28edo: Difference between revisions
Instruments section |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|28}} | {{Harmonics in equal|28}} | ||
{{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|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]]. | ||
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! colspan="2" | Just (j) | ! colspan="2" | Just (j) | ||
! rowspan="2" | Delta <br> (e-j) | ! rowspan="2" | Delta <br> (e-j) | ||
! rowspan="2" colspan="3" | [[Ups and | ! rowspan="2" colspan="3" | [[Ups and downs notation]] | ||
|- | |- | ||
! Cents | ! Cents | ||
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|} | |} | ||
== Chord | == Notation == | ||
=== Sagittal notation === | |||
This notation uses the same sagittal sequence as EDOs [[23edo#Sagittal notation|23]] and [[33edo#Sagittal notation|33]], and is a superset of the notations for EDOs [[14edo#Sagittal notation|14]] and [[7edo#Sagittal notation|7]]. | |||
<imagemap> | |||
File:28-EDO_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 447 0 607 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 447 106 [[Fractional_3-limit_notation#Bad-fifths_limma-fraction_notation | limma-fraction notation]] | |||
default [[File:28-EDO_Sagittal.svg]] | |||
</imagemap> | |||
== Chord names == | |||
Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | Ups and downs can be used to name 28edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. | ||
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* 0-7-16-23 = C vE G vB = Cv7 = C down-seven | * 0-7-16-23 = C vE G vB = Cv7 = C down-seven | ||
For a more complete list, see [[Ups and | For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]]. | ||
== Rank | == Regular temperament properties == | ||
=== Rank-2 temperaments === | |||
{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods <br> per | ! Periods<br>per 8ve | ||
! Generator | ! Generator | ||
! Temperaments | ! Temperaments | ||
| Line 329: | Line 344: | ||
| 1 | | 1 | ||
| 11\28 | | 11\28 | ||
| [[ | | [[A-team]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 341: | Line 356: | ||
| 2 | | 2 | ||
| 3\28 | | 3\28 | ||
| [[ | | [[Octokaidecal]] | ||
|- | |- | ||
| 2 | | 2 | ||
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|} | |} | ||
== Commas == | === Commas === | ||
28et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 28 44 65 79 97 104 }}. | |||
{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
|- | |- | ||
! [[Harmonic Limit|Prime<br> | ! [[Harmonic Limit|Prime<br>limit]] | ||
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
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| 62.57 | | 62.57 | ||
| Quadgu | | Quadgu | ||
| | | Diminished comma, major diesis | ||
|- | |- | ||
| 5 | | 5 | ||
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| 48.77 | | 48.77 | ||
| Rugu | | Rugu | ||
| | | Mint comma, septimal quartertone | ||
|- | |- | ||
| 7 | | 7 | ||
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| 34.98 | | 34.98 | ||
| Biruyo | | Biruyo | ||
| | | Jubilisma, tritonic diesis | ||
|- | |- | ||
| 7 | | 7 | ||
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| 21.18 | | 21.18 | ||
| Triru-aquinyo | | Triru-aquinyo | ||
| Gariboh | | Gariboh comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 13.79 | | 13.79 | ||
| Zotrigu | | Zotrigu | ||
| | | Starling comma, septimal semicomma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 2.35 | | 2.35 | ||
| Lazoquinyo | | Lazoquinyo | ||
| Horwell | | Horwell comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 0.34 | | 0.34 | ||
| Trisa-seprugu | | Trisa-seprugu | ||
| [[Akjaysma]] | | [[Akjaysma]] | ||
|- | |- | ||
| 11 | | 11 | ||
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| 3.03 | | 3.03 | ||
| Triluyo | | Triluyo | ||
| Wizardharry | | Wizardharry comma | ||
|} | |} | ||
<references/> | <references/> | ||
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== Instruments == | == Instruments == | ||
28edo can be played on the [[Lumatone]]. See | 28edo can be played on the [[Lumatone]]. See [[Lumatone mapping for 28edo]]. | ||
28edo can also be played on a [[14edo]] [[guitar]] with very little effort. See [[User:MisterShafXen/Skip fretting system 28 2 3]]. | |||
== Music == | == Music == | ||
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; [[Beheld]] | ; [[Beheld]] | ||
* [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe''] | * [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe''] | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025) | |||
; [[duckapus]] | ; [[duckapus]] | ||