32edo: Difference between revisions
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{{EDO | {{EDO intro|32}} | ||
While even advocates of less-common [[EDO]]s can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Pařízek]]'s [[sixix]] temperament, which tempers out the [[5-limit|5-limit]] sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Pařízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune mohavila, an 11-limit temperament which does not temper out sixix. | While even advocates of less-common [[EDO]]s can struggle to find something about it worth noting, it does provide an excellent tuning for [[Petr Pařízek]]'s [[sixix]] temperament, which tempers out the [[5-limit|5-limit]] sixix comma, 3125/2916, using its 9\32 generator of size 337.5 cents. Pařízek's preferred generator for sixix is (128/15)^(1/11), which is 337.430 cents and which gives equal error to fifths and major thirds, so 32edo does sixix about as well as sixix can be done. It also can be used (with the 9\32 generator) to tune mohavila, an 11-limit temperament which does not temper out sixix. | ||
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=Z function= | == Z function == | ||
Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third. | Below is a plot of the [[Zeta]] function, showing how its peak (ie most negative) value is shifted above 32, corresponding to a zeta tuning with octaves flattened to 1197.375 cents. This will improve the fifth, at the expense of the third. | ||
[[File:plot32.png|alt=plot32.png|plot32.png]] | [[File:plot32.png|alt=plot32.png|plot32.png]] | ||
=Music= | == Music == | ||
* [https://www.youtube.com/watch?v=00kH3CqSgMY Zinnia Riplet (32-EDO)] by [[Stephen Weigel]] (featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 Possible Worlds Vol. 4] of Spectropol Records) | * [https://www.youtube.com/watch?v=00kH3CqSgMY Zinnia Riplet (32-EDO)] by [[Stephen Weigel]] (featured in [https://spectropolrecords.bandcamp.com/album/possible-worlds-vol-4 Possible Worlds Vol. 4] of Spectropol Records) | ||
* [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo Admin's Hot Tub] by [[Stephen Weigel]] | * [https://soundcloud.com/overtoneshock/admins-hot-tub-32-edo Admin's Hot Tub] by [[Stephen Weigel]] | ||
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[[Category:32edo| ]] <!-- main article --> | [[Category:32edo| ]] <!-- main article --> | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | ||
[[Category: | [[Category:Listen]] | ||
[[Category: | [[Category:Sixix]] | ||
[[Category: | [[Category:Zeta]] | ||