User:UnbihexiumFan/Temperaments - Revision history

UnbihexiumFan at 19:21, 8 February 2026

2026-02-08T19:21:24Z

← Older revision		Revision as of 19:21, 8 February 2026
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	A collection of temperaments that I have found that may or may not have yet been discovered. ~~A lot of these are~~ the ~~same as already-known temperaments but with non-octave periods. I am not very good with technical details so even though they are included as info on most temperaments I will not be putting it here~~.		A collection of temperaments that I have found that may or may not have yet been discovered. If you find any inaccuracies feel free to point them out on the [[User talk:UnbihexiumFan/Temperaments\|talk page]].

	== Stearnsmic 7/4-period temperaments ==		== Stearnsmic 7/4-period temperaments ==

2026-01-24T18:22:59Z

243/242+2079/2048-based temperaments: I'm actually unsure how I made such glaring errors

← Older revision		Revision as of 18:22, 24 January 2026
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	=== No-5's 19-limit extension ===		=== No-5's 19-limit extension ===

	While the major third is too sharp to be seen as [[5/4]], it can be seen as [[24/19]] or [[64/51]]. Treating it equal to both tempers out [[513/512]] and [[4131/4096]], providing a comma basis of [[2057/2052]], [[513/512]], [[154/153]], and [[243/242]]. The 17th harmonic is mapped to the minor second (-8 generators, D{{flat}} on C) and the 19th harmonic is mapped to the minor third (-6 generators, E{{flat}} on C). The 13th harmonic can be added by setting [[28/27]] equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented ~~second~~ (D{{sesquisharp}} on C).		While the major third is too sharp to be seen as [[5/4]], it can be seen as [[24/19]] or [[64/51]]. Treating it equal to both tempers out [[513/512]] and [[4131/4096]], providing a comma basis of [[2057/2052]], [[513/512]], [[154/153]], and [[243/242]]. The 17th harmonic is mapped to the minor second (-10 generators, D{{flat}} on C) and the 19th harmonic is mapped to the minor third (-6 generators, E{{flat}} on C). The 13th harmonic can be added by setting [[28/27]] equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented fifth (+23 generators, G{{sesquisharp}} on C).

2026-01-21T22:39:44Z

243/242+2079/2048-based temperaments

← Older revision		Revision as of 22:39, 21 January 2026
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	'''Bolded''' ratios are octave-reduced harmonics up to 21.		'''Bolded''' ratios are octave-reduced harmonics up to 21.

	=== ~~2.3.7.11.13~~ extension ===		=== No-5's 19-limit extension ===

	~~One extension to~~ the ~~2.3.7.11.13 subgroup~~ is to ~~temper~~ [[28/27]] to be equal to [[27/26]], ~~tempering out~~ [[~~729~~/~~728~~]]~~. This maps the 13th harmonic~~, [[13/8]], to the ~~sesqui~~-~~augmented second~~, D{{~~sesquisharp~~}}.		While the major third is too sharp to be seen as [[5/4]], it can be seen as [[24/19]] or [[64/51]]. Treating it equal to both tempers out [[513/512]] and [[4131/4096]], providing a comma basis of [[2057/2052]], [[513/512]], [[154/153]], and [[243/242]]. The 17th harmonic is mapped to the minor second (-8 generators, D{{flat}} on C) and the 19th harmonic is mapped to the minor third (-6 generators, E{{flat}} on C). The 13th harmonic can be added by setting [[28/27]] equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented second (D{{sesquisharp}} on C).

	~~2.3.7.11.17.19 extension:~~ [[~~2057~~/~~2052~~]], [[~~513~~/~~512~~]], [[~~154~~/~~153~~]], [[~~243~~/~~242~~]]

2026-01-19T18:27:53Z

243/242+2079/2048-based temperaments: accidental symbols

2026-01-18T19:07:00Z

243/242+2079/2048-based temperaments

← Older revision		Revision as of 19:07, 18 January 2026
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	== 243/242+2079/2048-based temperaments ==		== 243/242+2079/2048-based temperaments ==

	These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible full 7-limit extension, though this will focus on tunings sharper than mohajira.		These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible full 11-limit extension, though this will focus on tunings sharper than mohajira.

	Interval chain in the 2.3.7.11-limit:		Interval chain in the 2.3.7.11-limit:

2026-01-17T20:00:07Z

fix typo

← Older revision		Revision as of 20:00, 17 January 2026
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	== 243/242+2079/2048-based temperaments ==		== 243/242+2079/2048-based temperaments ==

	These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible ~~fukk~~ 7-limit extension, though this will focus on tunings sharper than mohajira.		These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible full 7-limit extension, though this will focus on tunings sharper than mohajira.

	Interval chain in the 2.3.7.11-limit:		Interval chain in the 2.3.7.11-limit:

2026-01-17T18:53:07Z

243/242+2079/2048-based temperaments

← Older revision		Revision as of 18:53, 17 January 2026
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	== 243/242+2079/2048-based temperaments ==		== 243/242+2079/2048-based temperaments ==

	These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth.		These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible fukk 7-limit extension, though this will focus on tunings sharper than mohajira.

	Interval chain in the 2.3.7.11-limit:		Interval chain in the 2.3.7.11-limit:
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	\| +4		\| +4
	\| 196.30		\| 196.30
	\| [[9/8]]		\| '''[[9/8]]'''
	\| -4		\| -4
	\| Bb		\| Bb
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	\| Fd		\| Fd
	\| 458.32		\| 458.32
	\| [[21/16]]		\| '''[[21/16]]'''
	\|-		\|-
	\| B		\| B
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	\|		\|
	\|}		\|}

			'''Bolded''' ratios are octave-reduced harmonics up to 21.

			=== 2.3.7.11.13 extension ===

			One extension to the 2.3.7.11.13 subgroup is to temper [[28/27]] to be equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented second, D{{sesquisharp}}.

	2.3.7.11.17.19 extension: [[2057/2052]], [[513/512]], [[154/153]], [[243/242]]		2.3.7.11.17.19 extension: [[2057/2052]], [[513/512]], [[154/153]], [[243/242]]

2026-01-17T02:26:50Z

2026-01-17T02:20:14Z

2026-01-15T22:53:33Z

← Older revision		Revision as of 22:53, 15 January 2026
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	[[29ed7/4]] provides a good tuning for this temperament.		[[29ed7/4]] provides a good tuning for this temperament.

			== 243/242+2079/2048-based temperaments ==

			These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]].

			2.3.7.11.17.19 extension: [[2057/2052]], [[513/512]], [[154/153]], [[243/242]]