13edo and optimal octave stretching: Difference between revisions

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[[Category:13-tone scales]]
[[Category:13-tone scales]]
[[Category:Tempered scales]]
[[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]]


[[Category:Zeta]]
[[Category:Zeta]]
[[Category:13edo]]
[[Category:13edo]]
[[Category:Pages with Scala files]]
[[Category:Pages with Scala files]]

Revision as of 02:24, 24 June 2025

13edo has its local zeta peak at 12.96866 edo, which corresponds to an octave equivalence of 1202.9 cents.

Interestingly, this stretching improves both its acoustic phi interval (9\13), which now has an error of only -0.3 cents, as well as its logarithmic phi interval (21\13), which now has an error of only +1.5 cents.

! 13edo_optimal-stretching.scl
!
13 equal divisions of 13edo local zeta peak
13
!
92.530775
185.061549
277.592324
370.123099
462.653873
555.184648
647.715422
740.246197
832.776972
925.307746
1017.838521
1110.369296
1202.90007