Marvel–syntonic equivalence continuum - Revision history

Xenllium at 12:46, 9 January 2026

2026-01-09T12:46:53Z

← Older revision		Revision as of 12:46, 9 January 2026
Line 3:		Line 3:
	The '''marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.		The '''marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.

	All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.		All temperaments in the continuum satisfy {{nowrap\|(225/224)<sup>''n''</sup> ~ 81/80}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"

FloraC: Cleanup. Mark as mathematical interest

2025-08-27T13:15:47Z

Cleanup. Mark as mathematical interest

← Older revision		Revision as of 13:15, 27 August 2025
Line 1:		Line 1:
	The '''Marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|Marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.		{{Mathematical interest}}

	All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel ~~family\|Marvel~~]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.		The '''marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.

			All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
Line 14:		Line 16:
	\|-		\|-
	\| 0		\| 0
	\| [[~~Didymus rank three family\|~~Didymus]]		\| [[Didymus]]
	\| [[81/80]]		\| [[81/80]]
	\| {{~~monzo~~\| -4 4 -1 0}}		\| {{Monzo\| -4 4 -1 0 }}
	\|-		\|-
	\| 1		\| 1
	\| [[~~Starling family\|~~Starling]]		\| [[Starling]]
	\| [[126/125]]		\| [[126/125]]
	\| {{~~monzo~~\|1 2 -3 1}}		\| {{Monzo\| 1 2 -3 1 }}
	\|-		\|-
	\| 2		\| 2
	\| [[~~Hemimean clan\|~~Hemimean]]		\| [[Hemimean]]
	\| [[3136/3125]]		\| [[3136/3125]]
	\| {{~~monzo~~\|6 0 -5 2}}		\| {{Monzo\| 6 0 -5 2 }}
	\|-		\|-
	\| 2.75		\| 2.75
	\| {{~~nowrap~~\|1205 &~~amp;~~ 612 &~~amp;~~ 1236}}		\| {{Nowrap\| 1205 & 612 & 1236 }}
	\| <abbr title="1087046872920473206784/1086294651031494140625">[very long]</abbr>		\| <abbr title="1087046872920473206784/1086294651031494140625">[very long]</abbr>
	\| {{~~monzo~~\|39 -6 -26 11}}		\| {{Monzo\| 39 -6 -26 11 }}
	\|-		\|-
	\| 3		\| 3
	\| [[Metric ~~microtemperaments\|Meter~~]]		\| [[Metric]]
	\| [[703125/702464]]		\| [[703125/702464]]
	\| {{~~monzo~~\|-11 2 7 -3}}		\| {{Monzo\| -11 2 7 -3 }}
	\|-		\|-
	\| ∞		\| ∞
	\| [[~~Marvel family\|~~Marvel]]		\| [[Marvel]]
	\| [[225/224]]		\| [[225/224]]
	\| {{~~monzo~~\|-5 2 2 -1}}		\| {{Monzo\| -5 2 2 -1 }}
	\|}		\|}

	[[Category:Equivalence continua]]		[[Category:Equivalence continua]]

ArrowHead294 at 14:24, 1 January 2025

2025-01-01T14:24:44Z

← Older revision		Revision as of 14:24, 1 January 2025
Line 1:		Line 1:
	The '''Marvel–syntonic equivalence continuum''' is a continuum of 7-limit rank-3 temperament families which equate a number of [[225/224\|Marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.		The '''Marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|Marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.

	All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel family\|Marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.		All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel family\|Marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.

ArrowHead294 at 14:24, 1 January 2025

2025-01-01T14:24:20Z

← Older revision		Revision as of 14:24, 1 January 2025
Line 29:		Line 29:
	\|-		\|-
	\| 2.75		\| 2.75
	\| 1205 & 612 & 1236		\| {{nowrap\|1205 & 612 & 1236}}
	\| <abbr title="1087046872920473206784/1086294651031494140625">[very long]</abbr>		\| <abbr title="1087046872920473206784/1086294651031494140625">[very long]</abbr>
	\| {{monzo\|39 -6 -26 11}}		\| {{monzo\|39 -6 -26 11}}

ArrowHead294 at 14:23, 1 January 2025

2025-01-01T14:23:52Z

← Older revision		Revision as of 14:23, 1 January 2025
Line 30:		Line 30:
	\| 2.75		\| 2.75
	\| 1205 & 612 & 1236		\| 1205 & 612 & 1236
	\| ~~colspan~~="2" \| {{monzo\|39 -6 -26 11}}		\| <abbr title="1087046872920473206784/1086294651031494140625">[very long]</abbr>
			\| {{monzo\|39 -6 -26 11}}
	\|-		\|-
	\| 3		\| 3

ArrowHead294 at 14:23, 1 January 2025

2025-01-01T14:23:00Z

← Older revision		Revision as of 14:23, 1 January 2025
Line 1:		Line 1:
	The '''~~marvel-syntonic~~ equivalence continuum''' is a continuum of 7-limit rank-3 temperament families which equate a number of [[225/224\|~~marvel~~ commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.		The '''Marvel–syntonic equivalence continuum''' is a continuum of 7-limit rank-3 temperament families which equate a number of [[225/224\|Marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.

	All temperaments in the continuum satisfy (81/80)<sup>''n''</sup> ~ 64/63. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel family\|~~marvel~~]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.~~788851128489581...~~, and temperaments having ''n'' near this value will be more accurate.		All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel family\|Marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
	\|+ Temperament families in the continuum		\|+ style="font-size: 105%;" \| Temperament families in the continuum
	\|-		\|-
	! rowspan="2" \| ''n''		! rowspan="2" \| ''n''
Line 30:		Line 30:
	\| 2.75		\| 2.75
	\| 1205 & 612 & 1236		\| 1205 & 612 & 1236
	\|colspan=2\| {{monzo\|39 -6 -26 11}}		\| colspan="2" \| {{monzo\|39 -6 -26 11}}
	\|-		\|-
	\| 3		\| 3

ArrowHead294: ArrowHead294 moved page Marvel-syntonic equivalence continuum to Marvel–syntonic equivalence continuum

2025-01-01T14:21:36Z

ArrowHead294 moved page Marvel-syntonic equivalence continuum to Marvel–syntonic equivalence continuum

← Older revision	Revision as of 14:21, 1 January 2025
(No difference)

Inthar at 15:00, 21 June 2023

2023-06-21T15:00:55Z

← Older revision		Revision as of 15:00, 21 June 2023
Line 14:		Line 14:
	\|-		\|-
	\| 0		\| 0
	\| [[~~Meantone~~ family\|~~Meantone~~]]		\| [[Didymus rank three family\|Didymus]]
	\| [[81/80]]		\| [[81/80]]
	\| {{monzo\| -4 4 -1 0}}		\| {{monzo\| -4 4 -1 0}}

Inthar at 15:22, 20 June 2023

2023-06-20T15:22:27Z

← Older revision		Revision as of 15:22, 20 June 2023
Line 30:		Line 30:
	\| 2.75		\| 2.75
	\| 1205 & 612 & 1236		\| 1205 & 612 & 1236
	\|~~rowspan~~=2\| {{monzo\|39 -6 -26 11}}		\|colspan=2\| {{monzo\|39 -6 -26 11}}
	\|-		\|-
	\| 3		\| 3

Inthar at 15:22, 20 June 2023

2023-06-20T15:22:15Z

← Older revision		Revision as of 15:22, 20 June 2023
Line 27:		Line 27:
	\| [[3136/3125]]		\| [[3136/3125]]
	\| {{monzo\|6 0 -5 2}}		\| {{monzo\|6 0 -5 2}}
			\|-
			\| 2.75
			\| 1205 & 612 & 1236
			\|rowspan=2\| {{monzo\|39 -6 -26 11}}
	\|-		\|-
	\| 3		\| 3

← Older revision		Revision as of 12:46, 9 January 2026
Line 3:		Line 3:
	The '''marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.		The '''marvel–syntonic equivalence continuum''' is a [[equivalence continuum\|continuum]] of 7-limit rank-3 temperament families which equate a number of [[225/224\|marvel commas (225/224)]] with a [[81/80\|syntonic comma (81/80)]]. This continuum is theoretically interesting in that these are all 7-limit rank-3 temperament families supported by [[septimal meantone]] temperament.

	All temperaments in the continuum satisfy {{nowrap\|(81/80)<sup>''n''</sup> ~ 64/63}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.		All temperaments in the continuum satisfy {{nowrap\|(225/224)<sup>''n''</sup> ~ 81/80}}. Varying ''n'' results in different temperament families listed in the table below. It converges to [[marvel]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[7-limit]] temperament families supported by septimal meantone (due to it being the unique rank-2 temperament that tempers both commas and thus tempers all combinations of them). The just value of ''n'' is approximately 2.788851, and temperaments having ''n'' near this value will be more accurate.

	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"