150edo - 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"

2026-03-13T13:31:34Z

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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	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	\|}		\|}
	<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

ArrowHead294 at 17:07, 18 February 2025

2025-02-18T17:07:29Z

← Older revision		Revision as of 17:07, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|150~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	150edo is [[contorted]] in the 5-limit, [[tempering out]] the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. However, every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88 ~~cents~~ provides a generator.		150edo is [[contorted]] in the 5-limit, [[tempering out]] the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. However, every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88{{c}} provides a generator.

	The equal temperament tempers out [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[385/384]], [[896/891]], and [[1375/1372]] in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit.		The equal temperament tempers out [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[385/384]], [[896/891]], and [[1375/1372]] in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit.

ArrowHead294 at 16:15, 15 January 2025

2025-01-15T16:15:46Z

← Older revision		Revision as of 16:15, 15 January 2025
Line 42:		Line 42:
	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:19:41Z

Partial undo

← Older revision		Revision as of 13:19, 16 November 2024
Line 15:		Line 15:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{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
Line 34:		Line 41:
	\| 15/13<br />(176/175)		\| 15/13<br />(176/175)
	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	~~{{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

ArrowHead294 at 01:36, 16 November 2024

2024-11-16T01:36:54Z

← Older revision		Revision as of 01:36, 16 November 2024
Line 15:		Line 15:
	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| 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
Line 41:		Line 34:
	\| 15/13<br />(176/175)		\| 15/13<br />(176/175)
	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:54, 16 November 2024

2024-11-16T00:54:44Z

← Older revision		Revision as of 00:54, 16 November 2024
Line 16:		Line 16:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ 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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	\|-		\|-
	\| 10		\| 10
	\| 31\150<br>(1\150)		\| 31\150<br />(1\150)
	\| 248.00<br>(8.00)		\| 248.00<br />(8.00)
	\| 15/13<br>(176/175)		\| 15/13<br />(176/175)
	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	\|}		\|}
	~~<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}}

FloraC: Rework and cleanup

2024-05-14T09:29:21Z

Rework and cleanup

← Older revision		Revision as of 09:29, 14 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~Every~~ 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out [[245/243]], [[~~4000~~/~~3969~~]] and [[~~2401~~/~~2400~~]] in the 7-limit, [[~~896~~/~~891~~]], [[~~385~~/~~384~~]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. It provides a good tuning for octacot, for which 88 cents provides a generator.		150edo is [[contorted]] in the 5-limit, [[tempering out]] the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. However, every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88 cents provides a generator.

			The equal temperament tempers out [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[385/384]], [[896/891]], and [[1375/1372]] in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 16:		Line 18:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 39:		Line 41:
	\| [[Decoid]] (150e)		\| [[Decoid]] (150e)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: Rework temps table

2023-08-02T06:45:51Z

Rework temps table

← Older revision		Revision as of 06:45, 2 August 2023
Line 31:		Line 31:
	\| 232.00		\| 232.00
	\| 8/7		\| 8/7
	\| [[~~Mothra~~]] (~~150be~~)		\| [[Quadrawell]]
			\|-
			\| 10
			\| 31\150<br>(1\150)
			\| 248.00<br>(8.00)
			\| 15/13<br>(176/175)
			\| [[Decoid]] (150e)
	\|}		\|}

FloraC: Cleanup; +subsets and supersets

2023-08-02T06:38:55Z

Cleanup; +subsets and supersets

← Older revision		Revision as of 06:38, 2 August 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|150}}		{{EDO intro\|150}}
	==Theory==
	Every 11th step of 150edo is equal to the [[~~88cET\|~~88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the ~~134~~-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[~~75edo\|~~75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for ~~[[Tetracot_family#Octacot\|Tetracot family]]~~, for which 88 cents provides a generator.		== Theory ==
			Every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out [[245/243]], [[4000/3969]] and [[2401/2400]] in the 7-limit, [[896/891]], [[385/384]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. It provides a good tuning for octacot, for which 88 cents provides a generator.

			=== Odd harmonics ===
	{{Harmonics in equal\|150\|columns=10}}		{{Harmonics in equal\|150\|columns=10}}
	==Regular temperament properties==
	===Rank-2 temperaments===		=== Subsets and supersets ===
			Since 150 factors into 2 × 3 × 5<sup>2</sup>, 150edo has subset edos {{EDOs\| 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75 }}.

			== Regular temperament properties ==
			=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
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	\| 8/7		\| 8/7
	\| [[Mothra]] (150be)		\| [[Mothra]] (150be)
	~~[[Category:Equal divisions of the octave~~\|~~###]] <!-- 3-digit number -->~~		\|}

Godtone: add tuning profile

2023-08-02T05:12:03Z

add tuning profile

← Older revision		Revision as of 05:12, 2 August 2023
Line 3:		Line 3:
	==Theory==		==Theory==
	Every 11th step of 150edo is equal to the [[88cET\|88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo\|75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot_family#Octacot\|Tetracot family]], for which 88 cents provides a generator.		Every 11th step of 150edo is equal to the [[88cET\|88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo\|75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot_family#Octacot\|Tetracot family]], for which 88 cents provides a generator.
			{{Harmonics in equal\|150\|columns=10}}
	==Regular temperament properties==		==Regular temperament properties==
	===Rank-2 temperaments===		===Rank-2 temperaments===