Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

gamma / Γ(upper-case), γ(lower-case)

[Joe Monzo]

Third letter of the Greek alphabet, with the following current musical uses in its lower-case form γ :

. . . . . . . . .
1. Wendy Carlos scale

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:

. . . . . . . . .
2. Erv Wilson notation symbol

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.

. . . . . . . . .
3. Lowest note of medieval gamut

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.

. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level