56/45 - Revision history

Lucius Chiaraviglio: Some intervals had no links — added these

2026-06-11T04:09:26Z

Some intervals had no links — added these

← Older revision		Revision as of 04:09, 11 June 2026
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	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
	'''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9 – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64\|Pythagorean major third]] by [[3645/3584]], namely a [[81/80\|syntonic comma]] plus a [[225/224\|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561\|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''.		'''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – [[5/4]] and [[14/9]], [[9/7]] and [[8/5]], [[9/8]] and [[7/5]], and [[10/7]] and [[16/9]] – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64\|Pythagorean major third]] by [[3645/3584]], namely a [[81/80\|syntonic comma]] plus a [[225/224\|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561\|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''.

	According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music\|Turkish maqam music]] should range from 56/45 to 5/4.		According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music\|Turkish maqam music]] should range from 56/45 to 5/4.

FloraC: Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

2026-06-06T12:39:14Z

Text replacement - "Category:Hemifamity" to "Category:Aberschismic"

← Older revision		Revision as of 12:39, 6 June 2026
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	[[Category:Fourth]]		[[Category:Fourth]]
	[[Category:Diminished fourth]]		[[Category:Diminished fourth]]
	[[Category:~~Hemifamity~~]]		[[Category:Aberschismic]]

FloraC: Make this marvel-ptolemaic until 3645/3584 has an accepted name

2026-01-06T12:27:34Z

Make this marvel-ptolemaic until 3645/3584 has an accepted name

← Older revision		Revision as of 12:27, 6 January 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septimal narrow major third, ~~marvelous~~ major third		\| Name = septimal narrow major third, marvel-ptolemaic major third, hemifamity diminished fourth
	\| Color name = zg4, zogu 4th		\| Color name = zg4, zogu 4th
	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
	'''56/45''', the '''septimal narrow major third''', or '''~~marvelous~~ major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds ~~like any other~~, and turns chords like ~~1-5~~/~~4-8~~/5 or ~~1-5~~/~~4-14~~/9 into [[~~Dyadic_chord\|~~essentially tempered dyadic ~~chords~~]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.		'''56/45''', the '''septimal narrow major third''', or '''marvel-ptolemaic major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9 – with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. It is flat of the [[81/64\|Pythagorean major third]] by [[3645/3584]], namely a [[81/80\|syntonic comma]] plus a [[225/224\|marvel comma]]. [[Marvel]] tempering makes all of these intervals into classical major thirds, and turns chords like 1–5/4–8/5 or 1–5/4–14/9 into [[essentially tempered dyadic chord]]s. It is a third of a cent flatter than the 6\19 major third of [[19edo]]; however, it functionally doubles as a type of diminished fourth, flat of the [[8192/6561\|Pythagorean diminished fourth]] by [[5120/5103]]. This gives rise to the name '''hemifamity diminished fourth'''.

			According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian music\|Turkish maqam music]] should range from 56/45 to 5/4.

	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|56/45}}		{{Interval edo approximation\|56/45}}

	== See also ==		== See also ==
	* [[45/28]] – its [[octave complement]]		* [[45/28]] – its [[octave complement]]
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	[[Category:Third]]		[[Category:Third]]
	[[Category:Major third]]		[[Category:Major third]]
	[[Category:~~Marvel~~]]		[[Category:Fourth]]
			[[Category:Diminished fourth]]
			[[Category:Hemifamity]]

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:08:28Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:08, 3 November 2025
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	'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.		'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 56/45}}		{{Interval edo approximation\|56/45}}
	== See also ==		== See also ==
	* [[45/28]] – its [[octave complement]]		* [[45/28]] – its [[octave complement]]

Pailiaq at 07:09, 3 November 2025

2025-11-03T07:09:37Z

← Older revision		Revision as of 07:09, 3 November 2025
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	}}		}}
	'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.		'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.
			== Approximation ==
			{{Interval_Edo_Approximation \| 56/45}}
	== See also ==		== See also ==
	* [[45/28]] – its [[octave complement]]		* [[45/28]] – its [[octave complement]]

Fredg999: Explicit "odd limit"

2024-05-14T03:12:33Z

Explicit "odd limit"

← Older revision		Revision as of 03:12, 14 May 2024
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	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
	'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.		'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various [[9-odd-limit]] consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.

	== See also ==		== See also ==

FloraC: To 5/4. It had been there.

2024-05-13T14:05:07Z

To 5/4. It had been there.

← Older revision		Revision as of 14:05, 13 May 2024
Line 4:		Line 4:
	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
	'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances- 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45~~. <!-- from 56~~/~~45 to..~~.~~? --> {{todo\|clarify}}~~		'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances – 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45 to 5/4.

	== See also ==		== See also ==

TallKite: added color name

2022-12-04T02:50:00Z

added color name

← Older revision		Revision as of 02:50, 4 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = septimal narrow major third, marvelous major third		\| Name = septimal narrow major third, marvelous major third
			\| Color name = zg4, zogu 4th
	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T16:21:40Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 16:21, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 56/45~~		\| Name = septimal narrow major third, marvelous major third
	~~\| Monzo = 3 -2 -1 1~~
	~~\| Cents = 378.60219~~
	\| Name = septimal narrow major third, ~~<br>~~ marvelous major third
	~~\| Color name =~~
	~~\| FJS name = d4<sup>7</sup><sub>5</sub>~~
	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:7-limit]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Major third]]		[[Category:Major third]]
	[[Category:Marvel]]		[[Category:Marvel]]

Fredg999: Misc. edits, categories

2022-03-31T15:41:18Z

Misc. edits, categories

← Older revision		Revision as of 15:41, 31 March 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 56/45		\| Ratio = 56/45
	\| Monzo = 3 -2 -1 1		\| Monzo = 3 -2 -1 1
Line 9:		Line 8:
	\| Sound = jid_56_45_pluck_adu_dr220.mp3		\| Sound = jid_56_45_pluck_adu_dr220.mp3
	}}		}}
			'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances- 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of [[Arabic, Turkish, Persian\|Turkish maqam music]] should range from 56/45. <!-- from 56/45 to...? --> {{todo\|clarify}}
	'''56/45''', the '''septimal narrow major third''', or '''marvelous major third''', is the interval between various 9-limit consonances- 5/4 and 14/9, 9/7 and 8/5, 9/8 and 7/5, and 10/7 and 16/9- with it also being [[6/5]] away from the marvelous fifth, [[112/75]]. [[Marvel]] tempering makes all of these intervals into major thirds like any other, and turns chords like 1-5/4-8/5 or 1-5/4-14/9 into [[Dyadic_chord\|essentially tempered dyadic chords]]. It is a third of a cent flatter than the 6\19 major third of [[19edo]], however, it functionally doubles as a type of diminished fourth. According to [[Ozan Yarman]], the perde segah of ~~Turkish~~ [[maqam music]] should range from 56/45.

	== See also ==		== See also ==
			* [[45/28]] – its [[octave complement]]
	* [[45/28]] – its octave complement		* [[135/112]] – its [[fifth complement]]
	* [[135/112]] – its fifth complement
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:7-limit]]		[[Category:7-limit]]
	~~[[Category:Just interval]]~~
	[[Category:Third]]		[[Category:Third]]
	[[Category:Major third]]		[[Category:Major third]]
	~~[[Category:19edo]]~~
	[[Category:Marvel]]		[[Category:Marvel]]