source file: m1389.txt Date: Sat, 18 Apr 1998 17:13:21 -0400 Subject: A puzzle for scale builders From: Daniel Wolf I am in the process of revising an old article. It concerns a scale with the following properties: (1) There are seven pitch classes in the system, which I will number ascending from 1 to 7. Octave equivalence is assumed, but may actually vary to create beating for coloristic or perhaps a vibrato-like effect to cover the difference of the tuning from a small-number-ratio just intonation. (2) There are three distinct pentatonic 'keys', beginning at degrees 1 (12 456), 2 (23 567) and 5 (56 123) of the seven tone system, that is to say, at 'fifths' apart. (3) the intervals 1-5, 2-6 and 3-7 are recognizable as 'fifths' (let's say +/- 25 cents of a 3/2) and = are used as dyads. (4) 5-2', 6-3', and 4-1' _may_ be recognizeable as fifths. The interval 7-4' is not used as a dyad. (5) the intervals 1-2, 2-3 and 5-6 are between 80 and 190 cents apart. (6) the intervals 1-2-3, 4-5-6, and 5-6-7 encompass an interval between an 8/7 and a 6/5. (7) the interval 1-2 is smaller than 2-3 and the interval 5-6 is smaller than 6-7. (The relationship between the intervals 4-5 and 5-6 is not so fixed). = = I am interested in what kinds of tunings others can come up with that will meet the above specifications in order to find out if the set of specifications above is sufficient and necessary. Anyone game to try? Best regards, Daniel Wolf Frankfurt =