128edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:31:48Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:31, 13 March 2026
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	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:18:01Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:18, 11 April 2025
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	== Theory ==		== Theory ==
			The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap\|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap\|60 & 68}} temperament.

	See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)		See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)

	The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap\|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap\|60 & 68}} temperament. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.		Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:42:18Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:42, 11 April 2025
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	== Theory ==		== Theory ==
	~~The equal temperament~~ [~~[tempering out\|tempers out]] 2109375~~/~~2097152 ([[semicomma]]) in the [[5-limit]]; [[245~~/~~243]], [[1029~~/~~1024~~]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap\|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap\|60 & 68}} temperament.		See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)

	~~See also~~ [~~https:~~//~~www~~.~~youtube~~.~~com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone~~] ~~(Demo by Philipp Gerschlauer~~)		The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap\|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap\|60 & 68}} temperament. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.		Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 17:00, 18 February 2025

2025-02-18T17:00:20Z

← Older revision		Revision as of 17:00, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|128~~}} It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes.		{{ED intro}} It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes.

	== Theory ==		== Theory ==

ArrowHead294 at 16:47, 15 January 2025

2025-01-15T16:47:12Z

← Older revision		Revision as of 16:47, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the 41 & 87 temperament, as well as for 7-limit [[fourfives]], the 60 & 68 temperament.		The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap\|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap\|60 & 68}} temperament.

	See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)		See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)
Line 71:		Line 71:
	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T13:20:00Z

Partial undo

← Older revision		Revision as of 13:20, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 01:35, 16 November 2024

2024-11-16T01:35:52Z

← Older revision		Revision as of 01:35, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 4/3		\| 4/3
	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:53, 16 November 2024

2024-11-16T00:53:55Z

← Older revision		Revision as of 00:53, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+~~Rank~~-2 temperaments by ~~generators~~		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 4		\| 4
	\| 53\128<br>(11\128)		\| 53\128<br />(11\128)
	\| 496.875<br>(103.125)		\| 496.875<br />(103.125)
	\| 4/3		\| 4/3
	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	\|}		\|}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==

FloraC: Cleanup

2024-05-27T17:30:03Z

Cleanup

← Older revision		Revision as of 17:30, 27 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|128}} It is notable for being the equal division corresponding to a standard MIDI piano roll of 128 notes.		{{EDO intro\|128}} It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes.

	== Theory ==		== Theory ==
	~~128edo~~ [[tempers out]] 2109375/2097152 in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the 41 & 87 temperament, as well as for 7-limit [[fourfives]], the 60 & 68 temperament.		The equal temperament [[tempering out\|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the 41 & 87 temperament, as well as for 7-limit [[fourfives]], the 60 & 68 temperament.

	See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)		See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|128~~\|columns=11~~}}		{{Harmonics in equal\|128}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
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	\|+Rank-2 temperaments by generators		\|+Rank-2 temperaments by generators
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Undim]] (7-limit)		\| [[Undim]] (7-limit)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

Eliora: /* Subsets and supersets */ remove the statement since that is already said in the intro

2023-06-30T14:02:58Z

Subsets and supersets: remove the statement since that is already said in the intro

← Older revision		Revision as of 14:02, 30 June 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.		Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs\| 2, 4, 8, 16, 32, and 64 }}.

	~~=== Miscellaneous properties ===~~
	Being the power of two closest to division of the octave by the Germanic [[Wikipedia: long hundred\|long hundred]], 128edo has a unit step which is the binary (fine) relative cent (or relative heptamu in MIDI terms) of [[1edo]].

	== Regular temperament properties ==		== Regular temperament properties ==