Beta Scale
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Beta Scale
Perfect fourth (just: 498.04 cents  , 12-tet: 500 cents  , Beta scale: 512 cents  )

The ? (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,[1] or eight equal parts of approximately 64 cents each[2] . This totals approximately 18.8 steps per octave. It may be derived from using 11:6   to approximate the interval ,[3] 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)[3][4]  though both have nice triads[1] (, , 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 ? as ? is 'up'."[5]

 interval name size (steps) size (cents) just ratio just (cents) error minor third 5 319.00 6:5 315.64 +3.35 major third 6 382.80 5:4 386.31 -3.52 perfect fifth 11 701.79 3:2 701.96 -0.16 harmonic seventh 15 956.99 7:4 968.83 -11.84

## Sources

1. ^ a b Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
2. ^ Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
3. ^ a b Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "Carlos has 18.809 ?-scale degrees to the octave, corresponding to a scale degree of 63.8 cents."
4. ^ Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 63.8 cents.
5. ^ Taruskin, Richard (1996). Stravinsky and the Russian Traditions: A Biography of the Works through Mavra, p.1394. ISBN 0-520-07099-2.