1ed88c - Revision history

BudjarnLambeth: /* Scales */ capitalisation

2025-09-28T03:18:06Z

Scales: capitalisation

← Older revision		Revision as of 03:18, 28 September 2025
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	== Scales ==		== Scales ==
	* [[~~symmetrical~~ scales of 88cET]]		* [[Symmetrical scales of 88cET]]

	== Music ==		== Music ==

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:20:43Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:20, 1 August 2025
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	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	~~[[Category:Edonoi]]~~

Fredg999: Add "88cET" to lead section (probably the most common term, although it is not currently the page title due to Talk:CET)

2025-08-01T05:08:57Z

Add "88cET" to lead section (probably the most common term, although it is not currently the page title due to Talk:CET)

← Older revision		Revision as of 05:08, 1 August 2025
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	'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).		'''88-cent equal temperament''' ('''88cET''', also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).

	== Theory ==		== Theory ==

Fredg999: Markup

2025-07-28T18:55:06Z

Markup

← Older revision		Revision as of 18:55, 28 July 2025
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	== Theory ==		== Theory ==
	88-cent [[Equal-step tuning\|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered ~~chords~~]].		88-cent [[Equal-step tuning\|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered chord]]s.

	Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)<sup>4</sup>/(3/2)<sup>9</sup> = [[20000/19683]], the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)<sup>8</sup>/(3/2)<sup>11</sup> = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields [[245/243]], which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.		Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)<sup>4</sup>/(3/2)<sup>9</sup> = [[20000/19683]], the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)<sup>8</sup>/(3/2)<sup>11</sup> = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields [[245/243]], which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot.

Lériendil: Lériendil moved page 88cET to 1ed88c: consistency with other APSes

2025-04-10T21:28:40Z

Lériendil moved page 88cET to 1ed88c: consistency with other APSes

← Older revision	Revision as of 21:28, 10 April 2025
(No difference)

Sintel: Delete broken infobox

2025-04-10T21:17:05Z

Delete broken infobox

← Older revision		Revision as of 21:17, 10 April 2025
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	~~{{Infobox ET\|150ed2048}}~~
	'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).		'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).

Sintel: /* Intervals */ -nonet, todo:cleanup

2025-03-31T16:01:53Z

Intervals: -nonet, todo:cleanup

← Older revision		Revision as of 16:01, 31 March 2025
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	== Intervals ==		== Intervals ==
			{{todo\|cleanup\|inline=true}}
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
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	! Some Nearby <br>JI Intervals		! Some Nearby <br>JI Intervals
	\|-		\|-
	! colspan="6" \| ~~'''''~~first octave~~'''''~~		! colspan="6" \| first octave
	!		!
	\|-		\|-
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	\| 27/14=1137.039, 31/16=1145.036		\| 27/14=1137.039, 31/16=1145.036
	\|-		\|-
	! colspan="6" \| ~~'''''~~second octave~~'''''~~		! colspan="6" \| second octave
	!		!
	\|-		\|-
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	\| re		\| re
	\| 9/8=203.910		\| 9/8=203.910
	\|-
	~~! colspan="6" \|''second nonet''~~
	!
	\|-		\|-
	\| 17		\| 17
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	\| 63/32=1172.736, 160/81=1178.494		\| 63/32=1172.736, 160/81=1178.494
	\|-		\|-
	! colspan="6" \| ~~'''''~~third octave~~'''''~~		! colspan="6" \| third octave
	!		!
	\|-		\|-
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	\| maa		\| maa
	\| 81/64=407.820, 33/26=412.745, 14/11=417.508		\| 81/64=407.820, 33/26=412.745, 14/11=417.508
	\|-
	~~! colspan="6" \|''third nonet''~~
	!
	\|-		\|-
	\| 33		\| 33
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	\| 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463		\| 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463
	\|-		\|-
	! colspan="6" \| ~~'''''~~fourth octave~~'''''~~ (near match)		! colspan="6" \| fourth octave (near match)
	!		!
	\|-		\|-

Zhenlige: /* The 88cET family */

2024-10-23T03:11:55Z

The 88cET family

← Older revision		Revision as of 03:11, 23 October 2024
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	== The 88cET family ==		== The 88cET family ==
	[[Gary Morrison]] originally conceived of 88-cent equal temperament as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales – in particular, the 41ed8 (equivalent to taking three steps of [[41edo]] as a generator with no octaves), the 68ed32 (taking every 5 steps of [[68edo]]), the 109ed256 (taking every 8 steps of [[109edo]]), the 150ed2048 (taking every 11 steps of [[150edo]]), the [[8edf]], and the 11ed7/4, the latter being a preferred variant of composer and software designer [[X. J. Scott]]. These cousins of strict 88cET have single steps of approximately 87.805¢, 88.235¢, 88.073¢, 88¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below.		[[Gary Morrison]] originally conceived of 88-cent equal temperament as composed of steps of exactly 88¢. Nonetheless, composers have recognized a kinship between strict 88cET and some other scales – in particular, the 41ed8 (equivalent to taking three steps of [[41edo]] as a generator with no octaves), the 68ed32 (taking every 5 steps of [[68edo]]), the 109ed256 (taking every 8 steps of [[109edo]]), the 150ed2048 (taking every 11 steps of [[150edo]] i.e. the strict 88cET), the [[8edf]], and the 11ed7/4, the latter being a preferred variant of composer and software designer [[X. J. Scott]]. These cousins of strict 88cET have single steps of approximately 87.805¢, 88.235¢, 88.073¢, 88¢, 87.744¢, and 88.075¢, respectively. These small differences add up, as can be seen by examining the interval list below.

	== Intervals ==		== Intervals ==

BudjarnLambeth: + == Further reading == * Gary Morrison’s 2001 [https://soundcloud.com/mr88cet/sets/88cet-lecture-demo-gary-morrison-june-2001 lecture about 88cET]

2024-09-21T01:46:44Z

+ == Further reading == * Gary Morrison’s 2001 [https://soundcloud.com/mr88cet/sets/88cet-lecture-demo-gary-morrison-june-2001 lecture about 88cET]

← Older revision		Revision as of 01:46, 21 September 2024
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	* "To Become Water" from ''Mundoworld III'' (2021) – [https://open.spotify.com/track/39gEeGXprXGbAnbq0iyjMF Spotify] \| [https://www.youtube.com/watch?v=RBv9c_qlFEk YouTube]		* "To Become Water" from ''Mundoworld III'' (2021) – [https://open.spotify.com/track/39gEeGXprXGbAnbq0iyjMF Spotify] \| [https://www.youtube.com/watch?v=RBv9c_qlFEk YouTube]
	* "Mirage Passage" from ''Mirage Passage'' (2024) – [https://open.spotify.com/track/2hAyfHr9XPG96SZPvBNHPP Spotify] \| [https://www.youtube.com/watch?v=dWgmmK80I9U YouTube]		* "Mirage Passage" from ''Mirage Passage'' (2024) – [https://open.spotify.com/track/2hAyfHr9XPG96SZPvBNHPP Spotify] \| [https://www.youtube.com/watch?v=dWgmmK80I9U YouTube]

			== Further reading ==
			* [[Gary Morrison]]’s 2001 [https://soundcloud.com/mr88cet/sets/88cet-lecture-demo-gary-morrison-june-2001 lecture about 88cET]

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

ArrowHead294 at 23:27, 11 May 2024

2024-05-11T23:27:44Z

← Older revision		Revision as of 23:27, 11 May 2024
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	{{Infobox ET\|150ed2048}}		{{Infobox ET\|150ed2048}}

	'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).		'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step).

	== Theory ==		== Theory ==

	88-cent [[Equal-step tuning\|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered chords]].		88-cent [[Equal-step tuning\|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered chords]].