Third letter of the Greek alphabet, with the following current musical uses in its lower-case form γ :
A scale devised by Wendy Carlos which does not have octaves, because of its equal "step size" of ~35.099 cents, with 34.188 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 first octave of the gamma scale is as follows (values rounded to the nearest cent):
1228 1193 1158 1123 1088 1053 1018 983 948 913 877 842 807 772 737 702 667 632 597 562 526 491 456 421 386 351 316 281 246 211 175 140 105 70 35 0
Paul Hahn (Yahoo tuning group message 1873, Fri Mar 19, 1999 1:59 pm) has pointed out that the number of steps per octave is very nearly the sum of the numbers of steps per octave in Carlos's alpha and beta scales.
Examples of the gamma scale can be found on Carlos's album Beauty In The Beast.
Various EDOs give approximations to the Carlos gamma scale:
Used in its lower-case form γ as an additional letter-name used in Erv Wilson's notations, signifying a note near "G", but with a musical function which is separate from "G", in whatever particular scale the notation is describing.
see The Wilson Archives for examples and explanations of his notation.
During medieval times (c.900 AD), the ancient Greek tetrachord system was adapted to the needs of the "Gregorian" plainchant used in church services by the Franks, by reorganizing the intervallic structure of the tetrachords as if they ocurred a tone lower.
Since the lowest Greek note, which had been called proslambanomenos by them, had already been labeled as "A" by the Franks, they needed a new capital letter to represent the note a tone lower. Thus, Γ was added at the bottom of the complete system.