13edo and optimal octave stretching: Difference between revisions
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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 | 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. | ||
<pre> | <pre> | ||
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1202.90007 | 1202.90007 | ||
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[[Category:13-tone scales]] | |||
[[Category:Tempered scales]] | |||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Zeta]] | |||
[[Category:13edo]] | |||
[[Category:Pages with Scala files]] | |||
Latest revision as of 02:56, 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