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7.6 — Music: How It Is Built, and Where It Came From
Music is the one art that is mathematics you can feel, and almost every question about it has an answer in ratios.
Why notes sound the way they do
Why do two notes an octave apart sound like the same note?
Because one is exactly twice the frequency of the other, and the ear treats that relationship as identity.
Play a string at 220 Hz and again at 440 Hz and they blend so completely that people across every musical culture name them the same note. The physical reason is that a vibrating string does not produce one frequency. It produces a fundamental plus a whole series of harmonics at 2, 3, 4, 5 times that frequency, and the two notes an octave apart share nearly all of them.
The same logic explains the other intervals. A ratio of 3:2 is a perfect fifth — the most consonant interval after the octave, because the two notes' harmonic series overlap heavily. 4:3 is a fourth. 5:4 is a major third. As the numbers get larger and less simple, fewer harmonics coincide, and the interval sounds progressively more tense.
Dissonance is not a cultural convention at the physical level. When two notes are close but not identical, their harmonics interfere and produce a rapid wavering called beating, which the ear registers as roughness. Which dissonances a culture uses, and which it treats as needing resolution, is convention; the roughness is physics.
Pythagoras is credited with discovering the ratios around the sixth century BCE, reportedly by dividing a stretched string, and the connection between whole-number ratios and beauty became the foundation of an entire philosophical tradition.
Why does a piano have twelve notes and not some other number?
Because twelve is the smallest number of equal steps in an octave that gets acceptably close to the simple ratios.
Start on a note and go up by perfect fifths — multiplying by 3/2 each time. After twelve fifths you arrive very nearly, but not exactly, back where you started, several octaves up. The mismatch is about a quarter of a semitone and is called the Pythagorean comma.
That small error is the central problem of tuning, and it cannot be eliminated. You can have pure fifths or a closed circle of twelve notes, and not both. Every tuning system in history is a different compromise about where to hide the error.
Equal temperament, standard since the eighteenth century, divides the octave into twelve exactly equal steps, each a ratio of the twelfth root of two — about 1.0595. Every interval except the octave is then slightly out of tune, and equally so in every key. That is the trade: no key sounds pure, and every key sounds the same, so a piece can change key freely and an instrument does not need retuning.
Bach's Well-Tempered Clavier — two sets of pieces in all twenty-four keys — is the celebrated demonstration of what this makes possible.
Why are there black keys, and why not five white and seven black?
Because the white keys are the older system and the black keys were inserted into it.
Western music was built on a seven-note diatonic scale long before the other five notes were regularised. The keyboard's white keys give that scale — the notes of C major — and the black keys were added as accidentals for transposition and for modes.
The uneven pattern of two blacks and then three blacks is not decoration: it is what makes the keyboard navigable by touch, and it reflects the actual structure of the major scale, whose steps are not all equal. From C to D is a whole step, from E to F is a half step, and the black keys sit exactly where the whole steps are.
The scale's uneven steps are also why a major scale sounds the way it does. Equal steps would produce a whole-tone scale, which has no pull towards a home note, and is used in film scores precisely for the feeling of drifting.
Indian music
How does the Indian system differ?
In what it fixes and what it leaves free.
Western music generally fixes pitch relationships absolutely — a piece is in a key at a defined pitch — and treats harmony, notes sounding together, as the central structure.
Indian classical music fixes a drone and builds everything relative to it. The tanpura sounds the tonic, Sa, continuously, and every other note is heard against it. There is no harmony in the Western sense and no key change; instead, melody and rhythm carry all the structure and are developed at enormous length.
The seven notes — Sa, Re, Ga, Ma, Pa, Dha, Ni — correspond broadly to the Western seven, and the system recognises twelve semitones as Western music does. But it also uses shruti, microtonal shadings within a note, which are not separate scale degrees but inflections that define how a particular note is approached and left in a particular raga.
What is a raga, and what is a tala?
A raga is not a scale, and translating it as one is the most common error.
It specifies which notes are used, but also which are emphasised, how each is approached, which ornaments are obligatory, which phrases are characteristic, and which movements are forbidden. Two ragas can use exactly the same notes and be entirely different, because the rules of movement differ. A raga is closer to a grammar than to a vocabulary.
Ragas are traditionally associated with times of day and seasons, and performing one at the wrong time is considered a genuine breach rather than a superstition by many musicians.
A tala is the rhythmic cycle. Rather than bars of a fixed number of beats repeating uniformly, a tala is a cycle of a defined length with an internal structure of stressed and unstressed divisions. Teentaal is 16 beats in four groups of four; Jhaptaal is 10 in groups of 2-3-2-3; Rupak is 7.
The first beat of the cycle, the sam, is the point everything resolves to, and a great deal of the drama in a performance comes from a soloist and a percussionist departing from the cycle in complicated ways and arriving back on the sam together.
What is the difference between Hindustani and Carnatic?
Two classical traditions with a common root, diverging from roughly the thirteenth century as northern Indian music absorbed Persian and Central Asian influence.
Hindustani, in the north, emphasises slow improvisational development. A performance typically opens with an alap, an unmetered exploration of the raga with no percussion, which can last half an hour before the rhythm enters. Instruments: sitar, sarod, sarangi, bansuri, santoor, tabla.
Carnatic, in the south, is more composition-centred. The repertoire of fixed compositions — largely by the eighteenth and nineteenth-century composers Tyagaraja, Muthuswami Dikshitar and Syama Sastri — is central, and improvisation happens around and within them. It is more rhythmically intricate and generally faster. Instruments: veena, violin, flute, nadaswaram, mridangam, ghatam.
The violin is worth a note: it was adopted into Carnatic music in the eighteenth century from European visitors, retuned and held differently — seated, with the scroll on the player's foot — and is now completely central to the tradition. A borrowed instrument that became indigenous.
Instruments and how they work
What makes instruments sound different from each other?
The pattern of harmonics, called the timbre, and the way the note starts.
Play the same note on a flute and a violin and both produce the same fundamental frequency. What differs is the relative strength of the harmonics above it: a flute is dominated by the fundamental with weak upper harmonics, giving a pure, hollow sound; a violin has strong upper harmonics, giving a bright, complex one; a clarinet suppresses the even-numbered harmonics almost entirely because of the way a tube closed at one end resonates, which is why it sounds hollow in a different way.
The attack matters as much as the harmonics, and this is easy to demonstrate. Record a piano note and cut off the first tenth of a second — the hammer strike — and most listeners can no longer identify the instrument. The characteristic identity of many instruments is concentrated in a fraction of a second at the start.
The four families are grouped by how the vibration is produced: strings (bowed, plucked or struck), wind (a vibrating air column, driven by a reed or by air across an edge), brass (the player's lips vibrating into a mouthpiece), and percussion. Indian classification uses a similar four-way scheme from the Natya Shastra: string, wind, membrane and solid.
Why is A tuned to 440 Hz?
By agreement, and the agreement was contested and is fairly recent.
Historical pitch varied enormously — surviving organs and wind instruments indicate reference pitches from below 400 to above 460 Hz depending on city and century. A piece of Baroque music played at modern pitch is being played substantially higher than it was written for, which is why period-instrument ensembles usually tune to about 415.
An international conference in 1939 settled on 440 Hz for A above middle C, and it was standardised formally in 1955. Orchestras routinely ignore it, and many European orchestras tune to 442 or 443, on the argument that a slightly higher pitch sounds brighter.
The occasionally circulated claim that 432 Hz is a natural or healing frequency and that 440 was imposed for sinister reasons has no evidence behind it of any kind.
Popular music
Why do so many songs use the same four chords?
Because a small number of chord sequences resolve satisfyingly, and one in particular has an unusually strong pull.
The most used is the I-V-vi-IV progression — in C major, that is C, G, A minor, F. It appears in an enormous number of pop songs across decades and genres, to the point where medleys demonstrating it are a standing musical joke.
The reason it works is functional. The tonic establishes home, the dominant creates tension pulling back to it, the relative minor provides a shift in colour without leaving the key, and the subdominant returns towards home. Each chord shares notes with its neighbours, so the movement is smooth, and the sequence loops without a definite ending — which is exactly what a verse needs.
That songs share chord progressions is not plagiarism and cannot be, since progressions are not copyrightable. Melody is. The distinction has been tested repeatedly in court and the results have been inconsistent enough to worry musicians.
How did recorded music change what music is?
Completely, and in ways that are easy to miss because we have never known otherwise.
Before recording, music existed only at the moment of performance. A piece was known by its score or by memory, and every hearing was different. The composer was the author and the performer was an interpreter.
Recording inverted that. A particular performance became the definitive object, which is why in popular music the recording is the work and a live performance is judged against it. It also made music portable across the world, which is how blues from the American south became rock in Britain and returned.
Two constraints of the medium became conventions. The three-minute song length comes from the capacity of a 10-inch 78 rpm disc. The album as a form comes from the 12-inch LP's roughly 22 minutes a side — which is why so many classic albums have a shape, with a strong opening on each side and a closer.
Both constraints are gone and both conventions persist, which is the usual pattern in this book.
Which single instrument changed popular music most?
Two candidates, and each has a good case.
The electric guitar, because amplification changed the balance of an ensemble. An acoustic guitar cannot compete with drums; an amplified one can lead. And once the signal is electrical, it can be deliberately distorted, which turned a fault in the equipment into the defining sound of half a century of music.
The multitrack tape recorder, because it separated performance from recording. Once each instrument could be recorded separately and combined later, the studio became an instrument rather than a room, and a record could contain something no group of people could play at once. Les Paul — who also has a fair claim on the first — developed it, and by the mid-1960s it had changed what a record was.
The synthesiser, the sampler and the drum machine each extended the same idea: music that exists only as a recording, made by people who need not be in a room together.
What comes next
The next Part turns to what hangs on walls and stands in squares — painting, sculpture, architecture and the wonders of the world.