97edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|97}} | {{EDO intro|97}} | ||
== Theory == | == Theory == | ||
In the [[patent val]], 97edo tempers out 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242, 100/99, 385/384 and 441/440 in the 11-limit, and 196/195, 352/351 and 676/675 in the 13-limit. It provides the optimal patent val for the 13-limit 41&97 temperament tempering out 100/99, 196/195, 245/242 and 385/384. 97edo is the 25th prime edo. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|97}} | |||
Since 97edo has a step of 12.371 cents, it also allows one to use its | == Scales == | ||
Since 97edo has a step of 12.371 cents, it also allows one to use its [[mos]] scales as [[circulating temperament]]s{{clarify}}. It is the first prime edo which does this and the first edo which allows one to use an mos scale with a step 20 degrees or larger as a circulating temperament. | |||
{| class="wikitable mw-collapsible mw-collapsed collapsible" | {| class="wikitable mw-collapsible mw-collapsed collapsible" | ||
|+Circulating temperaments in 97edo | |+Circulating temperaments in 97edo | ||
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|} | |} | ||
== | == JI approximation == | ||
97edo has the worst approximation for [[superparticular]] intervals among edos up to 200. It has errors of well above one standard deviation (about 15.87%) in superparticular intervals with denominators up to 14. The first good approximation is the 16/15 semitone using the 9th note, with an error of 3%, meaning 97edo can be used as a rough version of [[16/15ths equal temperament]]. | 97edo has the worst approximation for [[superparticular]] intervals among edos up to 200. It has errors of well above one standard deviation (about 15.87%) in superparticular intervals with denominators up to 14. The first good approximation is the 16/15 semitone using the 9th note, with an error of 3%, meaning 97edo can be used as a rough version of [[16/15ths equal temperament]]. | ||
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| 17/16 || 48.3 | | 17/16 || 48.3 | ||
|} | |} | ||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=3JwH0gZmXHk Thanatonautical Tetrapharmacon (Demo version, July 2021)] by [[Mercury Amalgam]] | |||
[[Category:Listen]] | [[Category:Listen]] | ||