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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== Intervals ==

== Instruments ==

A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).

== Music ==

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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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; [[Mercury Amalgam]]

* [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)

~~== Instruments ==~~

~~A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).~~

[[Category:Listen]]

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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 ===
@@ Line 21: / Line 21: @@
 == Intervals ==
 {{Interval table}}
+== Instruments ==
+A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).
 == Music ==
@@ Line 26: / 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]]
@@ Line 32: / Line 36: @@
 ; [[Mercury Amalgam]]
 * [https://www.youtube.com/watch?v=3JwH0gZmXHk ''Thanatonautical Tetrapharmacon''] (2023)
-== Instruments ==
-A [[Lumatone mapping for 97edo]] has now been demonstrated (see the Unnamed high-limit temperament mapping for full gamut coverage).
 [[Category:Listen]]