Alpha scale
The α (alpha) scale is a non-octave-repeating musical scale. In one version it splits the perfect fifth (3:2) into nine equal parts of approximately 78.0 cents.[citation needed] In another it splits the minor third into two equal parts,[1] or four equal parts of approximately 78 cents each[2] <phonos file="Alpha scale step on C.mid">Play</phonos>. At 78 cents per step, this totals approximately 15.385 steps per octave. The scale step may be precisely derived from using 9:5 <phonos file="Greater just minor 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 Wendy Carlos and used on her album Beauty in the Beast (1986).
Though it does not have an octave, the alpha scale produces, "wonderful triads," (<phonos file="Alpha scale major triad on C.mid">Play major</phonos> and <phonos file="Alpha scale minor triad on C.mid">minor triad</phonos>) and the beta scale has similar properties but the sevenths are more in tune.[1] However, the alpha scale has, "excellent harmonic seventh chords...using the inversion of 7/4, i.e., 8/7."[4] <phonos file="Alpha scale harmonic seventh chord on C.mid">Play</phonos> More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.[3][5]
See also
Sources
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- ↑ 1.0 1.1 Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- ↑ Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
- ↑ 3.0 3.1 Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "This actually differs very slightly from Carlos' figure of 15.385 α-scale degrees to the octave. This is obtained by approximating the scale degree to 78.0 cents."
- ↑ Carlos, Wendy (1989–96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
- ↑ Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 78 cents.
