97edo: Difference between revisions

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=== Dissonance ===

97edo ~~is one of~~ the ~~least harmonic EDOs within double digits or early hundreds, resulting in~~ 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]].

Since 97edo is a prime EDO, it lacks specific modulation circles, symmetrical chords or sub-EDOs that are present in composite EDOs. When edos like [[19edo|19]], [[29edo|29]], [[31edo|31]], [[41edo|41]], or [[53edo|53]] have mathematically justified harmony, 97edo is essentially "irredeemable" in terms of either modulation or approximation rationales. However, this might result in interest towards this tuning through emancipation of the dissonance.

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[[Category:Equal divisions of the octave|##]]

[[Category:Equal divisions of the octave|##]]

== Music ==

* [https://www.youtube.com/watch?v=3JwH0gZmXHk Thanatonautical Tetrapharmacon (Demo version, July 2021)] by [[Mercury Amalgam]]

[[Category:Prime EDO]]

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 === Dissonance ===
-edo is one of the least harmonic EDOs within double digits or early hundreds, resulting in 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]].
+edo 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]].
 Since 97edo is a prime EDO, it lacks specific modulation circles, symmetrical chords or sub-EDOs that are present in composite EDOs. When edos like [[19edo|19]], [[29edo|29]], [[31edo|31]], [[41edo|41]], or [[53edo|53]] have mathematically justified harmony, 97edo is essentially "irredeemable" in terms of either modulation or approximation rationales. However, this might result in interest towards this tuning through emancipation of the dissonance.
@@ Line 287: / Line 287: @@
 |}
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
+[[Category:Equal divisions of the octave|##]]
+== Music ==
+* [https://www.youtube.com/watch?v=3JwH0gZmXHk Thanatonautical Tetrapharmacon (Demo version, July 2021)] by [[Mercury Amalgam]]<!-- 2-digit number -->
 [[Category:Prime EDO]]