How Maths and Music go Hand in Hand
Robin Wilson, The Open University
Part of the show Science of Sound, Music and Voices
Chris - Tell us a bit about your work, and why maths and music go hand in hand.
Robin - I am a professional mathematician and I am interested in the history of maths, but ever since I was a child I have been interested in music. I am a recorder player and a singer. In recent years, I got more and more interested in the mathematical basis of music; in scales, chords and the structure of music. Quite a lot of music has mathematical structure in how composers build a piece of music from ideas.
Kat - Our music and our scales have twelve notes in them. How are they constructed?
Robin - Our scale is constructed from semitones. You go up twelve of them every time you go up an octave and the frequency doubles. There are other cultures that use different numbers of notes. A Balanese gamalan orchestra is based on a scale with seven notes in it; some Chinese scales have 53 notes in the octave; and one interesting scale has 31. The reason you have so many notes in the octave is that you can then get very accurate thirds, fourths and fifths.
Kat - Here is a piece of music called Organum based on this 31 note scale [MUSIC]. How long has Western music been based on a twelve note system?
Robin - The twelve notes have been around a long time. The Ancient Greeks were very interested in finding ratios. If you have an octave, the ratio is 2:1, and a perfect fifth 3:2 etc.. Up until about the 1300s or so much of the music used octaves, fourths and fifths, and then other intervals such a thirds and sixths. It turned out that in one key it worked but in other keys it sounded wrong. That is when the equal temper scale was brought in, so you could play in any key you like.
Kat - I remember hearing about Bach's Well-Tempered Klavier, when they learn how to tune pianos.
Robin - It was certainly around that time that there were lots of different tunings going on, and it is not certain which one Bach wrote things in. But the idea of the Well-Tempered Klavier was to allow you to play music in all 24 keys; major and minor.