28edo - Revision history

BudjarnLambeth: /* Music */ typo

2026-05-29T16:57:54Z

Music: typo

← Older revision		Revision as of 16:57, 29 May 2026
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	* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)		* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)
	* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)		* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)
	* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (~~2028~~)		* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (2026)

	; [[duckapus]]		; [[duckapus]]

Lucius Chiaraviglio: /* Music */ Eliora's ''Fantasy for Piano (and strings)'' Fix title and date

2026-05-28T06:10:46Z

Music: Eliora's ''Fantasy for Piano (and strings)'' Fix title and date

← Older revision		Revision as of 06:10, 28 May 2026
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	; [[User:Eliora\|Eliora]]		; [[User:Eliora\|Eliora]]
	* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']		* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano (and strings)''] (2021)

	; [[Francium]]		; [[Francium]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Fantasy in 28edo'' (2028)

2026-05-28T02:06:53Z

Music: Add Bryan Deister's ''Fantasy in 28edo'' (2028)

← Older revision		Revision as of 02:06, 28 May 2026
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	* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)		* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)
	* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)		* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)
			* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (2028)

	; [[duckapus]]		; [[duckapus]]

Hotcrystal0: affect -> effect

2026-03-24T19:20:24Z

affect -> effect

← Older revision		Revision as of 19:20, 24 March 2026
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	== Notation ==		== Notation ==
	=== Ups and downs notation ===		=== Ups and downs notation ===
	As 28edo tempers out the [[2187/2048\|Pythagorean apotome]], the traditional sharps and flats have no ~~affect~~ on the pitch. Therefore, with [[ups and downs notation]], arrows are required.		As 28edo tempers out the [[2187/2048\|Pythagorean apotome]], the traditional sharps and flats have no effect on the pitch. Therefore, with [[ups and downs notation]], arrows are required.
	{{ups and downs sharpness}}		{{ups and downs sharpness}}

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''28edo blues'' (2023)

2026-01-15T12:22:56Z

Music: Add Bryan Deister's ''28edo blues'' (2023)

← Older revision		Revision as of 12:22, 15 January 2026
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022)		* [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022)
			* [https://www.youtube.com/shorts/sCE0MjUyRUk ''28edo blues''] (2023)
	* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)		* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)

Hotcrystal0: / not :

2026-01-08T02:10:47Z

/ not :

← Older revision		Revision as of 02:10, 8 January 2026
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	{{Harmonics in equal\|28\|start=12\|collapsed=1\|intervals=odd}}		{{Harmonics in equal\|28\|start=12\|collapsed=1\|intervals=odd}}

	28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out\|tempers out]] the [[greater diesis]] [[648/~~625\|648:~~625]]. It does not however temper out the [[128/~~125\|128:~~125]] [[lesser_diesis\|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].		28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out\|tempers out]] the [[greater diesis]] [[648/625]]. It does not however temper out the [[128/125]] [[lesser_diesis\|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].

	28edo can approximate the [[7-limit\|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family\|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords\|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.		28edo can approximate the [[7-limit\|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family\|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords\|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''28edo improvisation'' (2022)

2025-12-14T08:58:57Z

Music: Add Bryan Deister's ''28edo improvisation'' (2022)

← Older revision		Revision as of 08:58, 14 December 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/1nWL2qEcI-Q ''28edo improvisation''] (2022)
	* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)		* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)

Phanomium: /* Music */ Added music

2025-10-30T18:56:42Z

Music: Added music

← Older revision		Revision as of 18:56, 30 October 2025
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	* [https://www.youtube.com/watch?v=26UpCbrb3mE ''28 tone Prelude'']		* [https://www.youtube.com/watch?v=26UpCbrb3mE ''28 tone Prelude'']

	; [[Claudi Meneghin]]		; [[User:Phanomium\|Phanomium]]
			* ''[https://www.youtube.com/watch?v=zZJ5b4SkT7Q Euxenite]'' (2025)

			;[[Claudi Meneghin]]
	* [https://www.youtube.com/watch?v=30XUKJsaINU ''Happy Birthday Canon'', 5-in-1 Canon in 28edo]		* [https://www.youtube.com/watch?v=30XUKJsaINU ''Happy Birthday Canon'', 5-in-1 Canon in 28edo]
	* [https://www.youtube.com/watch?v=wYdRAzp8Qi0 ''Canon on Twinkle Twinkle Little Star'', for Baroque Oboe & Viola] (2023) – ([https://www.youtube.com/watch?v=B1KZoLR8UTI for Organ])		* [https://www.youtube.com/watch?v=wYdRAzp8Qi0 ''Canon on Twinkle Twinkle Little Star'', for Baroque Oboe & Viola] (2023) – ([https://www.youtube.com/watch?v=B1KZoLR8UTI for Organ])

Francium: /* Music */ +music

2025-10-08T11:18:46Z

Music: +music

← Older revision		Revision as of 11:18, 8 October 2025
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	; [[User:Eliora\|Eliora]]		; [[User:Eliora\|Eliora]]
	* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']		* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']

			; [[Francium]]
			* [https://www.youtube.com/watch?v=8dubV7STjJA ''According to a Tomato''] (2025)

	; [[Kosmorksy]]		; [[Kosmorksy]]

BudjarnLambeth: /* Scales */

2025-09-29T20:44:30Z

Scales

← Older revision		Revision as of 20:44, 29 September 2025
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	* Melodic Major [16] 2122221222122212		* Melodic Major [16] 2122221222122212

			; Oneirotonic scales
	Interestingly, as it has a near perfect 21/16, 28edo can also generate Oneirotonic scales (see [[13edo\|13edo]]) by stacking it's 11th degree, and they actually sound better in this temperament.		Interestingly, as it has a near perfect 21/16, 28edo can also generate Oneirotonic scales (see [[13edo\|13edo]]) by stacking it's 11th degree, and they actually sound better in this temperament.

← Older revision		Revision as of 02:10, 8 January 2026
Line 5:		Line 5:
	{{Harmonics in equal\|28\|start=12\|collapsed=1\|intervals=odd}}		{{Harmonics in equal\|28\|start=12\|collapsed=1\|intervals=odd}}

	28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out\|tempers out]] the [[greater diesis]] [[648/~~625\|648:~~625]]. It does not however temper out the [[128/~~125\|128:~~125]] [[lesser_diesis\|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].		28edo is a multiple of both [[7edo]] and [[14edo]] (and of course [[2edo]] and [[4edo]]). It shares three intervals with [[12edo]]: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it [[tempering_out\|tempers out]] the [[greater diesis]] [[648/625]]. It does not however temper out the [[128/125]] [[lesser_diesis\|lesser diesis]], as 28 is not divisible by 3. It has the same perfect fourth and fifth as 7edo. It also has decent approximations of several septimal intervals, of which [[9/7]] and its inversion [[14/9]] are also found in 14edo. Its approximation to [[5/4]] is unusually good for an edo of this size, being the next convergent to log<sub>2</sub>5 after [[3edo]].

	28edo can approximate the [[7-limit\|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family\|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords\|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.		28edo can approximate the [[7-limit\|7-limit]] subgroup 2.27.5.21 quite well, and on this subgroup it has the same commas and tunings as 84edo. The temperament corresponding to [[Semicomma_family\|orwell temperament]] now has a major third as generator, though as before 225/224, 1728/1715 and 6144/6125 are tempered out. The 225/224-tempered version of the [[Marvel_chords\|augmented triad]] has a very low complexity, so many of them appear in the [[MOS scales]] for this temperament, which have sizes 7, 10, 13, 16, 19, 22, 25.