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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.
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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}}


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; Diatonic scales
; Diatonic scales
However, unlike 15, 28 is complex enough to do recognisable approximations of various diatonic scales and their modes, although they will sound noticeably out of tune and it's obviously not the best method of using the temperament.  
However, unlike 15, 28 is complex enough to do recognizable approximations of various diatonic scales and their modes, although they will sound noticeably out of tune and it's obviously not the best method of using the temperament.  


* Diatonic Major [7] 5434552
* Diatonic Major [7] 5434552
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* Melodic Major [16] 2122221222122212
* Melodic Major [16] 2122221222122212


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


* Oneirotonic [5] 65656
* Oneirotonic [5] 65656
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* Oneirotonic [13] 4141141411411
* Oneirotonic [13] 4141141411411
* Oneirotonic [18] 311311131131113111
* Oneirotonic [18] 311311131131113111
* Pathological Oneirotonic [23] 21112111121112111121111
* Pathological{{idiosyncratic}} Oneirotonic [23] 21112111121112111121111
* [[machine5]]
* [[machine5]]
* [[machine6]]
* [[machine6]]
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; [[Beheld]]
; [[Beheld]]
* [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe'']
* [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe'']
; [[User:Fynn_Cerulean|Fynn Cerulean]]
* [https://youtu.be/CUhs-60GdO4 ''Semichromatic''] (2026)


; [[Bryan Deister]]
; [[Bryan Deister]]
* [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)
* [https://www.youtube.com/shorts/vEcihDrmddg ''Fantasy in 28edo''] (2026)
* [https://www.youtube.com/shorts/EVZtaYK5mcQ ''28edo groove''] (2026)


; [[duckapus]]
; [[duckapus]]
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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]]
* "According to a Tomato" from ''TOTMC 2025'' (2025) – [https://open.spotify.com/track/7ulkhYBppJCsBKP3cdMdjZ Spotify] | [https://francium223.bandcamp.com/track/according-to-a-tomato Bandcamp] | [https://www.youtube.com/watch?v=8dubV7STjJA YouTube]
* [https://www.youtube.com/watch?v=4hTXsifzkZU ''Happy Birthday in 28edo''] (2026)


; [[Kosmorksy]]
; [[Kosmorksy]]
* [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])
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