240edo - 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"

2026-03-13T13:30:06Z

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 13:30, 13 March 2026
Line 68:		Line 68:
	\| [[Compton]]		\| [[Compton]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|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: /* Regular temperament properties */ - user-namespace temp

2025-11-15T09:59:21Z

Regular temperament properties: - user-namespace temp

← Older revision		Revision as of 09:59, 15 November 2025
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	\| 104976/78125		\| 104976/78125
	\| [[Countermeantone]]		\| [[Countermeantone]]
	\|-
	~~\| 12~~
	~~\| 1\240~~
	~~\| 5.00~~
	~~\| ?~~
	~~\| [[Substitute harmonic#Romcom\|Romcom]]~~
	\|-		\|-
	\| 12		\| 12

FloraC: Misc. cleanup

2025-11-15T09:58:50Z

Misc. cleanup

← Older revision		Revision as of 09:58, 15 November 2025
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	== Theory ==		== Theory ==
	240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705{{c}} sharp fifth inherited from [[80edo]].		240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for [[harmonic]] [[3/1\|3]] is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705{{c}} sharp fifth inherited from [[80edo]].

	Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out\|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.		Although no longer consistent to the higher limits, 240edo's [[patent val]] [[tempering out\|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] with harmonics 3, [[5/1\|5]], [[7/1\|7]] having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.

	240edo is similar to [[197edo]] in terms of intonation in the 7-limit. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 43 & 197 temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.		240edo is similar to [[197edo]] in terms of intonation in the 7-limit. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the {{nowrap\| 43 & 197 }} temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.

	For higher limits, 240edo tempers out [[243/242]] in the 11-limit, [[351/350]] in the 13-limit, and [[375/374]] in the 17-limit, and adding these to the mix converts marvel temperament into [[spectacle]] temperament. This is still a ~~planar~~ temperament, but more complex as two undecimal neutral thirds of [[11/9]] make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350-cent interval often employed in [[24edo]] versions of [[Arabic, Turkish, Persian music\|Arabic music]].)		For higher limits, 240edo tempers out [[243/242]] in the 11-limit, [[351/350]] in the 13-limit, and [[375/374]] in the 17-limit, and adding these to the mix converts marvel temperament into [[spectacle]] temperament. This is still a [[rank-3 temperament]], but more complex as two undecimal neutral thirds of [[11/9]] make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350-cent interval often employed in [[24edo]] versions of [[Arabic, Turkish, Persian music\|Arabic music]].)

	~~=== Subsets and supersets ===~~
	~~240edo is the 12th [[highly composite edo]], with subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 }}.~~

	~~In addition, as every fifth step of [[1200edo]], it is the largest highly composite edo expressible in integer cents.~~

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|240}}		{{Harmonics in equal\|240}}

			=== Subsets and supersets ===
			240edo is the 12th [[highly composite edo]], with subset edos {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 }}. In addition, as every fifth step of [[1200edo]], it is the largest highly composite edo expressible in integer cents.

	== Interval table ==		== Interval table ==
Line 28:		Line 26:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\| 2.3.5		\| 2.3.5
	\| 531441/524288, {{monzo\| -29 -11 20 }}		\| 531441/524288, {{monzo\| -29 -11 20 }}
	\| {{~~mapping~~\| 240 380 557 }}		\| {{Mapping\| 240 380 557 }}
	\| 0.5998		\| 0.5998
	\| 0.5044		\| 0.5044
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	\|+ style="font-size: 105%;" \| 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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	\|-		\|-
	\| 12		\| 12
	\| 77\240<br />(3\240)		\| 77\240<br>(3\240)
	\| 385.00<br />(15.00)		\| 385.00<br>(15.00)
	\| 5/4<br />(81/80)		\| 5/4<br>(81/80)
	\| [[Compton]]		\| [[Compton]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
Line 90:		Line 88:

	== Instruments ==		== Instruments ==

	A [[Lumatone mapping for 240edo]] is now available.		A [[Lumatone mapping for 240edo]] is now available.

	== Music ==		== Music ==
	; [[Chris Charles]] (via [https://www.youtube.com/@microtonalguitar Microtonal Guitar - Tolgahan Çoğulu])		; [[Chris Charles]] (via [https://www.youtube.com/@microtonalguitar Microtonal Guitar - Tolgahan Çoğulu])
	* [https://www.youtube.com/watch?v=6GoGlj5IyZc ''Balinese Gamelan Music on Microtonal Guitar - Chris Charles''] (2017) (Uses a 5-tone subset of 240edo for all three pieces performed in the ~~recording — as~~ explained in the video description: "''The scale we used in the piece: Pelog Selisir: D, Eb +30 F -15 A -30 Bb -15''".)		* [https://www.youtube.com/watch?v=6GoGlj5IyZc ''Balinese Gamelan Music on Microtonal Guitar - Chris Charles''] (2017) (Uses a 5-tone subset of 240edo for all three pieces performed in the recording—as explained in the video description: "''The scale we used in the piece: Pelog Selisir: D, Eb +30 F -15 A -30 Bb -15''".)

	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/Nu-xBrsd8_o ''microtonal improvisation in 240edo''] (2025)		* [https://www.youtube.com/shorts/Nu-xBrsd8_o ''microtonal improvisation in 240edo''] (2025)

	== ~~Links~~ ==		== Trivia ==
	[[Shaahin Mohajeri]], an [[Arabic, Turkish, Persian music\|Iranian]] Tombak player and composer, calls his personal [https://sites.google.com/site/240edo/ Google site] "240edo", where he makes the point that five cents is a size close to the [[~~Just~~-~~noticeable_difference\|just~~ noticeable difference]] between pitches.		[[Shaahin Mohajeri]], an [[Arabic, Turkish, Persian music\|Iranian]] Tombak player and composer, calls his personal [https://sites.google.com/site/240edo/ Google site] "240edo", where he makes the point that five cents is a size close to the [[just-noticeable difference]] between pitches.

	[[Category:Compton]]		[[Category:Compton]]
	[[Category:Marvel]]		[[Category:Marvel]]

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 240edo is available

2025-11-15T08:25:37Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 240edo is available

← Older revision		Revision as of 08:25, 15 November 2025
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	* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 – [[Compton]][24]		* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 – [[Compton]][24]
	* 23 31 80 23 83 – [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning		* 23 31 80 23 83 – [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning

			== Instruments ==

			A [[Lumatone mapping for 240edo]] is now available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Change formatting of existing entry to standard for Music sections; add Bryan Deister's ''microtonal improvisation in 240edo'' (2025)

2025-11-14T00:04:45Z

Music: Change formatting of existing entry to standard for Music sections; add Bryan Deister's ''microtonal improvisation in 240edo'' (2025)

← Older revision		Revision as of 00:04, 14 November 2025
Line 90:		Line 90:

	== Music ==		== Music ==
	~~The video~~ [https://www.youtube.com/watch?v=6GoGlj5IyZc ''Balinese Gamelan Music on Microtonal Guitar - Chris Charles''] ~~on the YouTube channel [https://www.youtube.com/@microtonalguitar Microtonal Guitar - Tolgahan Çoğulu] uses~~ a 5-tone subset of 240edo for all three pieces performed in the recording~~. As~~ explained in the video description: "''The scale we used in the piece: Pelog Selisir: D, Eb +30 F -15 A -30 Bb -15''".		; [[Chris Charles]] (via [https://www.youtube.com/@microtonalguitar Microtonal Guitar - Tolgahan Çoğulu])
			* [https://www.youtube.com/watch?v=6GoGlj5IyZc ''Balinese Gamelan Music on Microtonal Guitar - Chris Charles''] (2017) (Uses a 5-tone subset of 240edo for all three pieces performed in the recording — as explained in the video description: "''The scale we used in the piece: Pelog Selisir: D, Eb +30 F -15 A -30 Bb -15''".)

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/Nu-xBrsd8_o ''microtonal improvisation in 240edo''] (2025)

	== Links ==		== Links ==

ArrowHead294 at 14:23, 20 February 2025

2025-02-20T14:23:10Z

← Older revision		Revision as of 14:23, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|240~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705~~-cent~~ sharp fifth inherited from [[80edo]].		240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705{{c}} sharp fifth inherited from [[80edo]].

	Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out\|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.		Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out\|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.

FloraC: /* Theory */ cleanup

2025-01-17T15:41:42Z

Theory: cleanup

← Older revision		Revision as of 15:41, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	240edo ~~is [[consistent]] in the [[5-odd-limit]] and~~ notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, ~~its~~ mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]~~, with alternate~~ mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].		240edo notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, it is only [[consistent]] in the [[5-odd-limit]]. Its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]]; its alternative mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].

	Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempers out]] the [[225/224]] in the 7-limit, ~~supporting~~ [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.		Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempering out\|tempers out]] the [[225/224]] in the 7-limit, [[support]]ing [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.

	~~From a regular temperament theory perspective in the 7-limit,~~ 240edo is similar to [[197edo]]. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 43 & 197 temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.		240edo is similar to [[197edo]] in terms of intonation in the 7-limit. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 43 & 197 temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.

	For higher limits, 240edo tempers out [[243/242]] in the 11-limit, [[351/350]] in the 13-limit, and [[375/374]] in the 17-limit, and adding these to the mix converts marvel temperament into [[spectacle]] temperament. This is still a planar temperament, but more complex as two undecimal neutral thirds of [[11/9]] make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350-cent interval often employed in [[24edo]] versions of [[Arabic, Turkish, Persian music\|Arabic music]].)		For higher limits, 240edo tempers out [[243/242]] in the 11-limit, [[351/350]] in the 13-limit, and [[375/374]] in the 17-limit, and adding these to the mix converts marvel temperament into [[spectacle]] temperament. This is still a planar temperament, but more complex as two undecimal neutral thirds of [[11/9]] make up a fifth (which is in fact the same fifth as that of 12edo, and the 11/9 is the 350-cent interval often employed in [[24edo]] versions of [[Arabic, Turkish, Persian music\|Arabic music]].)

ArrowHead294 at 15:00, 16 January 2025

2025-01-16T15:00:55Z

← Older revision		Revision as of 15:00, 16 January 2025
Line 5:		Line 5:
	240edo is [[consistent]] in the [[5-odd-limit]] and notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]], with alternate mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].		240edo is [[consistent]] in the [[5-odd-limit]] and notably provides the [[optimal patent val]] for the 5-limit [[compton]] temperament, the rank-2 temperament associated with the [[Pythagorean comma]]. However, its mapping for 3 is not well approximated, meaning it is a [[dual-fifth system]], with alternate mapping for 3/2 is the 705-cent sharp fifth inherited from [[80edo]].

	Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[~~tempering out\|~~tempers out]] the [[225/224]] in the 7-limit, supporting [[marvel]] ~~temperaments~~ with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.		Although no longer consistent to to the higher limits, 240edo's [[patent val]] [[tempers out]] the [[225/224]] in the 7-limit, supporting [[marvel]] with harmonics 3, 5, 7 having less than two cents of error. Retuning 5-limit scales to 240edo is a simple way to to make them function as 7-limit scales while retaining very accurate tuning.

	From a regular temperament theory perspective in the 7-limit, 240edo is similar to [[197edo]]. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 43 & 197 temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.		From a regular temperament theory perspective in the 7-limit, 240edo is similar to [[197edo]]. The main difference is that 197edo, despite a flatter third, gives generally better results and may be preferred, whitherfore a compromise between good results and an accurate 5 may be worked out by means of retuning 5-limit scales to the 43 & 197 temperament, which has a comma basis {225/224, {{monzo\| -49 19 -10 15 }}} in the 7-limit.
Line 22:		Line 22:
	See [[Table of 240edo intervals]].		See [[Table of 240edo intervals]].

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	\|-		\|-
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	\| [[Compton]]		\| [[Compton]]
	\|}		\|}
	<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 ==
	; Scales derived from marvel and spectacle temperaments		; Scales derived from marvel and spectacle temperaments
	* 23 17 23 14 23 17 23 23 14 26 14 23 ~~–~~ [[Alexander Ellis\|Ellis]]'s [[Duodene]] genus [33355] retuned to 240edo		* 23 17 23 14 23 17 23 23 14 26 14 23 – [[Alexander Ellis\|Ellis]]'s [[Duodene]] genus [33355] retuned to 240edo
	* 23 17 14 23 23 17 23 23 14 17 23 23 ~~–~~ [[Carl Lumma]]'s scale		* 23 17 14 23 23 17 23 23 14 17 23 23 – [[Carl Lumma]]'s scale
	* 14 9 14 17 23 23 23 17 14 9 14 23 17 23 ~~–~~ Pum[14] scale		* 14 9 14 17 23 23 23 17 14 9 14 23 17 23 – Pum[14] scale
	* 16 10 7 7 16 7 7 16 7 10 7 16 7 7 16 7 7 10 16 7 7 16 7 ~~–~~ Ellis duodene union [[11/9]] times the duodene		* 16 10 7 7 16 7 7 16 7 10 7 16 7 7 16 7 7 10 16 7 7 16 7 – Ellis duodene union [[11/9]] times the duodene

	=== Other scales ===		=== Other scales ===
	* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 ~~–~~ [[Compton]][24]		* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 – [[Compton]][24]
	* 23 31 80 23 83 ~~–~~ [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning		* 23 31 80 23 83 – [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning

	== Music ==		== Music ==

ArrowHead294 at 12:03, 16 November 2024

2024-11-16T12:03:49Z

← Older revision		Revision as of 12:03, 16 November 2024
Line 23:		Line 23:

	==Regular temperament properties==		==Regular temperament properties==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
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	\| 0.5044		\| 0.5044
	\| 10.09		\| 10.09
	~~{{comma basis end}~~}		\|}

	=== 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
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	\| 5/4<br />(81/80)		\| 5/4<br />(81/80)
	\| [[Compton]]		\| [[Compton]]
	~~{{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 05:37, 16 November 2024

2024-11-16T05:37:15Z

← Older revision		Revision as of 05:37, 16 November 2024
Line 23:		Line 23:

	==Regular temperament properties==		==Regular temperament properties==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 39:		Line 31:
	\| 0.5044		\| 0.5044
	\| 10.09		\| 10.09
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 12		\| 12
	\| 77\240<br>(3\240)		\| 77\240<br />(3\240)
	\| 385.00<br>(15.00)		\| 385.00<br />(15.00)
	\| 5/4<br>(81/80)		\| 5/4<br />(81/80)
	\| [[Compton]]		\| [[Compton]]
	\|}		{{rank-2 end}}
	~~<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 ==

	; Scales derived from marvel and spectacle temperaments		; Scales derived from marvel and spectacle temperaments
	* 23 17 23 14 23 17 23 23 14 26 14 23 - [[Alexander Ellis\|Ellis]]'s [[Duodene]] genus [33355] retuned to 240edo		* 23 17 23 14 23 17 23 23 14 26 14 23 – [[Alexander Ellis\|Ellis]]'s [[Duodene]] genus [33355] retuned to 240edo
	* 23 17 14 23 23 17 23 23 14 17 23 23 - [[Carl Lumma]]'s scale		* 23 17 14 23 23 17 23 23 14 17 23 23 – [[Carl Lumma]]'s scale
	* 14 9 14 17 23 23 23 17 14 9 14 23 17 23 - Pum[14] scale		* 14 9 14 17 23 23 23 17 14 9 14 23 17 23 – Pum[14] scale
	* 16 10 7 7 16 7 7 16 7 10 7 16 7 7 16 7 7 10 16 7 7 16 7 - Ellis duodene union [[11/9]] times the duodene		* 16 10 7 7 16 7 7 16 7 10 7 16 7 7 16 7 7 10 16 7 7 16 7 – Ellis duodene union [[11/9]] times the duodene

	~~; Other scales~~

	* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 - [[Compton]][24]		=== Other scales ===
	* 23 31 80 23 83 - [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning		* 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 17 3 – [[Compton]][24]
			* 23 31 80 23 83 – [[Indonesian\|Balinese]] pentatonic [[pelog]] scale; [[Tolgahan Çoğulu]]'s tuning

	== Music ==		== Music ==