2187/1250 - Revision history

FloraC: +1

2026-01-18T09:08:53Z

← Older revision		Revision as of 09:08, 18 January 2026
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	\| Color name = g<sup>4</sup>7, quadgu 7th		\| Color name = g<sup>4</sup>7, quadgu 7th
	}}		}}
	'''2187/1250''', the '''tetraptolemaic diminished ~~seventh''' or '''ragismic 5-limit harmonic~~ seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is sharp of the [[32768/19683\|Pythagorean diminished seventh]] by four [[81/80\|syntonic commas]], hence the name. It can also be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the ~~marvel 5-limit harmonic seventh~~ [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.		'''2187/1250''', the '''tetraptolemaic diminished seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is sharp of the [[32768/19683\|Pythagorean diminished seventh]] by four [[81/80\|syntonic commas]], hence the name. It can also be created by stacking two [[27/25]] and [[3/2]].

			It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the diptolemaic augmented sixth [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4. As such, it can also be called the '''ragismic 5-limit harmonic seventh'''.

	== Approximation ==		== Approximation ==

FloraC: Review

2026-01-18T08:56:17Z

Review

← Older revision		Revision as of 08:56, 18 January 2026
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	{{Infobox Interval\|2187/1250		{{Infobox Interval
			\| Ratio = 2187/1250
	\| Name = tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh		\| Name = tetraptolemaic diminished seventh, ragismic 5-limit harmonic seventh
	\| Color name = g<sup>4</sup>7, quadgu 7th		\| Color name = g<sup>4</sup>7, quadgu 7th
	}}		}}
	'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It can be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.		'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is sharp of the [[32768/19683\|Pythagorean diminished seventh]] by four [[81/80\|syntonic commas]], hence the name. It can also be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.

	== Approximation ==		== Approximation ==
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	== See also ==		== See also ==
	* [[2500/2187]] — its [[octave complement]]		* [[2500/2187]] – its [[octave complement]]

	[[Category:~~Ragismic~~]]		[[Category:Seventh]]
			[[Category:Diminished seventh]]

Overthink: fix typo

2026-01-18T01:19:12Z

fix typo

← Older revision		Revision as of 01:19, 18 January 2026
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	== Temperaments ==		== Temperaments ==
	2187/1250 is the eigenmonzo of [[4/9-comma meantone]], and further equating it to [[7/4]] gives a tuning of [[flattone]]		2187/1250 is the eigenmonzo of [[4/9-comma meantone]], and further equating it to [[7/4]] gives a tuning of [[flattone]].

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

Overthink: add temperaments section

2026-01-18T01:18:59Z

add temperaments section

← Older revision		Revision as of 01:18, 18 January 2026
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	'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It can be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.		'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It can be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.

	==Approximation==		== Approximation ==
	[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.		[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.

	==See also==		== Temperaments ==
			2187/1250 is the eigenmonzo of [[4/9-comma meantone]], and further equating it to [[7/4]] gives a tuning of [[flattone]]

			== See also ==
	* [[2500/2187]] — its [[octave complement]]		* [[2500/2187]] — its [[octave complement]]

	[[Category:Ragismic]]		[[Category:Ragismic]]

Hotcrystal0: Hotcrystal0 moved page User:Hotcrystal0/2187/1250 to 2187/1250: Page is finished

2026-01-18T00:07:50Z

Hotcrystal0 moved page User:Hotcrystal0/2187/1250 to 2187/1250: Page is finished

← Older revision	Revision as of 00:07, 18 January 2026
(No difference)

Hotcrystal0 at 13:35, 15 January 2026

2026-01-15T13:35:26Z

← Older revision		Revision as of 13:35, 15 January 2026
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	==Approximation==		==Approximation==
	[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.		[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.

			==See also==
			* [[2500/2187]] — its [[octave complement]]

	[[Category:Ragismic]]		[[Category:Ragismic]]

Hotcrystal0 at 13:29, 15 January 2026

2026-01-15T13:29:55Z

← Older revision		Revision as of 13:29, 15 January 2026
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	\| Color name = g<sup>4</sup>7, quadgu 7th		\| Color name = g<sup>4</sup>7, quadgu 7th
	}}		}}
	'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.		'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It can be created by stacking two [[27/25]] and [[3/2]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.

	==Approximation==		==Approximation==

Hotcrystal0: link

2026-01-15T00:42:02Z

link

← Older revision		Revision as of 00:42, 15 January 2026
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	==Approximation==		==Approximation==
	57edo contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.		[[57edo]] contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.

	[[Category:Ragismic]]		[[Category:Ragismic]]

Hotcrystal0 at 22:35, 14 January 2026

2026-01-14T22:35:21Z

← Older revision		Revision as of 22:35, 14 January 2026
Line 3:		Line 3:
	\| Color name = g<sup>4</sup>7, quadgu 7th		\| Color name = g<sup>4</sup>7, quadgu 7th
	}}		}}
	'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4. ~~It is~~ very ~~accurately approximated by the~~ 46th step ~~of [[57edo]]~~ (46\57), which is only 0.009{{cent}} flat of ~~this interval~~.		'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4.

			==Approximation==
			57edo contains a very accurate approximation of 2187/1250 at its 46th step (46\57), which is only 0.009{{cent}} flat of 2187/1250.

	[[Category:Ragismic]]		[[Category:Ragismic]]

Hotcrystal0: why did I mix up my slashes

2026-01-14T22:18:45Z

why did I mix up my slashes

← Older revision		Revision as of 22:18, 14 January 2026
Line 3:		Line 3:
	\| Color name = g<sup>4</sup>7, quadgu 7th		\| Color name = g<sup>4</sup>7, quadgu 7th
	}}		}}
	'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225\128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4. It is very accurately approximated by the 46th step of [[57edo]] (46\57), which is only 0.009{{cent}} flat of this interval.		'''2187/1250''', the '''tetraptolemaic diminished seventh''' or '''ragismic 5-limit harmonic seventh''', is a [[5-limit]] interval very closely approximating [[7/4]]. It is a [[4375/4374\|ragisma]] below 7/4, a [[15625/15552\|kleisma]] below the marvel 5-limit harmonic seventh [[225/128]], and [[250/243]] below [[9/5]]. In the [[ragismic]] temperament, it is equated with 7/4. It is very accurately approximated by the 46th step of [[57edo]] (46\57), which is only 0.009{{cent}} flat of this interval.

	[[Category:Ragismic]]		[[Category:Ragismic]]