Alpha scale
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Minor_third_on_C.png/250px-Minor_third_on_C.png)
12-tet: 300 cents ,
Alpha scale: 312 cents
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] . At 78 cents per step, this totals approximately 15.385 steps per octave. The scale step may be precisely derived from using 9:5 to approximate the interval 3:2⁄5:4,[3] which equals 6:5 .
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," ( and ) 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 [octave] inversion of 7⁄4, i.e., 8⁄7."[4] More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.[3][5]
interval name | size (steps) |
size (cents) |
just ratio | just (cents) |
error |
septimal major second | 3 | 233.90 | 8:7 | 231.17 | +2.72 |
major third | 5 | 389.83 | 5:4 | 386.31 | +3.51 |
perfect fifth | 9 | 701.69 | 3:2 | 701.96 | −0.27 |
harmonic seventh | 12 | 935.58 | 7:4 | 968.83 | −33.25 |
octave | 15 | 1169.48 | 2:1 | 1200.00 | −30.52 |
octave | 16 | 1247.44 | 2:1 | 1200.00 | +47.44 |
See also
Sources
- ^ a b Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- ^ Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
- ^ a b 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.