45edo - Revision history

BudjarnLambeth: /* Music */ add 1

2026-05-29T14:11:12Z

Music: add 1

← Older revision		Revision as of 14:11, 29 May 2026
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	* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)		* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)
	* [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''] (2026)		* [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''] (2026)
			* [https://www.youtube.com/watch?v=cXZ3RkTDE-I ''Chmelui-Múzeq - Haoýoze (45edo Microtonal Ambient)''] (2026)

	[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->		[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->

VectorGraphics: 5/4 is not THE major third

2026-05-10T10:33:32Z

5/4 is not THE major third

← Older revision		Revision as of 10:33, 10 May 2026
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	== Theory ==		== Theory ==
	45edo effectively has two approximate [[5/4\|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with harmonics [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat. However, harmonics [[11/1\|11]] and [[13/1\|13]] are sharp, but this can be fixed with the 45ef val.		45edo effectively has two approximate [[5/4]] major thirds, each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with harmonics [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat. However, harmonics [[11/1\|11]] and [[13/1\|13]] are sharp, but this can be fixed with the 45ef val.

	=== Odd harmonics ===		=== Odd harmonics ===

Lucius Chiaraviglio: /* Scales / JUMBLE's Moment of Chaos scale used in several works; / Music */ Add JUMBLE's ''FERAL (45edo microtonal ambient track)'' (2026), which also uses the Moment of Chaos scale

2026-04-17T08:51:05Z

Scales: JUMBLE's Moment of Chaos scale used in several works; Music: Add JUMBLE's ''FERAL (45edo microtonal ambient track)'' (2026), which also uses the Moment of Chaos scale

← Older revision		Revision as of 08:51, 17 April 2026
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	== Scales ==		== Scales ==
	* [[Cloudtone]][10] - recommended by [[Maeve Gutierrez]]: 8 1 8 1 8 1 8 1 8 1		* [[Cloudtone]][10] - recommended by [[Maeve Gutierrez]]: 8 1 8 1 8 1 8 1 8 1
	* [[JUMBLE]]'s "moment of chaos scale": 3 9 6 1 4 7 2 5 8 (''used in [https://www.youtube.com/watch?v=WqEOi4cd1Og Archipelago Arpeggio]'')		* [[JUMBLE]]'s "moment of chaos scale": 3 9 6 1 4 7 2 5 8 (used in several works including [https://www.youtube.com/watch?v=WqEOi4cd1Og ''Archipelago Arpeggio''] and [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''])
	* 13-tone 5&9edo scale: 5 4 1 5 3 2 5 2 3 5 1 4 5		* 13-tone 5&9edo scale: 5 4 1 5 3 2 5 2 3 5 1 4 5
	* 12-tone 5&9edo scale{{idio}}: 5 4 1 5 3 2 5 2 3 5 5 5		* 12-tone 5&9edo scale{{idio}}: 5 4 1 5 3 2 5 2 3 5 5 5
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	* [https://www.youtube.com/watch?v=K2p7HOI3TUE ''Sodium Light (45edo Microtonal Chillwave)''] (2026)		* [https://www.youtube.com/watch?v=K2p7HOI3TUE ''Sodium Light (45edo Microtonal Chillwave)''] (2026)
	* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)		* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)
			* [https://www.youtube.com/watch?v=4iwJFVIWEII ''FERAL (45edo microtonal ambient track)''] (2026)

	[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->		[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->

Lucius Chiaraviglio: /* Theory */ Fix grammar

2026-04-15T06:21:40Z

Theory: Fix grammar

← Older revision		Revision as of 06:21, 15 April 2026
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	== Theory ==		== Theory ==
	45edo effectively has two approximate [[5/4\|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat. However, ~~the~~ [[11/1\|11]] and [[13/1\|13]] is sharp, but this can be fixed with the 45ef val.		45edo effectively has two approximate [[5/4\|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with harmonics [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat. However, harmonics [[11/1\|11]] and [[13/1\|13]] are sharp, but this can be fixed with the 45ef val.

	=== Odd harmonics ===		=== Odd harmonics ===

Fitzgerald Lee: /* Theory */Added approximation to JI section, added line about 45ef val to Theory

2026-04-15T05:24:01Z

Theory: Added approximation to JI section, added line about 45ef val to Theory

← Older revision		Revision as of 05:24, 15 April 2026
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	== Theory ==		== Theory ==
	45edo effectively has two approximate [[5/4\|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat, ~~but~~ the [[11/1\|11]] is sharp.		45edo effectively has two approximate [[5/4\|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2\|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all flat. However, the [[11/1\|11]] and [[13/1\|13]] is sharp, but this can be fixed with the 45ef val.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 45 factors into primes as {{nowrap\| 3<sup>2</sup> × 5 }}, 45edo has subset edos {{EDOs\| 3, 5, 9, and 15 }}. [[135edo]], which triples it, corrects its primes 3, 7, and 11 to near-just qualities, and 270edo offers even more.		Since 45 factors into primes as {{nowrap\| 3<sup>2</sup> × 5 }}, 45edo has subset edos {{EDOs\| 3, 5, 9, and 15 }}. [[135edo]], which triples it, corrects its primes 3, 7, and 11 to near-just qualities, and 270edo offers even more.

	== Intervals ==		== Intervals ==

Fitzgerald Lee at 05:20, 15 April 2026

2026-04-15T05:20:34Z

← Older revision		Revision as of 05:20, 15 April 2026
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	In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.		In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

			== Approximation to JI==
			=== Interval mappings ===
			{{Q-odd-limit intervals\|45}}{{Q-odd-limit intervals\|44.9\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 45ef val mapping}}

	== Regular temperament properties ==		== Regular temperament properties ==

Pizzabagel shef: Added 207zpi to the octave stretching section.

2026-04-13T01:08:29Z

Added 207zpi to the octave stretching section.

← Older revision		Revision as of 01:08, 13 April 2026
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	== Octave stretch and compression ==		== Octave stretch and compression ==
	45edo's approximations of 3/1, 5/1, 7/1, 11/1 and 13/1 and 17/1 are all improved by a [[Octave stretch\|stretched-octave]] version of 45edo, such as [[ed12\|161ed12]] or [[ed6\|116ed6]]. The trade-off is a slightly worse 2/1.		45edo's approximations of 3/1, 5/1, 7/1, 11/1 and 13/1 and 17/1 are all improved by a [[Octave stretch\|stretched-octave]] version of 45edo, such as [[ed12\|161ed12]] or [[ed6\|116ed6]]. The trade-off is a slightly worse 2/1. [[207zpi]] also improves on all of those harmonics except for 17/1.

	The tuning [[equal tuning\|183ed17]] may also be used, it improves 3/1, 5/1, 7/1, 11/1, 13/1 ''and'' 17/1 (with different mappings for many) but at the cost of a noticeably worse 2/1 than the others.		The tuning [[equal tuning\|183ed17]] may also be used, it improves 3/1, 5/1, 7/1, 11/1, 13/1 ''and'' 17/1 (with different mappings for many) but at the cost of a noticeably worse 2/1 than the others.

BudjarnLambeth: /* Scales */ document scale

2026-04-07T00:49:00Z

Scales: document scale

← Older revision		Revision as of 00:49, 7 April 2026
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	== Scales ==		== Scales ==
	* [[Cloudtone]][10] - recommended by [[Maeve Gutierrez]]: 8 1 8 1 8 1 8 1 8 1		* [[Cloudtone]][10] - recommended by [[Maeve Gutierrez]]: 8 1 8 1 8 1 8 1 8 1
			* [[JUMBLE]]'s "moment of chaos scale": 3 9 6 1 4 7 2 5 8 (''used in [https://www.youtube.com/watch?v=WqEOi4cd1Og Archipelago Arpeggio]'')
	* 13-tone 5&9edo scale: 5 4 1 5 3 2 5 2 3 5 1 4 5		* 13-tone 5&9edo scale: 5 4 1 5 3 2 5 2 3 5 1 4 5
	* 12-tone 5&9edo scale{{idio}}: 5 4 1 5 3 2 5 2 3 5 5 5		* 12-tone 5&9edo scale{{idio}}: 5 4 1 5 3 2 5 2 3 5 5 5

Lucius Chiaraviglio: /* Music */ ''Yēú Zee Kiidhai (45edo microtonal ambient)'' (2026)

2026-03-29T07:52:28Z

Music: ''Yēú Zee Kiidhai (45edo microtonal ambient)'' (2026)

← Older revision		Revision as of 07:52, 29 March 2026
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	* [https://www.youtube.com/watch?v=24gnhAbHtiw ''Qúchze úzeq Qávka''] (2025)		* [https://www.youtube.com/watch?v=24gnhAbHtiw ''Qúchze úzeq Qávka''] (2025)
	* [https://www.youtube.com/watch?v=K2p7HOI3TUE ''Sodium Light (45edo Microtonal Chillwave)''] (2026)		* [https://www.youtube.com/watch?v=K2p7HOI3TUE ''Sodium Light (45edo Microtonal Chillwave)''] (2026)
			* [https://www.youtube.com/watch?v=ex9WfmWVibY ''Yēú Zee Kiidhai (45edo microtonal ambient)''] (2026)

	[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->		[[Category:Equal divisions of the octave\|##]] <!-- 2-digit number -->

Hotcrystal0 at 12:51, 19 March 2026

2026-03-19T12:51:55Z

← Older revision		Revision as of 12:51, 19 March 2026
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	\| 5		\| 5
	\| 133.3		\| 133.3
	\| [[13/12]], [[14/13]], ''[[16/15]]''		\| [[13/12]], [[14/13]], [[27/25]], ''[[16/15]]''
	\| Minor 2nd		\| Minor 2nd
	\| m2		\| m2
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	\| 40		\| 40
	\| 1066.7		\| 1066.7
	\| [[13/7]], [[24/13]], ''[[15/8]]''		\| [[13/7]], [[24/13]], [[50/27]], ''[[15/8]]''
	\| Major 7th		\| Major 7th
	\| M7		\| M7