First letter of the Greek alphabet, with the following current musical uses of the lower-case form α :
A scale devised by Wendy Carlos which does not have octaves, because of its equal step size of ~77.965 cents, or ~15.392 steps per "octave".
It is "defined strictly as a local minimum of the root-mean-square error function that Wendy set up with 3/2, 5/4, 6/5, 7/4, and 11/8 as target intervals." [Paul Hahn, Onelist Tuning Digest 116] ... the plot that Wendy includes with her Computer Music Journal (Spring 1987) article includes three different curves/functions. They include the first three, the first four, and all five of the target intervals listed above. The one from which she derives alpha, beta, and gamma is actually the first, i.e. the one which only targets 3/2, 5/4, and 6/5. [Paul Hahn, Yahoo tuning group, message 2232, Thu Apr 8, 1999 4:35 pm]
The Carlos alpha tuning splits a tempered minor-3rd into two equal parts, which in turn are each divided in half -- thus, the minor-3rd subtends 4 equal steps of ~78 cents each. The alpha tuning also contains a very good approximation to the "pure" pythagorean 3:2 perfect-5th, which is split into 9 equal divisions. The first octave of the alpha scale is covered by the following notes in descending order (step size = 77.965 cents, all figures rounded to the nearest cent):
degree cents 16 1247 15 1169 14 1092 13 1014 12 936 11 858 10 780 9 702 8 624 7 546 6 468 5 390 4 312 3 234 2 156 1 78 0 0
Examples of its use can be found on her album Beauty In The Beast.
Various EDOs give approximations to the Carlos alpha scale:
Used in its lower-case form α as an additional letter-name in Erv Wilson's notations, signifying a note near "A", but with a musical function separate from "A", in whatever particular scale the notation is describing.
see The Wilson Archives for examples and explanations of his notation.
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