97edo: Difference between revisions

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== Theory ==

97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[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 {{nowrap|41 &~~amp; 97~~}} temperament ~~tempering~~ out 100/99, 196/195, 245/242 and 385/384.

97edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[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 [[superana]] ({{nowrap| 41 & 56 }}) temperament, which tempers out 100/99, 196/195, 245/242 and 385/384.

=== Odd harmonics ===

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97edo is the 25th [[prime edo]], following [[89edo]] and before [[101edo]].

[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[~~The Riemann zeta function and tuning|~~zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.

[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.

== Approximation to JI ==

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* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)

* [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025)

* [https://www.youtube.com/shorts/U1X3oo9CGHg ''Washing Machine Heart - Mitski (microtonal cover in 97edo)''] (2025)

; [[User:Francium|Francium]]

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 == Theory ==
-edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[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 {{nowrap|41 &amp; 97}} temperament tempering out 100/99, 196/195, 245/242 and 385/384.
+edo is only [[consistent]] to the [[5-odd-limit]]. The [[patent val]] of 97edo [[tempering out|tempers out]] [[875/864]], [[1029/1024]], and [[4000/3969]] in the 7-limit, [[100/99]], [[245/242]], [[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 [[superana]] ({{nowrap| 41 & 56 }}) temperament, which tempers out 100/99, 196/195, 245/242 and 385/384.
 === Odd harmonics ===
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 edo is the 25th [[prime edo]], following [[89edo]] and before [[101edo]].
-[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[The Riemann zeta function and tuning|zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.
+[[388edo]] and [[2619edo]], which contain 97edo as a subset, have very high consistency limits – 37 and 33 respectively. [[3395edo]], which divides the edostep in 35, is a [[zeta edo]]. The [[berkelium]] temperament realizes some relationships between them through a regular temperament perspective.
 == Approximation to JI ==
@@ Line 29: / Line 29: @@
 * [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)
 * [https://www.youtube.com/shorts/6iXy1D9RZ-U ''Charlie's Inferno - That Handsome Devil (microtonal cover in 97edo)''] (2025)
+* [https://www.youtube.com/shorts/U1X3oo9CGHg ''Washing Machine Heart - Mitski (microtonal cover in 97edo)''] (2025)
 ; [[User:Francium|Francium]]