Hemififths - Revision history

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

2026-06-06T12:39:41Z

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

← Older revision		Revision as of 12:39, 6 June 2026
Line 674:		Line 674:
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Breedsmic temperaments]]		[[Category:Breedsmic temperaments]]
	[[Category:~~Hemifamity~~ temperaments]]		[[Category:Aberschismic temperaments]]
	[[Category:Hemimage temperaments]]		[[Category:Hemimage temperaments]]

FloraC: Cleanup on hatnote & infobox

2026-02-09T09:18:34Z

Cleanup on hatnote & infobox

← Older revision		Revision as of 09:18, 9 February 2026
Line 1:		Line 1:
	~~: ''This page is about~~ the regular temperament~~. For~~ the irrational interval of a hemififth~~, see [[sqrt~~(3/2)~~]].''~~		{{About\|the regular temperament\|the irrational interval of a hemififth\|Sqrt(3/2)}}
	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Hemififths		\| Title = Hemififths
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
	\| Comma basis = [[2401/2400]], [[5120/5103]] (7-limit); <br> [[243/242]], [[441/440]], [[896/891]] (11-limit); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (13-limit)		\| Comma basis = [[2401/2400]], [[5120/5103]] (7-limit); <br> [[243/242]], [[441/440]], [[896/891]] (11-limit); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (13-limit)
	\| ~~Generator~~ = ~~49/40~~		\| Edo join 1 = 41 \| Edo join 2 = 58
	\| Mapping = 1; 2 25 13 5 -1		\| Mapping = 1; 2 25 13 5 -1
			\| Generators = 49/40
			\| Generators tuning = 351.5
			\| Optimization method = CWE
	\| Pergen = (P8, P5/2)		\| Pergen = (P8, P5/2)
	~~\| Edo join 1 = 41 \| Edo join 2 = 58~~
	~~\| Optimization method = CTE~~
	~~\| Generator tuning = 351.4~~
	\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]		\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 41		\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 41
	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 41		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 41
	}}		}}

	'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the argent comma, [[5120/5103]].		'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the argent comma, [[5120/5103]].

FloraC: Make shorter

2026-01-30T06:31:40Z

Make shorter

← Older revision		Revision as of 06:31, 30 January 2026
Line 3:		Line 3:
	\| Title = Hemififths		\| Title = Hemififths
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
	\| Comma basis = [[2401/2400]], [[5120/5103]] (~~2.3.5.~~7); <br> [[243/242]], [[441/440]], [[896/891]] (~~2.3.5.7.~~11); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (~~2.3.5.7.11.~~13)		\| Comma basis = [[2401/2400]], [[5120/5103]] (7-limit); <br> [[243/242]], [[441/440]], [[896/891]] (11-limit); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (13-limit)
	\| Generator = 49/40		\| Generator = 49/40
	\| Mapping = 1; 2 25 13 5 -1		\| Mapping = 1; 2 25 13 5 -1

Overthink: style

2026-01-30T04:37:11Z

style

← Older revision		Revision as of 04:37, 30 January 2026
Line 3:		Line 3:
	\| Title = Hemififths		\| Title = Hemififths
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
	\| Comma basis = [[2401/2400]], [[5120/5103]] (L7); <br> [[243/242]], [[441/440]], [[896/891]] (~~L11~~); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (~~L13~~)		\| Comma basis = [[2401/2400]], [[5120/5103]] (2.3.5.7); <br> [[243/242]], [[441/440]], [[896/891]] (2.3.5.7.11); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (2.3.5.7.11.13)
	\| Generator = 49/40		\| Generator = 49/40
	\| Mapping = 1; 2 25 13 5 -1		\| Mapping = 1; 2 25 13 5 -1
Line 12:		Line 12:
	\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]		\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 41		\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 41
	\| Odd limit 2 = (13-limit) 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 41		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 41
	}}		}}

FloraC: /* Interval chain */ - the 17-form detemperament table cuz it's not easy to read. The diagram is just way better

2025-12-07T10:44:03Z

Interval chain: - the 17-form detemperament table cuz it's not easy to read. The diagram is just way better

Show changes

FloraC: /* Chords */ -> chords and harmony

2025-12-07T10:33:08Z

Chords: -> chords and harmony

← Older revision		Revision as of 10:33, 7 December 2025
Line 581:		Line 581:
	<nowiki/>* In 7-limit CWE tuning, octave reduced		<nowiki/>* In 7-limit CWE tuning, octave reduced

	== Chords ==		== Chords and harmony ==
	{{~~Main~~\| Chords of hemififths }}		{{See also\| Chords of hemififths }}

	== Scales ==		== Scales ==

FloraC: Move ups and downs notation to the notation section

2025-12-07T10:32:03Z

Move ups and downs notation to the notation section

Show changes

Tristanbay: Switched 5120/5103 to new name

2025-10-23T18:24:13Z

Switched 5120/5103 to new name

← Older revision		Revision as of 18:24, 23 October 2025
Line 15:		Line 15:
	}}		}}

	'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the ~~hemifamity~~ comma, [[5120/5103]].		'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the argent comma, [[5120/5103]].

	It extends fairly naturally to the [[11-limit\|11-]] and [[13-limit]] by treating the generator as [[11/9]][[~]][[16/13]]. This lowers the overall accuracy, but supplies more harmonic resources. The no-5 subgroup [[restriction]], called '''hemif''', is also notable. Possible tunings include [[41edo\|41-]], [[58edo\|58-]], and [[99edo]] (using the 99ef val in the 13-limit).		It extends fairly naturally to the [[11-limit\|11-]] and [[13-limit]] by treating the generator as [[11/9]][[~]][[16/13]]. This lowers the overall accuracy, but supplies more harmonic resources. The no-5 subgroup [[restriction]], called '''hemif''', is also notable. Possible tunings include [[41edo\|41-]], [[58edo\|58-]], and [[99edo]] (using the 99ef val in the 13-limit).

Overthink: Updated infobox

2025-10-22T15:54:34Z

Updated infobox

← Older revision		Revision as of 15:54, 22 October 2025
Line 2:		Line 2:
	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Hemififths		\| Title = Hemififths
	\| Subgroups = 2.3.5.7, 2.3.5.7.11.13		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
	\| Comma basis = [[2401/2400]], [[5120/5103]] (~~2.3.5.7~~); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (~~2.3.5.7.11.13~~)		\| Comma basis = [[2401/2400]], [[5120/5103]] (L7); <br> [[243/242]], [[441/440]], [[896/891]] (L11); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (L13)
	\| Generator = 11/9		\| Generator = 49/40
	\| Mapping = 1; 2 25 13 5 -1		\| Mapping = 1; 2 25 13 5 -1
	\| Pergen = (P8, P5/2)		\| Pergen = (P8, P5/2)
Line 11:		Line 11:
	\| Generator tuning = 351.4		\| Generator tuning = 351.4
	\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]		\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 58		\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 41
	\| Odd limit 2 = (13-limit) 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 58		\| Odd limit 2 = (13-limit) 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 41
	}}		}}

Overthink: Added temperament infobox, plus some minor changes

2025-10-14T17:12:06Z

Added temperament infobox, plus some minor changes

← Older revision		Revision as of 17:12, 14 October 2025
Line 1:		Line 1:
	: ''This page is about the regular temperament. For the irrational interval of a hemififth, see [[sqrt(3/2)]].''		: ''This page is about the regular temperament. For the irrational interval of a hemififth, see [[sqrt(3/2)]].''
			{{Infobox regtemp
			\| Title = Hemififths
			\| Subgroups = 2.3.5.7, 2.3.5.7.11.13
			\| Comma basis = [[2401/2400]], [[5120/5103]] (2.3.5.7); <br>[[144/143]], [[196/195]], [[243/242]], [[364/363]] (2.3.5.7.11.13)
			\| Generator = 11/9
			\| Mapping = 1; 2 25 13 5 -1
			\| Pergen = (P8, P5/2)
			\| Edo join 1 = 41 \| Edo join 2 = 58
			\| Optimization method = CTE
			\| Generator tuning = 351.4
			\| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[17L 7s]], [[17L 24s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 1.90 \| Complexity 1 = 58
			\| Odd limit 2 = (13-limit) 21 \| Mistuning 2 = 7.77 \| Complexity 2 = 58
			}}

	'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]].		'''Hemififths''' is a [[regular temperament\|temperament]] that uses a neutral third as a [[generator]], just as the name suggests. A stack of 13 generators represents [[7/4]] and a stack of 25 generators represents [[5/4]], [[tempering out]] the breedsma, [[2401/2400]], and the hemifamity comma, [[5120/5103]].
Line 535:		Line 549:
	\|		\|
	\| 351.220		\| 351.220
	\| Lower bound of 11- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone		\| Lower bound of 11- to 15-odd-limit<br>and (13-limit) 21-odd-limit diamond monotone
	\|-		\|-
	\|		\|
Line 620:		Line 634:
	\| 15/13		\| 15/13
	\| 351.705		\| 351.705
	\| 15-odd-limit minimax		\| 15-odd-limit and (13-limit) 21-odd-limit minimax
	\|-		\|-
	\| [[58edo\|17\58]]		\| [[58edo\|17\58]]
Line 675:		Line 689:
	\|		\|
	\| 352.941		\| 352.941
	\| Upper bound of 7- to 15-odd-limit<br>and 13-limit 21-odd-limit diamond monotone		\| Upper bound of 7- to 15-odd-limit<br>and (13-limit) 21-odd-limit diamond monotone
	\|-		\|-
	\|		\|