Xenharmonic Wiki

28edo: Difference between revisions

← Older edit
VisualWikitext
Francium (talk | contribs)
4,621 edits
→Music: Sorted list
Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
6,129 edits
m Text replacement - "Ups and Downs Notation" to "Ups and downs notation"
 
(25 intermediate revisions by 10 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
'''28 equal divisions of the octave''' ('''28edo''') is the [[tuning system]] derived by dividing the [[octave]] into 28 equal steps of approximately 42.857{{cent}} each.
{{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]].
Line 22: Line 22:
! 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 Downs Notation]]
! rowspan="2" colspan="3" | [[Ups and downs notation]]
|-
|-
! Cents
! Cents
Line 247: Line 247:
| 1028.57
| 1028.57
| [[20/11]]
| [[20/11]]
| 1035
| 1035.00
| -6.43
| -6.43
| 7th
| 7th
Line 290: Line 290:
|}
|}


== Chord Names ==
== 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.


Line 303: Line 316:
* 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 Downs Notation #Chord names in other EDOs]].
For a more complete list, see [[Ups and downs notation #Chord names in other EDOs]].


== Rank two temperaments ==
== Regular temperament properties ==
=== Rank-2 temperaments ===
{| class="wikitable center-1 center-2"
{| class="wikitable center-1 center-2"
|-
|-
! Periods <br> per octave
! Periods<br>per 8ve
! Generator
! Generator
! Temperaments
! Temperaments
Line 330: Line 344:
| 1
| 1
| 11\28
| 11\28
| [[Oneirotonic]]
| [[A-team]]
|-
|-
| 1
| 1
Line 342: Line 356:
| 2
| 2
| 3\28
| 3\28
| [[Trienstonic_clan#Octokaidecal|Octokaidecal]]
| [[Octokaidecal]]
|-
|-
| 2
| 2
Line 369: Line 383:
|}
|}


== Commas ==
=== Commas ===
28 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 28 44 65 79 97 104 }}.)
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>Limit]]
! [[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]]
Line 393: Line 407:
| 62.57
| 62.57
| Quadgu
| Quadgu
| Major diesis, diminished comma
| Diminished comma, major diesis
|-
|-
| 5
| 5
Line 414: Line 428:
| 48.77
| 48.77
| Rugu
| Rugu
| Septimal quartertone
| Mint comma, septimal quartertone
|-
|-
| 7
| 7
Line 421: Line 435:
| 34.98
| 34.98
| Biruyo
| Biruyo
| Tritonic diesis, Jubilisma
| Jubilisma, tritonic diesis
|-
|-
| 7
| 7
Line 428: Line 442:
| 21.18
| 21.18
| Triru-aquinyo
| Triru-aquinyo
| Gariboh
| Gariboh comma
|-
|-
| 7
| 7
Line 435: Line 449:
| 13.79
| 13.79
| Zotrigu
| Zotrigu
| Septimal semicomma, Starling comma
| Starling comma, septimal semicomma
|-
|-
| 7
| 7
Line 442: Line 456:
| 2.35
| 2.35
| Lazoquinyo
| Lazoquinyo
| Horwell
| Horwell comma
|-
|-
| 7
| 7
Line 449: Line 463:
| 0.34
| 0.34
| Trisa-seprugu
| Trisa-seprugu
| [[Akjaysma]], 5\7-octave comma
| [[Akjaysma]]
|-
|-
| 11
| 11
Line 470: Line 484:
| 3.03
| 3.03
| Triluyo
| Triluyo
| Wizardharry
| Wizardharry comma
|}
|}
<references/>
<references/>
Line 536: Line 550:
* [[machine11]]
* [[machine11]]
* [[machine17]]
* [[machine17]]
== Instruments ==
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 ==
'''[[User:Eliora|Eliora]]'''
; [[Ambient Esoterica]]
* [https://www.youtube.com/watch?v=ghVCGlm7yOk Fantasy for Piano]
* [https://www.youtube.com/watch?v=d_55LCULX9g ''28 Mansions of the Moon'']
'''Kosmorksy'''
 
* [https://www.youtube.com/watch?v=26UpCbrb3mE 28 tone Prelude]
; [[Beheld]]
'''[[User:Userminusone|Userminusone]]'''
* [https://www.youtube.com/watch?v=0nvrUbw1VLQ ''Haze vibe'']
* [https://youtu.be/NbR3i45qQVQ Purple Skyes]
 
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/--BIQKJ9uvI ''minuet in 28edo''] (2025)
 
; [[duckapus]]
* [https://www.youtube.com/watch?v=F74B9qUpYi8 ''G.27 Variations in 28edo''] (2023)
 
; [[User:Eliora|Eliora]]
* [https://www.youtube.com/watch?v=ghVCGlm7yOk ''Fantasy for Piano'']
 
; [[Kosmorksy]]
* [https://www.youtube.com/watch?v=26UpCbrb3mE ''28 tone Prelude'']
 
; [[Claudi Meneghin]]
* [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])
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=vw6l5b3oGk0 ''Edolian - Machinery''] (2020)
 
; [[User:Userminusone|Userminusone]]
* [https://youtu.be/NbR3i45qQVQ ''Purple Skyes'']


[[Category:28edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Twentuning]]
[[Category:Twentuning]]
 
[[Category:Listen]]
[[Category:Todo:unify precision]]
Retrieved from "https://en.xen.wiki/w/28edo"