13edo and optimal octave stretching: Difference between revisions

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m Added to two categories, and fixed a red link
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[[13edo]] has its [[local zeta peak]] at 12.96866 edo, which corresponds to an [[octave equivalence]] of 1202.9 cents.
[[13edo]] has its [[The Riemann zeta function and tuning|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.
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.
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1202.90007
1202.90007
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[[Category:Zeta]]
[[Category:13edo]]

Revision as of 01:47, 14 April 2023

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