Leapday - Revision history

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

2026-06-06T12:39:51Z

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

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

FloraC: Leapfrog doesn't redirect here

2026-04-29T18:49:24Z

Leapfrog doesn't redirect here

← Older revision		Revision as of 18:49, 29 April 2026
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	Further extensions for [[prime]]s [[17/1\|17]] and [[23/1\|23]] are available, where 17/16 is represented by an octave-reduced triple-augmented sixth (C–A𝄪♯), and 23/16 is represented by an augmented fourth (C–F♯).		Further extensions for [[prime]]s [[17/1\|17]] and [[23/1\|23]] are available, where 17/16 is represented by an octave-reduced triple-augmented sixth (C–A𝄪♯), and 23/16 is represented by an augmented fourth (C–F♯).

	If ratios of 5 are omitted, the 2.3.7.11.13 [[subgroup]] version of leapday is known as ~~'''~~leapfrog~~'''~~, notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy~~, as 5/4 is complex and the canonical mapping for prime 19 is fairly inaccurate~~.		Since ratios of 5 are complex, they can be omitted, and the [[2.3.7.11.13 subgroup\|2.3.7.11.13-subgroup]] version of leapday is known as [[leapfrog]], notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy.

	Leapday was named by [[Herman Miller]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10589.html Yahoo! Tuning Group (Archive) \| ''Some 13-limit temperaments'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10604.html Yahoo! Tuning Group (Archive) \| ''24 13-limit temperaments supported by 46'']</ref>.		Leapday was named by [[Herman Miller]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10589.html Yahoo! Tuning Group (Archive) \| ''Some 13-limit temperaments'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10604.html Yahoo! Tuning Group (Archive) \| ''24 13-limit temperaments supported by 46'']</ref>.

	See [[Hemifamity temperaments #Leapday~~]] or [[No-fives subgroup temperaments #Leapfrog~~]] for ~~more~~ technical data.		See [[Hemifamity temperaments #Leapday]] for technical data.

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

FloraC: Correction

2026-03-27T11:09:03Z

Correction

← Older revision		Revision as of 11:09, 27 March 2026
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	\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]		\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 8.53 \| Complexity 1 = 29		\| Odd limit 1 = 9 \| Mistuning 1 = 8.53 \| Complexity 1 = 29
	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 11.1 \| Complexity 2 = 29		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 10.6 \| Complexity 2 = 29
	}}		}}
	: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''		: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''

FloraC: + infobox

2026-03-27T10:27:16Z

+ infobox

← Older revision		Revision as of 10:27, 27 March 2026
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			{{Infobox regtemp
			\| Title = Leapday
			\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
			\| Comma basis = [[686/675]], [[5120/5103]] (7-limit); <br>[[121/120]], [[441/440]], [[686/675]] (11-limit); <br>[[91/90]], [[121/120]], [[169/168]], [[352/351]]<br>(13-limit)
			\| Edo join 1 = 29 \| Edo join 2 = 46
			\| Mapping = 1; 1 21 15 11 8
			\| Generators = 3/2 \| Generators tuning = 704.2 \| Optimization method = CWE
			\| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 8.53 \| Complexity 1 = 29
			\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 11.1 \| Complexity 2 = 29
			}}
	: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''		: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''

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	\|-		\|-
	! 13-limit		! 13-limit
	! Additional ratios<br />of 17 and 23		! Additional ratios<br>of 17 and 23
	\|-		\|-
	\| 0		\| 0

FloraC: Rework on intro

2025-10-26T15:25:44Z

Rework on intro

← Older revision		Revision as of 15:25, 26 October 2025
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	: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''		: ''Not to be confused with calendar-based scales such as those in [[293edo]], [[400edo]], [[353edo]], or [[Irvic scale\|Irvian mode]].''

	'''Leapday''' is a [[regular temperament]] ~~for the 7-, 11-, 13-, 17-, and no-19 23-limit. It is~~ based on the [[chain of fifths]], but ~~here,~~ the fifth is tuned slightly sharp of just (approximately 704{{cent}}) so that ~~6 fifths give [[23/16]], 8 fifths give [[13/8]], 11 fifths give [[11/8]],~~ 15 fifths give [[7/4]], 21 fifths give [[5/4]], and ~~24 fifths give [[17~~/~~16]]~~.		'''Leapday''' is a [[regular temperament\|temperament]] based on the [[chain of fifths]], but the fifth is tuned slightly sharp of just (approximately 704{{cent}}) so that 15 fifths give [[7/4]] and 21 fifths give [[5/4]]. In other words, the classical major third (5/4) is represented by a triple-augmented unison (C–C𝄪♯), and the harmonic seventh (7/4) is represented by a double-augmented fifth (C–G𝄪).

	~~Equivalently:~~		Leapday can be easily extended to the [[13-limit]] by identifying [[14/11]] with the major third and [[13/11]] with the minor third. This implies 11/8 is represented by an augmented third (C–E♯) and 13/8 is represented by an augmented fifth (C–G♯).
	* 5/4, the ~~classical~~ major third~~, is represented by a triply augmented unison (C–C𝄪♯),~~
	* 7/4, the ~~harmonic seventh, is represented by a doubly augmented fifth (C–G𝄪),~~
	* 11/8 is represented by an augmented third (C–E♯),
	* 13/8 is represented by an augmented fifth (C–G♯),
	* 17/16 is represented by an octave-reduced triply augmented sixth (C–A𝄪♯), and
	* 23/16 is represented by an augmented fourth (C–F♯).

	As a result, leapday is very much the "opposite" of meantone in many respects, similar to [[superpyth]]: meantone (including [[12edo]]) has the fifth tuned flat so that intervals of harmonic 5 are simple while intervals of harmonics 7, 11, and 13 are complex, while leapday has the fifth tuned sharp so that intervals of 7, 11, and 13 are relatively simple while intervals of 5 are complex.		As a result, leapday is very much the "opposite" of meantone in many respects, similar to [[superpyth]]: meantone (including [[12edo]]) has the fifth tuned flat so that intervals of harmonic 5 are simple while intervals of harmonics 7, 11, and 13 are complex, while leapday has the fifth tuned sharp so that intervals of 7, 11, and 13 are relatively simple while intervals of 5 are complex.

			Further extensions for [[prime]]s [[17/1\|17]] and [[23/1\|23]] are available, where 17/16 is represented by an octave-reduced triple-augmented sixth (C–A𝄪♯), and 23/16 is represented by an augmented fourth (C–F♯).

	If ratios of 5 are omitted, the 2.3.7.11.13 [[subgroup]] version of leapday is known as '''leapfrog''', notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy, as 5/4 is complex and the canonical mapping for prime 19 is fairly inaccurate.		If ratios of 5 are omitted, the 2.3.7.11.13 [[subgroup]] version of leapday is known as '''leapfrog''', notable as tempering [[parapyth]] (a rank-3 temperament of the 2.3.7.11.13 subgroup) to rank 2 by finding [[~]][[13/8]] at ([[~]][[9/8]])<sup>4</sup>, that is, by tempering out the [[tetris comma]], and is a good combination of simplicity and accuracy, as 5/4 is complex and the canonical mapping for prime 19 is fairly inaccurate.

FloraC: /* Tunings */ rework for no-19 23-limit

2025-10-26T13:18:35Z

Tunings: rework for no-19 23-limit

Show changes

FloraC: + norm-based tunings. Switch to CWE in the interval table

2025-10-26T10:47:34Z

+ norm-based tunings. Switch to CWE in the interval table

Show changes

BudjarnLambeth: Add music section

2025-08-23T22:13:44Z

Add music section

← Older revision		Revision as of 22:13, 23 August 2025
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	\|}		\|}
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

			== Music ==
			; [[Claudi Meneghin]]
			* [https://www.youtube.com/watch?v=TgD7cN8a5D8 ''Lytel Twyelyghte Musicke (Little Twilight Music), for Brass, Winds, Strings, and Timpani, in 80-equal division of the octave, as the linear temperament generated by its fifth''] (2025)

	== References and external links ==		== References and external links ==

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"

2025-06-21T06:56:02Z

Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"

← Older revision		Revision as of 06:56, 21 June 2025
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	! Edo<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|~~Eigenmonzo~~<br>(~~unchanged-interval~~)]]*		! [[Eigenmonzo\|Unchanged interval<br>(eigenmonzo)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

ArrowHead294 at 19:11, 14 May 2025

2025-05-14T19:11:42Z

← Older revision		Revision as of 19:11, 14 May 2025
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	\|-		\|-
	! 13-limit		! 13-limit
	! ~~No-19~~ 23~~-limit extension~~		! Additional ratios<br />of 17 and 23
	\|-		\|-
	\| 0		\| 0