Beta scale

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Perfect fourth (just: 498.04 cents <phonos file="Just perfect fourth on C.mid">Play</phonos>, 12-tet: 500 cents <phonos file="Perfect fourth on C.mid">Play</phonos>, Beta scale: 512 cents <phonos file="Beta scale perfect fourth on C.mid">Play</phonos>)

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.[citation needed] Another interpretation splits the perfect fourth into two equal parts,[1] or eight equal parts of approximately 64 cents each[2] <phonos file="Beta scale step on C.mid">Play</phonos>. At 64 cents per step, this totals approximately 18.75 steps per octave. It may be derived from using 11:6 <phonos file="Neutral seventh on C.mid">Play</phonos> to approximate the interval 3:2/5:4,[3] which equals 6:5 <phonos file="Just minor third on C.mid">Play</phonos>.

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, <phonos file="Beta scale 15 steps on C.mid">Play</phonos> is a reasonable approximation to the seventh harmonic (7:4, 968.826 cents)[3][4] <phonos file="Harmonic seventh on C.mid">Play</phonos> though both have nice triads[1] (<phonos file="Beta scale major triad on C.mid">Play major triad</phonos>, <phonos file="Beta scale minor triad on C.mid">minor triad</phonos>, and <phonos file="Beta scale dominant seventh on C.mid">dominant seventh</phonos>).

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.'"[5]

See also

Sources

  1. ↑ 1.0 1.1 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. ↑ 3.0 3.1 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."
  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.

External links

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