Beta scale



The β (beta) scale is a non-octave-repeating musical scale. In one version, it splits the perfect fifth (3:2) into eleven equal parts of 63.8 cents each. Another interpretation splits the perfect fourth into two equal parts, or eight equal parts of approximately 64 cents each. This totals approximately 18.8 steps per octave. It may be derived from using 11:6 to approximate the interval $3:2/5:4$, which equals 6:5.

It was invented by and is a signature of Wendy Carlos and used on her album Beauty in the Beast (1986).

Although neither has an octave, one advantage to the beta scale over the alpha scale is that 15 steps, 957.494 cents, is a reasonable approximation to the seventh harmonic (7:4, 968.826 cents)  though both have nice triads (,, and ).

The delta scale may be regarded as the beta scale's reciprocal since it is "as far 'down' the (0 3 6 9) circle from α as β is 'up'."