90edo - Revision history

Hotcrystal0: fix typo

2026-05-01T21:21:16Z

fix typo

← Older revision		Revision as of 21:21, 1 May 2026
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	Since 90 factors into primes as 2 x 3<sup>2</sup> × 5, 90 has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 }}.		Since 90 factors into primes as 2 x 3<sup>2</sup> × 5, 90 has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 }}.

	As a composite edo, the smallest subsets it lacks are subsets of [[4edo\|4]], [[7edo\|7]] and [[8edo\|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\80 = 146.667{{cent}}, serving a similar function.		As a composite edo, the smallest subsets it lacks are subsets of [[4edo\|4]], [[7edo\|7]] and [[8edo\|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\90 = 146.667{{cent}}, serving a similar function.

	Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).		Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).

Lucius Chiaraviglio: /* Music */ Bryan Deister's Fantasy in 90edo: Add full version

2026-04-23T01:08:35Z

Music: Bryan Deister's Fantasy in 90edo: Add full version

← Older revision		Revision as of 01:08, 23 April 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)		* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)
	* [https://www.youtube.com/shorts/LdxUD1taOqI ''<nowiki>~~Fantasy in 90edo~~ [short clip]</nowiki>''] (~~2026~~)		* ''Fantasy in 90edo'' (2026)
			** [https://www.youtube.com/shorts/LdxUD1taOqI <nowiki>[short clip]</nowiki>] (Lumatone view)
			** [https://www.youtube.com/watch?v=YRNtKaWNjUU <nowiki>[full version]</nowiki>]

	; [[James Kukula]]		; [[James Kukula]]
	* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)		* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)

Lucius Chiaraviglio: /* Music */ Bryan Deister's 90edo improv (2026) is actually Fantasy in 90edo [short clip]

2026-04-17T08:07:33Z

Music: Bryan Deister's 90edo improv (2026) is actually Fantasy in 90edo [short clip]

← Older revision		Revision as of 08:07, 17 April 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)		* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)
	* [https://www.youtube.com/shorts/LdxUD1taOqI ''90edo ~~improv~~''] (2026)		* [https://www.youtube.com/shorts/LdxUD1taOqI ''<nowiki>Fantasy in 90edo [short clip]</nowiki>''] (2026)

	; [[James Kukula]]		; [[James Kukula]]
	* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)		* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)

Lucius Chiaraviglio: /* Theory */ 270edo stands out

2026-04-15T07:40:13Z

Theory: 270edo stands out

← Older revision		Revision as of 07:40, 15 April 2026
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	Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).		Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).

	Some supersets of 90edo include: {{EDOs\| 180, 270, 360, 450, 540, 630, 720, 810, 900... }}. Temperament mergers of these might produce [[90th-octave temperaments]] ''(see [[Fractional-octave temperaments]])''.		Some supersets of 90edo include: {{EDOs\| 180, 270, 360, 450, 540, 630, 720, 810, 900... }}. Of these, 270edo is notable for being the first to correct the tuning of harmonics [[3/1\|3]], [[7/1\|7]], [[11/1\|11]], and [[19/1\|19]] to near-just. Temperament mergers of these might produce [[90th-octave temperaments]] ''(see [[Fractional-octave temperaments]])''.

	== Interval table ==		== Interval table ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''90edo improv'' (2026)

2026-04-15T06:47:13Z

Music: Add Bryan Deister's ''90edo improv'' (2026)

← Older revision		Revision as of 06:47, 15 April 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)		* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)
			* [https://www.youtube.com/shorts/LdxUD1taOqI ''90edo improv''] (2026)

	; [[James Kukula]]		; [[James Kukula]]
	* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)		* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)

Hkm: /* Theory */

2026-03-16T02:30:27Z

Theory

← Older revision		Revision as of 02:30, 16 March 2026
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	== Theory ==		== Theory ==
	As an equal temperament, it [[tempering out\|tempers out]] 2048/2025 ([[diaschisma]]) in the 5-limit, [[245/243]] and [[3125/3087]] in the 7-limit, [[121/120]] and [[176/175]] in the 11-limit, and [[169/168]] and [[275/273]] in the 13-limit. It provides the [[optimal patent val]] for the 31 & 90 temperament in the 7-, 11- and 13-limit~~. Notably, it is the second lowest in a series of four consecutive edos to temper out the [[quartisma]]~~.		As an equal temperament, it [[tempering out\|tempers out]] 2048/2025 ([[diaschisma]]) in the 5-limit, [[245/243]] and [[3125/3087]] in the 7-limit, [[121/120]] and [[176/175]] in the 11-limit, and [[169/168]] and [[275/273]] in the 13-limit. It provides the [[optimal patent val]] for the 31 & 90 temperament in the 7-, 11- and 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

Yourmusic Productions: Add music.

2026-01-06T22:50:22Z

Add music.

← Older revision		Revision as of 22:50, 6 January 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)		* [https://www.youtube.com/shorts/0j33e4F-4jY ''microtonal improvisation in 90edo''] (2025)
			; [[James Kukula]]
			* [https://interdependentscience.blogspot.com/2026/01/90edo-diaschismic.html ''90edo diaschismic''] (2025)

BudjarnLambeth: /* Subsets and supersets */

2025-10-23T01:36:55Z

Subsets and supersets

← Older revision		Revision as of 01:36, 23 October 2025
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	Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).		Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).

	Some supersets of 90edo include: {{EDOs\| 180, 270, 360, 450, 540, 630, 720, 810, 900... }}. Temperament mergers of these might produce [[90th-octave temperaments]].		Some supersets of 90edo include: {{EDOs\| 180, 270, 360, 450, 540, 630, 720, 810, 900... }}. Temperament mergers of these might produce [[90th-octave temperaments]] ''(see [[Fractional-octave temperaments]])''.

	== Interval table ==		== Interval table ==

BudjarnLambeth: /* Theory */ add subsets section

2025-10-23T01:36:31Z

Theory: add subsets section

← Older revision		Revision as of 01:36, 23 October 2025
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|90}}		{{Harmonics in equal\|90}}

			=== Subsets and supersets ===
			Since 90 factors into primes as 2 x 3<sup>2</sup> × 5, 90 has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 }}.

			As a composite edo, the smallest subsets it lacks are subsets of [[4edo\|4]], [[7edo\|7]] and [[8edo\|8]], but 13\90 = 173.333{{cent}} offers a good approximation to 1\7 = 171.428{{c}}, and instead of 1\8 = 150{{cent}}, it has 27\80 = 146.667{{cent}}, serving a similar function.

			Like [[80edo]], this may offer a relatively unexplored strategy of "tempered [[detempering]]", a sort of middle path between complete detempering to JI (which lacks the simplifications and unique comma pumping and structural opportunities of tempering) and not detempering the small edo at all (which can lead to challenging interpretation of harmony if one's goal is approximation to JI).

			Some supersets of 90edo include: {{EDOs\| 180, 270, 360, 450, 540, 630, 720, 810, 900... }}. Temperament mergers of these might produce [[90th-octave temperaments]].

	== Interval table ==		== Interval table ==

BudjarnLambeth: /* Scales */

2025-10-23T01:18:59Z

Scales

← Older revision		Revision as of 01:18, 23 October 2025
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	* Amulet{{idiosyncratic}}, (approximated from [[magic]] in [[25edo]]): 7 4 7 7 4 7 11 7 7 4 7 11 7		* Amulet{{idiosyncratic}}, (approximated from [[magic]] in [[25edo]]): 7 4 7 7 4 7 11 7 7 4 7 11 7
	* Decimetra[20]: 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2		* Decimetra[20]: 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2
	* [[Maeve Gutierrez\|Gutierrez Moonglade scale]]		* [[Maeve Gutierrez\|Gutierrez Moonglade scale]]: 1 6 7 1 7 1 6 8 2 5 7 2 1 5 6 1 7 1 2 4 1 2 5 2

	== Instruments ==		== Instruments ==