3. Staccato

The Atoms of Music

We make most music from notes—but where do they come from? There is an infinite number of different pitches in the audible range, each corresponding to a different frequency of vibration. Yet out of this continuous range we select just a handful of notes from which to make music. How do we choose? Is that choice determined by nature, by acoustic physics, or by cultural convention? I argue that, despite what many music theorists have claimed throughout the ages, there is little that is “natural” in musical scales. Just about the only thing they have in common across cultures is that there is something special about the octave: two notes an octave apart sound somehow like higher or lower versions of the same note. The reason for this can probably be found in the way most natural sounds are built up from many pitches whose frequencies are related in simple numerical ratios. That may also account for why the interval of a fifth—in Western scales, the distance between a C and the G above it—is also very common throughout the world. But as for the other notes in between: they seem mostly to be a matter of convenience and convention. You only have to listen to the scales of music from India or Indonesia to appreciate that there is nothing special about the so-called diatonic scales used in Western music. More important than the pitches of the notes is the way that they are spaced in a scale: the unequal steps between notes in the western scales are echoed in the scales of non-Western cultures. This uneven staircase helps us to locate where we are in pitch space—in other words, it helps us make sense of music.

Systems of Intonation

  Equal Just Pythagorean Meantone Werckmeister
Major Scale Listen Listen Listen Listen Listen
Major Third Listen Listen Listen Listen Listen
Major Triad Listen Listen Listen Listen Listen


Podcast 3
Fig3.6 Harmonic minor
Fig3.6 Majorscale
Fig3.6 Melodicminor down
Fig3.6 Melodicminor up
Fig3.11 Dorian
Fig3.11 Hypodorian
Fig3.11 Hypolydian
Fig3.11 Hypophrygian
Fig3.11 Lydian
Fig3.11 Mixolydian
Fig3.11 Phrygian
Fig3.12 Aeolian
Fig3.12 Dorian
Fig3.12 Hypodorian
Fig3.12 Hypolydian
Fig3.12 Hypomixolydian
Fig3.12 Hypophrygian
Fig3.12 Ionian
Fig3.12 Lydian
Fig3.12 Mixolydian
Fig3.12 Phrygian

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