Decimal - Revision history

FloraC: Cleanup on infobox

2026-02-09T09:05:19Z

Cleanup on infobox

← Older revision		Revision as of 09:05, 9 February 2026
Line 4:		Line 4:
	\| Comma basis = [[25/24]], [[49/48]]		\| Comma basis = [[25/24]], [[49/48]]
	\| Edo join 1 = 4 \| Edo join 2 = 6		\| Edo join 1 = 4 \| Edo join 2 = 6
	\| ~~Generator~~ = 7/4 \| ~~Generator~~ tuning = 951.0 \| Optimization method = CWE		\| Mapping = 2; 2 1 1
			\| Generators = 7/4 \| Generators tuning = 951.0 \| Optimization method = CWE
	\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]		\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]
	~~\| Mapping = 2; 2 1 1~~
	\| Pergen = (P8/2, P4/2)		\| Pergen = (P8/2, P4/2)
	\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6		\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6
	\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 10		\| Odd limit 2 = 7-limit 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 10
	}}		}}
	'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is a [[weak extension\|weak]] [[extension]] of [[dicot]], the [[5-limit]] temperament tempering out [[25/24]], splitting the octave in two parts, each representing [[7/5]][[~]][[10/7]]. It is also the prototypical fully [[hemipyth]] temperament, with [[sqrt(2)]] representing 7/5~10/7, [[sqrt(3)]] representing [[7/4]]~[[12/7]], [[sqrt(3/2)]] representng [[5/4]]~[[6/5]], and [[sqrt(4/3)]] representing [[7/6]]~[[8/7]], with a [[pergen]] of (P8/2, P4/2), splitting all Pythagorean intervals in two.		'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is a [[weak extension\|weak]] [[extension]] of [[dicot]], the [[5-limit]] temperament tempering out [[25/24]], splitting the octave in two parts, each representing [[7/5]][[~]][[10/7]]. It is also the prototypical fully [[hemipyth]] temperament, with [[sqrt(2)]] representing 7/5~10/7, [[sqrt(3)]] representing [[7/4]]~[[12/7]], [[sqrt(3/2)]] representng [[5/4]]~[[6/5]], and [[sqrt(4/3)]] representing [[7/6]]~[[8/7]], with a [[pergen]] of (P8/2, P4/2), splitting all Pythagorean intervals in two.

Overthink: note tetrads, remove 38-note mos (doesn't always appear), slight rewrite

2026-01-12T06:32:35Z

note tetrads, remove 38-note mos (doesn't always appear), slight rewrite

← Older revision		Revision as of 06:32, 12 January 2026
Line 13:		Line 13:
	'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is a [[weak extension\|weak]] [[extension]] of [[dicot]], the [[5-limit]] temperament tempering out [[25/24]], splitting the octave in two parts, each representing [[7/5]][[~]][[10/7]]. It is also the prototypical fully [[hemipyth]] temperament, with [[sqrt(2)]] representing 7/5~10/7, [[sqrt(3)]] representing [[7/4]]~[[12/7]], [[sqrt(3/2)]] representng [[5/4]]~[[6/5]], and [[sqrt(4/3)]] representing [[7/6]]~[[8/7]], with a [[pergen]] of (P8/2, P4/2), splitting all Pythagorean intervals in two.		'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is a [[weak extension\|weak]] [[extension]] of [[dicot]], the [[5-limit]] temperament tempering out [[25/24]], splitting the octave in two parts, each representing [[7/5]][[~]][[10/7]]. It is also the prototypical fully [[hemipyth]] temperament, with [[sqrt(2)]] representing 7/5~10/7, [[sqrt(3)]] representing [[7/4]]~[[12/7]], [[sqrt(3/2)]] representng [[5/4]]~[[6/5]], and [[sqrt(4/3)]] representing [[7/6]]~[[8/7]], with a [[pergen]] of (P8/2, P4/2), splitting all Pythagorean intervals in two.

	More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. ~~These~~ can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24~~, 38~~, … tones.		More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. This equates the [[4:5:6]] and [[6:7:8]] triads with their inverses, therefore also equating the [[4:5:6:7]] major tetrad with the [[70:84:105:120\|1/(12:10:8:7)]] minor tetrad. The neutral third and semifourth can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, … tones.

	Decimal ~~serves~~ as a structural archetype for a ~~10-tone~~ system that views the [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28\|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.		Decimal can serve as a structural archetype for a [[decatonic]] system that views the [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28\|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.

	A more accurate system based on 10 interval classes that ~~does not neutralize these~~ chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara. Both of these temperaments also temper out the marvel comma, [[225/224]].		A more accurate system based on 10 interval classes that distinguishes major and minor chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48 to half of 25/24 by tempering out [[2401/2400]], though its structure is more complex than that of pajara. Both of these temperaments also temper out the marvel comma, [[225/224]].

	~~For technical data, see [[~~Dicot family #Decimal~~]].~~		{{Tdlink\|Dicot family #Decimal}}

	== Interval chain ==		== Interval chain ==

Overthink: note weak extension, improve wording

2026-01-12T06:16:47Z

note weak extension, improve wording

← Older revision		Revision as of 06:16, 12 January 2026
Line 11:		Line 11:
	\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 10		\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 10
	}}		}}
	'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is ~~also~~ the ~~prototypical fully~~ [[~~hemipyth~~]] temperament, ~~with approximations of~~ [[7/5]][[~]][[10/7]] at [[sqrt(2)]], [[7/4]]~[[12/7]] at [[sqrt(3)]], [[5/4]]~[[6/5]] at [[sqrt(3/2)]] ~~and~~ [[7/6]]~[[8/7~~]] at [[sqrt(4/3)~~]], ~~and~~ [[pergen]] (P8/2, P4/2), splitting all Pythagorean intervals.		'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is a [[weak extension\|weak]] [[extension]] of [[dicot]], the [[5-limit]] temperament tempering out [[25/24]], splitting the octave in two parts, each representing [[7/5]][[~]][[10/7]]. It is also the prototypical fully [[hemipyth]] temperament, with [[sqrt(2)]] representing 7/5~10/7, [[sqrt(3)]] representing [[7/4]]~[[12/7]], [[sqrt(3/2)]] representng [[5/4]]~[[6/5]], and [[sqrt(4/3)]] representing [[7/6]]~[[8/7]], with a [[pergen]] of (P8/2, P4/2), splitting all Pythagorean intervals in two.

	More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.		More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.

Overthink: both can extend to the 11-limit

2026-01-12T04:10:07Z

both can extend to the 11-limit

← Older revision		Revision as of 04:10, 12 January 2026
Line 17:		Line 17:
	Decimal serves as a structural archetype for a 10-tone system that views the [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28\|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.		Decimal serves as a structural archetype for a 10-tone system that views the [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28\|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.

	A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara~~, but easily extends to the [[11-limit]]~~. Both of these temperaments also temper out the marvel comma, [[225/224]].		A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara. Both of these temperaments also temper out the marvel comma, [[225/224]].

	For technical data, see [[Dicot family #Decimal]].		For technical data, see [[Dicot family #Decimal]].

FloraC: Ploidacot in Template: Infobox regtemp was fixed

2025-11-21T18:02:12Z

Ploidacot in Template: Infobox regtemp was fixed

← Older revision		Revision as of 18:02, 21 November 2025
Line 1:		Line 1:
	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Decimal		\| Title = Decimal
	\| Subgroups = 2.3.5.7		\| Subgroups = 2.3.5.7
Line 7:		Line 7:
	\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]		\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]
	\| Mapping = 2; 2 1 1		\| Mapping = 2; 2 1 1
	~~\| Ploidacot = diploid dicot~~
	\| Pergen = (P8/2, P4/2)		\| Pergen = (P8/2, P4/2)
	\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6		\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6

FloraC: Override the ploidacot. Misc. cleanup

2025-10-22T16:13:45Z

Override the ploidacot. Misc. cleanup

← Older revision		Revision as of 16:13, 22 October 2025
Line 7:		Line 7:
	\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]		\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]
	\| Mapping = 2; 2 1 1		\| Mapping = 2; 2 1 1
			\| Ploidacot = diploid dicot
	\| Pergen = (P8/2, P4/2)		\| Pergen = (P8/2, P4/2)
	\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6		\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6
Line 15:		Line 16:
	More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.		More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.

	Decimal serves as a structural archetype for a 10-tone system that views the 4:5:6 and 1/(4:5:6) chords as a ~~major-minor~~ pair (which is equated in decimal temperament as 25/24 is tempered), and the 6:7:8 and 1/(6:7:8) chords as another ~~major-minor~~ pair, neutralized in decimal via ~~tempering~~ of 49/48.		Decimal serves as a structural archetype for a 10-tone system that views the [[4:5:6]] and [[10:12:15\|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28\|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.

	A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara, but easily extends to the [[11-limit]]. Both of these temperaments also temper out the marvel comma, [[225/224]].		A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara, but easily extends to the [[11-limit]]. Both of these temperaments also temper out the marvel comma, [[225/224]].

Overthink at 15:49, 22 October 2025

2025-10-22T15:49:32Z

← Older revision		Revision as of 15:49, 22 October 2025
Line 8:		Line 8:
	\| Mapping = 2; 2 1 1		\| Mapping = 2; 2 1 1
	\| Pergen = (P8/2, P4/2)		\| Pergen = (P8/2, P4/2)
	\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 10		\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 6
	\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 24		\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 10
	}}		}}
	'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is also the prototypical fully [[hemipyth]] temperament, with approximations of [[7/5]][[~]][[10/7]] at [[sqrt(2)]], [[7/4]]~[[12/7]] at [[sqrt(3)]], [[5/4]]~[[6/5]] at [[sqrt(3/2)]] and [[7/6]]~[[8/7]] at [[sqrt(4/3)]], and [[pergen]] (P8/2, P4/2), splitting all Pythagorean intervals.		'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is also the prototypical fully [[hemipyth]] temperament, with approximations of [[7/5]][[~]][[10/7]] at [[sqrt(2)]], [[7/4]]~[[12/7]] at [[sqrt(3)]], [[5/4]]~[[6/5]] at [[sqrt(3/2)]] and [[7/6]]~[[8/7]] at [[sqrt(4/3)]], and [[pergen]] (P8/2, P4/2), splitting all Pythagorean intervals.

	More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.		More precisely, it is the [[7-limit]] temperament that [[tempering out\|tempers out]] both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows 5/4~6/5 to be sqrt(3/2) a neutral third and 7/6~8/7 to be a sqrt(4/3) neutral semifourth. These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]]. Since {{nowrap\|(25/24)/(49/48) {{=}} [[50/49]] }}, it also tempers that out, splitting the octave in two equal parts. As both the generator and period are half that of the diatonic scale, this means it forms mos scales of 4, 6, 10, 14, 24, 38, … tones.

			Decimal serves as a structural archetype for a 10-tone system that views the 4:5:6 and 1/(4:5:6) chords as a major-minor pair (which is equated in decimal temperament as 25/24 is tempered), and the 6:7:8 and 1/(6:7:8) chords as another major-minor pair, neutralized in decimal via tempering of 49/48.
			A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara, but easily extends to the [[11-limit]]. Both of these temperaments also temper out the marvel comma, [[225/224]].

	For technical data, see [[Dicot family #Decimal]].		For technical data, see [[Dicot family #Decimal]].

2^67-1 at 05:28, 23 September 2025

2025-09-23T05:28:43Z

← Older revision		Revision as of 05:28, 23 September 2025
Line 7:		Line 7:
	\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]		\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]
	\| Mapping = 2; 2 1 1		\| Mapping = 2; 2 1 1
	\| Pergen = (P8/2, ~~cP5~~/2)		\| Pergen = (P8/2, P4/2)
	\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 10		\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 10
	\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 24		\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 24

Overthink: Added Infobox Regtemp

2025-09-21T18:04:51Z

Added Infobox Regtemp

← Older revision		Revision as of 18:04, 21 September 2025
Line 1:		Line 1:
			{{Infobox Regtemp
			\| Title = Decimal
			\| Subgroups = 2.3.5.7
			\| Comma basis = [[25/24]], [[49/48]]
			\| Edo join 1 = 4 \| Edo join 2 = 6
			\| Generator = 7/4 \| Generator tuning = 951.0 \| Optimization method = CWE
			\| MOS scales = [[4L 2s]], [[4L 6s]], [[10L 4s]]
			\| Mapping = 2; 2 1 1
			\| Pergen = (P8/2, cP5/2)
			\| Odd limit 1 = 7 \| Mistuning 1 = 35.3 \| Complexity 1 = 10
			\| Odd limit 2 = (7-limit) 21 \| Mistuning 2 = 35.3 \| Complexity 2 = 24
			}}
	'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is also the prototypical fully [[hemipyth]] temperament, with approximations of [[7/5]][[~]][[10/7]] at [[sqrt(2)]], [[7/4]]~[[12/7]] at [[sqrt(3)]], [[5/4]]~[[6/5]] at [[sqrt(3/2)]] and [[7/6]]~[[8/7]] at [[sqrt(4/3)]], and [[pergen]] (P8/2, P4/2), splitting all Pythagorean intervals.		'''Decimal''' is an [[exotemperament]] in the [[dicot family]], [[semaphoresmic clan]], and [[jubilismic clan]] of [[regular temperament\|temperaments]]. It is also the prototypical fully [[hemipyth]] temperament, with approximations of [[7/5]][[~]][[10/7]] at [[sqrt(2)]], [[7/4]]~[[12/7]] at [[sqrt(3)]], [[5/4]]~[[6/5]] at [[sqrt(3/2)]] and [[7/6]]~[[8/7]] at [[sqrt(4/3)]], and [[pergen]] (P8/2, P4/2), splitting all Pythagorean intervals.

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:05:54Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:05, 12 September 2025
Line 60:		Line 60:
	== Tunings ==		== Tunings ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|