Friday math movie: pentatonic scale

By Murray Bourne, 18 Feb 2011

This video has some nice math going on behind the music.

Penta is Latin for "5". (For example, a pentagon is a 5-sided figure.)

In music, the Western "major" scale consists of 7 notes (called heptatonic). For example the C major scale has no sharps and no flats and consists of the notes C, D, E, F, G, A, B. An octave is the interval between 8 of these notes, C and the next highest C. (Octo is Latin for "8").

C major scale
C major scale

On the other hand, the pentatonic scale has 5 notes, one possible scale being C, D, E, G, A. Pentatonic scales are heard in music across all cultures (for example, jazz, folk music, Indonesian gamelan, and Scottish bagpipes).

pentatonic scale
Pentatonic scale

One possible reason for the popularity of pentatonic scales is that if any 2 notes from the pentatonic scale are played together, there is no strong clash since their frequencies differ by a reasonable amount (e.g. C and D are 2 semitones apart), whereas in the 7-note Western scale, you get a discordant sound if you play E-F together or B-C together (they are only 1 semitone apart).

discordant notes
Discordant notes

In such cases, you hear "beats", where the sound waves add together in such a way that it gives a shimmering effect and can be unpleasant.

So let's get on with today's video. Bobby McFerrin, composer of "Don't Worry, Be Happy", gets his World Science Festival audience involved in the pentatonic scale.

For more on math in music, see:

What are the frequencies of music notes?

The math of music

A logarithmic music scale

Fast Fourier Transform

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