Secor wt17: Difference between revisions
Stub? I don't know what categories are appropriate. Didn’t find one for well temperaments |
CritDeathX (talk | contribs) Added reasoning for 17-WT |
||
| Line 1: | Line 1: | ||
This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'' | This is a 17-tone well tempered tuning by [[George Secor]], described in his article ''[http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle]'': | ||
Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents. | ''The requirements for a temperament having an irregular closed circle of fifths in 17... are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, ...6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g., ...7:9:11 in 17.'' | ||
''In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones).... While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.'' | |||
Secor advises using C = 264 Hz when playing alongside instruments tuned to [[17edo|17EDO]], so that corresponding pitches of the scales would not deviate by more than 6.7 cents. | |||
== Scala file == | == Scala file == | ||
Revision as of 22:02, 27 September 2020
This is a 17-tone well tempered tuning by George Secor, described in his article The 17-tone Puzzle:
The requirements for a temperament having an irregular closed circle of fifths in 17... are somewhat different from those for 12 in that many of the tempered intervals are used to represent two different just ratios. For example, ...6 system degrees of 17-ET (6º17) falls between 11:14 and 7:9. In a temperament with a circle of fifths of varying size, certain intervals will more closely approximate one of these ratios in one part of the circle and the other ratio in another part of the circle. The objective is to construct the temperament in such a way that the best approximations of these ratios will occur, in the desired keys, simultaneously in chords in which these intervals (or their inversions) are used in combination, e.g., ...7:9:11 in 17.
In my 17-WT, using primes 3, 7, 11, and 13, the best intonation occurs in five different keys (with B-flat, F, C, G, and D as fundamental tones).... While the 6:7:9 (subminor) triad in 17-WT is not as good as in 22-ET, the best 6:7:9:11 tetrads in 17-WT are considerably better than those in 22-ET. Even though a significant improvement is made in the harmonic effect of 17-WT over 17-ET, the former retains the general melodic characteristics of the latter.
Secor advises using C = 264 Hz when playing alongside instruments tuned to 17EDO, so that corresponding pitches of the scales would not deviate by more than 6.7 cents.
Scala file
! secor_wt17.scl ! George Secor's 17-tone well temperament 17 ! 66.741 144.856 214.441 278.339 353.610 428.882 492.780 562.364 640.479 707.220 771.118 849.233 921.661 985.559 1057.987 1136.102 1200.