unproductive time dealing with questions/explanations about why the fourth note is called a third and the fifth note is called a fourth or why the same note is sometimes called A-sharp and other times called B-flat, or why F-flat even exists.