97edo: Difference between revisions

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=== Odd harmonics ===

=== Subsets and supersets ===

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== Approximation to JI ==

97edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. 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 [[16/15 equal-step tuning]]~~.

97edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. 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%.

Since 97edo is a prime edo, it lacks specific modulation circles, symmetrical chords or sub-edos that are present in composite edos. When notable equal divisions like {{EDOs|19, 31, 41, or 53}} have strong JI-based harmony, 97edo does not have easily representable modulation because of its inability to represent superparticulars. However, this might result in interest in this tuning through JI-agnostic approaches.

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== Music ==

; [[Bryan Deister]]

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

; [[User:Francium|Francium]]

* [https://www.youtube.com/watch?v=h7bT1oL8T0w ''Joyous Stellaris''] (2023) – [[semiquartal]] in 97edo tuning

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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]]

@@ Line 6: / Line 6: @@
 === Odd harmonics ===
-{{Harmonics in equal|97}}
+{{Harmonics in equal|97|columns=14}}
 === Subsets and supersets ===
@@ Line 14: / Line 14: @@
 == Approximation to JI ==
-edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. 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 [[16/15 equal-step tuning]].
+edo has very poor direct approximation for [[superparticular]] intervals among edos up to 200, and the worst for intervals up to 9/8 among edos up to 100. 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%.
 Since 97edo is a prime edo, it lacks specific modulation circles, symmetrical chords or sub-edos that are present in composite edos. When notable equal divisions like {{EDOs|19, 31, 41, or 53}} have strong JI-based harmony, 97edo does not have easily representable modulation because of its inability to represent superparticulars. However, this might result in interest in this tuning through JI-agnostic approaches.
@@ Line 23: / Line 23: @@
 == Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=hXDdKO3-RL4 ''microtonal improvisation in 97edo''] (2025)
 ; [[User:Francium|Francium]]
 * [https://www.youtube.com/watch?v=h7bT1oL8T0w ''Joyous Stellaris''] (2023) – [[semiquartal]] in 97edo tuning
@@ Line 28: / Line 31: @@
 ; [[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]]