Why do we only use 12 notes in Western music?
Richard Ellam
Bristol, UK
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Notes with frequencies that are in simple whole-number ratios, like 1:2, 2:3 or 4:5, sound good when played together. This is the basis of musical harmony. After unison (1:1) and the octave (2:1), the next most harmonious interval is 3:2, known as a perfect fifth.
Starting at any (low) frequency, you can construct a series of tones, each a perfect fifth (3/2 the frequency) higher than the one below. The twelfth tone in this series sounds like a (much) higher version of the starting tone, because it is just over seven octaves higher in pitch.
For example, in modern orchestral pitch, we define the A above middle C (A4) to have a frequency of 440 hertz. The A above this (A5) has a frequency of 880 Hz, and the A below middle C (A3) has a frequency of 220Hz. If we set up a chain of notes, each having a frequency of 3/2 that of the previous note we find that, when we get to the twelfth note, it has a frequency that is just under 130 times the frequency of our starting note ((3/2)12 = 129.75). The frequency ratio of seven octaves is 27, which is 128, so our twelfth note is just over seven octaves higher than our starting note.
Indian and other cultures quite happily use microtones, but Western music is generally unwilling to do the same
If we now divide the frequencies down to bring all twelve tones within about one octave we find that the frequency of the twelfth tone is 129.75 梅 64 = 2.027 times our starting note. This is close enough to the 2:1 ratio that it sounds like the octave of the starting note, even though it isn鈥檛 quite in tune.
So, in practice, we set up our musical scales so that the octaves are exactly in tune, and fudge the rest depending on what we want to achieve.
In particular, modern Western instruments are mostly tuned to 鈥渆ven temperament鈥�, where the frequency ratio of successive semitones is defined as being the twelfth root of two. This makes the frequency of each ascending semitone just under 1.06 times the one below, and the frequency ratio of any two notes an octave apart is exactly 2:1. Such a scale is actually very precisely out of tune, but the errors are too small to be readily noticeable. Any problems this causes are far outweighed by the advantages of being able to play 鈥渋n tune鈥� in any key.
Guy Cox
Sydney, Australia
The fundamental unit of music is the octave 鈥� ratio 2:1. But to make music, we have to divide the octave up into divisions that are still harmonically related.
The earliest of these is the pentatonic scale, where it is divided into five. But in medieval times, musicians wanted to go further and divided the octave into eight unequal notes (hence the name octave). There were different versions, called modes. These were originally for monophonic music (plainsong) but by the Renaissance it was clear they worked for complex polyphonic music. In this context, semitones sometimes needed to be added for effect. So we ended up with 12 notes, but they weren鈥檛 the equal 12 we know today.
By Baroque times only two modes 鈥� which we now know as major and minor 鈥� were in use but musicians wanted to be able to use them in any key, hence the development of 鈥渢emperaments鈥�. That led to our current equal-temperament tuning where every note is a bit off but they all work together. So, 12 equal notes in the octave.
But what about smaller intervals? In Indian music they are a major part of the performance. In the early 20th century, the composer Alois H谩ba wrote some hauntingly beautiful music in the 鈥渟ixth tone鈥� system 鈥� dividing the octave into 36 parts. We hardly ever get to hear H谩ba鈥檚 music today 鈥� maybe because it is fiendishly difficult to perform!
Simon McLeish
Lechlade, Gloucestershire, UK
Indian and other cultures quite happily use microtones, but Western music is generally unwilling to do the same. There are exceptions, in modern music and where music of other cultures is influential (the jazz and blues traditions are probably the most familiar to the average Western music listener). At least part of the reason this is the case is tradition, familiarity and convenience. The piano is still a dominant instrument in Western music, and it is firmly rooted to the equal-temperament 12-note scale.
Even before the introduction of equal temperament, though, Western music was wedded to 12 notes, when taken in scales of eight notes. This is probably related to the dominance of Greek philosophy, which derived from Mesopotamian music. Grecian culture was immensely prestigious, and ideas about music attributed to Pythagoras became the basis of Western music, with the idea of modes (what you get if you use a scale of eight consecutive white notes on a piano, which are still given Greek names, such as Mixolydian, which starts on G and then goes up in sequence G, A, B, C, D, E, F, G).
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