16ed5/2 - Revision history

Fredg999 category edits: Removing from Category:Ed5/2 using Cat-a-lot

2025-08-01T18:40:39Z

← Older revision		Revision as of 18:40, 1 August 2025
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	* [[18/17 equal-step tuning\|AS18/17]] - relative [[AS\|ambitonal sequence]]		* [[18/17 equal-step tuning\|AS18/17]] - relative [[AS\|ambitonal sequence]]

	~~[[Category:Ed5/2]]~~
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

2024-10-04T08:41:49Z

Harmonics

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 | 1586.314
 |}
 == Regular temperaments ==

2023-06-24T01:48:10Z

← Older revision		Revision as of 01:48, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each~~. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval~~. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo\|12-tone scale]].		'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo\|12-tone scale]].
	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"

2023-06-24T01:42:11Z

remove moremajorthanmajor-speak

← Older revision		Revision as of 01:42, 24 June 2023
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	\| 1586.314		\| 1586.314
	\|}		\|}

	~~Coincidentally, 133 steps of the pyrite EDX of this size exceed 11 octaves by only 2.978¢.~~

	== Regular temperaments ==		== Regular temperaments ==

2023-05-23T00:29:49Z

Removing tenths that are definitively not major

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 ! Period
 !Notes
 |-
 |9\7
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 |104.1{{Overline|6}}
+|
 |}

2023-05-23T00:22:37Z

← Older revision		Revision as of 00:22, 23 May 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval.		'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo\|12-tone scale]].

	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
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	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! colspan="4" \|Major ~~tenths~~		! colspan="4" \|Major tenth
	! Period		! Period
	!Notes		!Notes

2023-05-23T00:21:20Z

2023-05-23T00:20:40Z

Merging some content from 16edX page

2023-05-07T19:04:01Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 19:04, 7 May 2023
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	{{Main\| Quintaleap family }}		{{Main\| Quintaleap family }}

	16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{~~Val list~~\| 12-, 109-, 121-, 133-, 145- }}, and [[157edo]].		16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{Optimal ET sequence\| 12-, 109-, 121-, 133-, 145- }}, and [[157edo]].

	Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145).		Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145).

2023-05-04T01:51:04Z