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 Play . This totals approximately 18.8 steps per octave. It may be derived from using 11:6 Play to approximate the interval 3:2/5:4, which equals 6:5 Play .
Although neither has an octave, one advantage to the beta scale over the alpha scale is that 15 steps, 957.494 cents, Play is a reasonable approximation to the seventh harmonic (7:4, 968.826 cents) Play though both have nice triads ( Play major triad , minor triad , and dominant seventh ).
- Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
- Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "Carlos has 18.809 β-scale degrees to the octave, corresponding to a scale degree of 63.8 cents."
- Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 63.8 cents.
- Taruskin, Richard (1996). Stravinsky and the Russian Traditions: A Biography of the Works through Mavra, p.1394. ISBN 0-520-07099-2.
- Carlos, Wendy (1989–96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.