Meantone intervals - Revision history

Fitzgerald Lee: Added links to intervals, 7-limit interpretations, phrasing

2026-02-27T04:43:34Z

Added links to intervals, 7-limit interpretations, phrasing

← Older revision		Revision as of 04:43, 27 February 2026
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	This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]]. Intervals in limits higher than 7 are in brackets.		This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]]. Intervals in limits higher than 7 are in brackets.

	In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.		In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except arguably for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.

	In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.		In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.

Fitzgerald Lee at 04:34, 27 February 2026

2026-02-27T04:34:01Z

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FloraC: Correct an obvious negligence

2025-12-22T10:49:47Z

Correct an obvious negligence

← Older revision		Revision as of 10:49, 22 December 2025
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	This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]].		This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]].

	In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. ~~None~~ of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.		In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.

	In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.		In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.

Overthink: grammar

2025-12-22T06:29:27Z

grammar

← Older revision		Revision as of 06:29, 22 December 2025
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	This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]].		This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]].

	In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit ~~descriptions~~.		In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.

	In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.		In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.

FloraC: Cleanup

2025-06-04T09:48:41Z

Cleanup

← Older revision		Revision as of 09:48, 4 June 2025
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	~~This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone~~\|~~septimal meantone]], which includes the entire [[7-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table~~ of ~~[[quarter-comma~~ meantone~~]] intervals and the table of [[31edo #Intervals\|31 edo~~ intervals~~]].~~		{{Wikipedia\|List of meantone intervals}}

	In [[~~12edo~~]] the ~~diminished second vanishes, so this cornucopia~~ of intervals ~~collapses to a mere 12. None~~ of the intervals ~~is inherently septimal in 12edo, because they all have simpler 5-limit descriptions~~.		This table shows all the simple intervals of [[POTE]] [[Meantone family #Septimal meantone\|septimal meantone]], which includes the entire [[7-odd-limit]] [[tonality diamond]]. Other relevant tables of meantone intervals are the table of [[quarter-comma meantone]] intervals and the table of [[31edo #Intervals\|31edo intervals]].

	In [[19edo]], in contrast, the ''double'' diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.		In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

			In [[19edo]], in contrast, the ''double''-diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because [[49/48]] vanishes.

	More complex meantone tunings such as [[31edo]] distinguish all intervals listed on this table.		More complex meantone tunings such as [[31edo]] distinguish all intervals listed on this table.

	~~See also [[Wikipedia: List of meantone intervals]]~~

	{\| class="wikitable right-2"		{\| class="wikitable right-2"
	\|-		\|-
	! Name		! Name
	! Size <br>(cents)		! Size<br>(cents)
	! Ratios		! Ratios
	\|-		\|-
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	\| Augmented unison (A1)		\| Augmented unison (A1)
	\| 75.46		\| 75.46
	\| 28/~~27~~~25/24~~~21~~/20		\| 21/20, 25/24, 28/27
	\|-		\|-
	\| Double augmented unison (AA1)		\| Double-augmented unison (AA1)
	\| 150.93		\| 150.93
	\| Close to 12/11		\| Close to 12/11
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	\| Diminished second (d2)		\| Diminished second (d2)
	\| 42.06		\| 42.06
	\| ~~128~~/~~125~~~64/63~~~50~~/~~49~36/35~~		\| 36/35, 50/49, 64/63, 128/125
	\|-		\|-
	\| Minor second (m2)		\| Minor second (m2)
	\| 117.53		\| 117.53
	\| 16/15~~~15/14~~		\| 15/14, 16/15
	\|-		\|-
	\| Major second (M2)		\| Major second (M2)
	\| 192.99		\| 192.99
	\| 10/9~~~9/8~~~28/25		\| 9/8, 10/9, 28/25
	\|-		\|-
	\| Augmented second (A2)		\| Augmented second (A2)
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	! colspan="3" \| Fourths		! colspan="3" \| Fourths
	\|-		\|-
	\| Double diminished fourth (dd4)		\| Double-diminished fourth (dd4)
	\| 352.58		\| 352.58
	\| Close to 11/9		\| Close to 11/9
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	\| 7/5		\| 7/5
	\|-		\|-
	\| Double augmented fourth (AA4)		\| Double-augmented fourth (AA4)
	\| 654.43		\| 654.43
	\| Close to 16/11		\| Close to 16/11
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	! colspan="3" \| Fifths		! colspan="3" \| Fifths
	\|-		\|-
	\| Double diminished fifth (dd5)		\| Double-diminished fifth (dd5)
	\| 545.57		\| 545.57
	\| Close to 11/8		\| Close to 11/8
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	\| 14/9 (a bit 11/7-ish)		\| 14/9 (a bit 11/7-ish)
	\|-		\|-
	\| Double augmented fifth (AA5)		\| Double-augmented fifth (AA5)
	\| 847.42		\| 847.42
	\| Close to 18/11		\| Close to 18/11
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	\| Minor seventh (m7)		\| Minor seventh (m7)
	\| 1007.01		\| 1007.01
	\| 16/9~~~9/5~~~25/14		\| 9/5, 16/9, 25/14
	\|-		\|-
	\| Major seventh (M7)		\| Major seventh (M7)
	\| 1082.47		\| 1082.47
	\| 15/8~28/15		\| 15/8, 28/15
	\|-		\|-
	\| Augmented seventh (A7)		\| Augmented seventh (A7)
	\| 1157.94		\| 1157.94
	\| 35/18~49/25~63/32		\| 35/18, 49/25, 63/32
	\|-		\|-
	! colspan="3" \| Octaves		! colspan="3" \| Octaves
	\|-		\|-
	\| Double diminished octave (dd8)		\| Double-diminished octave (dd8)
	\| 1049.07		\| 1049.07
	\| Close to 11/6		\| Close to 11/6
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	\| Diminished octave (d8)		\| Diminished octave (d8)
	\| 1124.54		\| 1124.54
	\| 27/14~48/25~~~40/21~~		\| 27/14, 40/21, 48/25
	\|-		\|-
	\| Perfect octave (P8)		\| Perfect octave (P8)

Xenllium at 08:18, 18 April 2023

2023-04-18T08:18:03Z

Show changes

BudjarnLambeth at 11:43, 15 April 2023

2023-04-15T11:43:58Z

← Older revision		Revision as of 11:43, 15 April 2023
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	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:Lists]]		[[Category:Lists of intervals]]

Fredg999 category edits: Moving from Category:List to Category:Lists using Cat-a-lot

2022-02-26T04:55:22Z

Moving from Category:List to Category:Lists using Cat-a-lot

← Older revision		Revision as of 04:55, 26 February 2022
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	[[Category:Meantone]]		[[Category:Meantone]]
	[[Category:~~List~~]]		[[Category:Lists]]

FloraC: Correction

2021-01-28T14:44:30Z

Correction

← Older revision		Revision as of 14:44, 28 January 2021
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	\|-		\|-
	\| Double diminished fourth (dd4)		\| Double diminished fourth (dd4)
	\| ~~343~~.5		\| 352.5
	\| 49/~~40~60/49~~		\| Close to 11/9
	\|-		\|-
	\| Diminished fourth (d4)		\| Diminished fourth (d4)
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	\|-		\|-
	\| Double augmented fifth (AA5)		\| Double augmented fifth (AA5)
	\| ~~842~~.5		\| 847.5
	\| 49/~~30~80/49~~		\| Close to 18/11
	\|-		\|-
	! colspan="3" \| Sixths		! colspan="3" \| Sixths

FloraC: Table formatting

2021-01-28T14:39:19Z

Table formatting

Show changes