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27edo: Difference between revisions

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→Intervals: split for a CLEAN interval table
→Regular temperament properties: not really "out of tune" for ennealimmal, just not precise enough
 
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! #
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|27et|limit=2.3.5.7.13.19-[[subgroup]]}}</ref>
! [[Interval region]]s
! [[Interval region]]s
! Approximate ratios<ref group="note">As a 2.3.5.7.13.19-[[subgroup]] temperament, inconsistent intervals in ''italic''. </ref>
! [[Kite's ups and downs notation|Ups and downs notation]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| Unison
| [[1/1]]
| [[1/1]]
| unison
| {{UDnote|step=0}}
|-
|-
| 1
| 1
| 44.4
| 44.4
| Diesis
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], ''[[81/80]]''
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], ''[[81/80]]''
| diesis
| {{UDnote|step=1}}
|-
|-
| 2
| 2
| 88.9
| 88.9
| Minor second
| ''[[16/15]]'', [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| ''[[16/15]]'', [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| minor second
| {{UDnote|step=2}}
|-
|-
| 3
| 3
| 133.3
| 133.3
| Neutral second
| [[15/14]], [[14/13]], [[13/12]]
| [[15/14]], [[14/13]], [[13/12]]
| neutral second
| {{UDnote|step=3}}
|-
|-
| 4
| 4
| 177.8
| 177.8
| Small major second
| [[10/9]]
| [[10/9]]
| small major second
| {{UDnote|step=4}}
|-
|-
| 5
| 5
| 222.2
| 222.2
| Large major second
| [[8/7]], [[9/8]]
| [[8/7]], [[9/8]]
| large major second
| {{UDnote|step=5}}
|-
|-
| 6
| 6
| 266.7
| 266.7
| Subminor third
| [[7/6]]
| [[7/6]]
| subminor third
| {{UDnote|step=6}}
|-
|-
| 7
| 7
| 311.1
| 311.1
| Minor third
| [[6/5]], [[19/16]]
| [[6/5]], [[19/16]]
| minor third
| {{UDnote|step=7}}
|-
|-
| 8
| 8
| 355.6
| 355.6
| Neutral third
| [[16/13]]
| [[16/13]]
| neutral third
| {{UDnote|step=8}}
|-
|-
| 9
| 9
| 400.0
| 400.0
| Major third
| [[5/4]], [[24/19]]
| [[5/4]], [[24/19]]
| major third
| {{UDnote|step=9}}
|-
|-
| 10
| 10
| 444.4
| 444.4
| Supermajor third
| [[9/7]], [[13/10]]
| [[9/7]], [[13/10]]
| supermajor third
| {{UDnote|step=10}}
|-
|-
| 11
| 11
| 488.9
| 488.9
| Perfect fourth
| [[4/3]]
| [[4/3]]
| fourth
| {{UDnote|step=11}}
|-
|-
| 12
| 12
| 533.3
| 533.3
| Superfourth
| [[19/14]], [[26/19]], [[27/20]], [[48/35]]
| [[19/14]], [[26/19]], [[27/20]], [[48/35]]
| superfourth
| {{UDnote|step=12}}
|-
|-
| 13
| 13
| 577.8
| 577.8
| Small tritone
| [[7/5]], [[18/13]]
| [[7/5]], [[18/13]]
| small tritone
| {{UDnote|step=13}}
|-
|-
| 14
| 14
| 622.2
| 622.2
| Large tritone
| [[10/7]], [[13/9]]
| [[10/7]], [[13/9]]
| large tritone
| {{UDnote|step=14}}
|-
|-
| 15
| 15
| 666.7
| 666.7
| Subfifth
| [[19/13]], [[28/19]], [[35/24]], [[40/27]]
| [[19/13]], [[28/19]], [[35/24]], [[40/27]]
| subfifth
| {{UDnote|step=15}}
|-
|-
| 16
| 16
| 711.1
| 711.1
| Perfect fifth
| [[3/2]]
| [[3/2]]
| fifth
| {{UDnote|step=16}}
|-
|-
| 17
| 17
| 755.6
| 755.6
| Subminor sixth
| [[14/9]], [[20/13]]
| [[14/9]], [[20/13]]
| subminor sixth
| {{UDnote|step=17}}
|-
|-
| 18
| 18
| 800.0
| 800.0
| Minor sixth
| [[8/5]], [[19/12]]
| [[8/5]], [[19/12]]
| minor sixth
| {{UDnote|step=18}}
|-
|-
| 19
| 19
| 844.4
| 844.4
| Neutral sixth
| [[13/8]]
| [[13/8]]
| neutral sixth
| {{UDnote|step=19}}
|-
|-
| 20
| 20
| 888.9
| 888.9
| Major sixth
| [[5/3]], [[32/19]]
| [[5/3]], [[32/19]]
| major sixth
| {{UDnote|step=20}}
|-
|-
| 21
| 21
| 933.3
| 933.3
| Supermajor sixth
| [[12/7]]
| [[12/7]]
| supermajor sixth
| {{UDnote|step=21}}
|-
|-
| 22
| 22
| 977.8
| 977.8
| Harmonic seventh
| [[7/4]], [[16/9]]
| [[7/4]], [[16/9]]
| harmonic seventh
| {{UDnote|step=22}}
|-
|-
| 23
| 23
| 1022.2
| 1022.2
| Large minor seventh
| [[9/5]]
| [[9/5]]
| large minor seventh
| {{UDnote|step=23}}
|-
|-
| 24
| 24
| 1066.7
| 1066.7
| Neutral seventh
| [[13/7]], [[24/13]], [[28/15]]
| [[13/7]], [[24/13]], [[28/15]]
| neutral seventh
| {{UDnote|step=24}}
|-
|-
| 25
| 25
| 1111.1
| 1111.1
| Major seventh
| ''[[15/8]]'', [[19/10]], [[36/19]], [[40/21]], [[48/25]]
| ''[[15/8]]'', [[19/10]], [[36/19]], [[40/21]], [[48/25]]
| major seventh
| {{UDnote|step=25}}
|-
|-
| 26
| 26
| 1155.6
| 1155.6
| Supermajor seventh
| [[27/14]], [[35/18]], [[49/25]], [[96/49]], ''[[160/81]]''
| [[27/14]], [[35/18]], [[49/25]], [[96/49]], ''[[160/81]]''
| supermajor seventh
| {{UDnote|step=26}}
|-
|-
| 27
| 27
| 1200.0
| 1200.0
| Octave
| [[2/1]]
| [[2/1]]
| octave
| {{UDnote|step=27}}
 
|}
|}
<references group="note" />
<references group="note" />
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|+ style="font-size: 105%;" | Circle of fifths in 27edo
|+ style="font-size: 105%;" | Circle of fifths in 27edo
|- style="white-space: nowrap;"
|- style="white-space: nowrap;"
!Cents
! Cents
! colspan="2" | Extended<br />Pythagorean<br />notation
! colspan="2" | Extended<br>Pythagorean<br>notation
! colspan="2" | Quartertone<br />notation
! colspan="2" | Quartertone<br>notation
|-
|-
| 0.0
| 0.0
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Using standard [[chain-of-fifths notation]], a sharp (an augmented unison) raises a note by 4 edosteps, just one edostep beneath the following nominal, and the flat conversely lowers. The sharp is quite wide at about 178¢, sounding like a narrow major 2nd. C to C♯ describes the approximate 10/9 and 11/10 interval. An accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats. The half-sharp is notated as a quartertone, but at about 89¢ it sounds more like a narrow semitone. The gamut from C to D is C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with many ascending intervals appearing to be descending on the staff.
Using standard [[chain-of-fifths notation]], a sharp (an augmented unison) raises a note by 4 edosteps, just one edostep beneath the following nominal, and the flat conversely lowers. The sharp is quite wide at about 178¢, sounding like a narrow major 2nd. C to C♯ describes the approximate 10/9 and 11/10 interval. An accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats. The half-sharp is notated as a quartertone, but at about 89¢ it sounds more like a narrow semitone. The gamut from C to D is C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with many ascending intervals appearing to be descending on the staff.


=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
27edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
{{Sharpness-sharp4-szg}}
 
=== Kite's ups and downs notation ===
27edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
{{Ups and downs sharpness}}
{{Ups and downs sharpness}}
[[Alternative symbols for ups and downs notation|Alternatively,]] sharps and flats with arrows can be used, borrowed from extended [[Helmholtz–Ellis notation]]:
{{Sharpness-sharp4}}


=== Sagittal notation ===
=== Sagittal notation ===
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| 3
| 3
| 2\27
| 2\27
| [[Augene]] (27e) / Eugene (27)
| [[Augene]] (27e) / eugene (27)
| [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]]
| [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]]
|-
|-
Line 1,004: Line 1,034:
| 9
| 9
| 1\27
| 1\27
| [[Niner]] (27e)<br>[[Ennealimmal]] (out of tune)
| [[Niner]] (27e)
| [[9L 9s]]
| [[9L 9s]]
|}
|}
In addition, 27edo can be used as a detempering target for [[ennealimmal]].


=== Commas ===
=== Commas ===
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; [[Brendan Byrnes]]
; [[Brendan Byrnes]]
* [https://www.youtube.com/watch?v=sWaqlAgSWcc ''Sunspots''] (2022)
* [https://www.youtube.com/watch?v=sWaqlAgSWcc ''Sunspots''] (2022)
* ''27 EDO Etude'' (2022)
** [https://brendanbyrnes.bandcamp.com/track/27-edo-etude on Bandcamp]
** [https://m.youtube.com/watch?v=Lml2cfJW9QI on YouTube] (with sheet music)
* [https://www.youtube.com/watch?v=lywpWPBYQi0 ''Istril Bloom''] (2025)
* [https://www.youtube.com/watch?v=lywpWPBYQi0 ''Istril Bloom''] (2025)


Line 1,383: Line 1,418:
; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=hDP8cfJqWOI ''microtonal improvisation in 27edo''] (2023)
* [https://www.youtube.com/watch?v=hDP8cfJqWOI ''microtonal improvisation in 27edo''] (2023)
* [https://www.youtube.com/shorts/FSPUebavRCQ ''27edo waltz''] (2025)
* [https://www.youtube.com/shorts/izpEen38Sps ''27edo improv''] (2025)
* [https://www.youtube.com/shorts/izpEen38Sps ''27edo improv''] (2025)
* ''Flies Control My Pain - 27edo'' (2026)
** [https://www.youtube.com/shorts/sKnjDPEOQtc <nowiki>[short 1]</nowiki>] (using [[tetracot]] Lumatone mapping)
** [https://www.youtube.com/shorts/QEebNJkcIlE <nowiki>[short 2]</nowiki>] (using [[Starling_temperaments#Kumonga|kumonga]] Lumatone mapping)


; [[Francium]]
; [[Francium]]
* [https://www.youtube.com/watch?v=3Ty3FpmAdGA ''Happy Birthday in 27edo''] (2025)
* [https://www.youtube.com/watch?v=3Ty3FpmAdGA ''Happy Birthday in 27edo''] (2025)
* [https://www.youtube.com/watch?v=Wfg2gWW9qZg ''Router-Pseudoscientist''] (2025)
* "Router-Pseudoscientist" from ''TOTMC 2025'' (2025) – [https://open.spotify.com/track/5qrXYuhz3XOEaUyFvP4ldp Spotify] | [https://francium223.bandcamp.com/track/router-pseudoscientist Bandcamp] | [https://www.youtube.com/watch?v=Wfg2gWW9qZg YouTube]
* [https://www.youtube.com/watch?v=hY0zo6MqQtU ''Waltz No. 11 in A flat major''] (2026)
* [https://www.youtube.com/watch?v=wY43YLa17s4 ''Plane Sonatina No. 4''] (2026)
 
; [[groundfault]]
* From ''A New Dusk'' (2024) – [https://groundfco.bandcamp.com/album/a-new-dusk Bandcamp] | [https://www.youtube.com/watch?v=1bnEO8vGvbo YouTube]
** "Back Stalk"
** "Superior Intermedial" – in part, the rest being in 31edo
** "Revelation of Your Forever"
* "Sakura Blade Minivan", from ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/track/sakura-blade-minivan-27-35edo-2 Bandcamp] | [https://www.youtube.com/watch?v=rrjuGmmodn0&t=1436 YouTube (23:56–27:58)] – in part, the rest being in 35edo


; [[Igliashon Jones]]
; [[Igliashon Jones]]
Line 1,437: Line 1,485:
* "Funkrotonal" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1zjNkbm8kIkuCxtodyFCL0 Spotify] | [https://xotla.bandcamp.com/track/funkrotonal-27edo Bandcamp] | [https://www.youtube.com/watch?v=7gt1BBJuJsE YouTube]
* "Funkrotonal" from ''Microtonal Allsorts'' (2023) – [https://open.spotify.com/track/1zjNkbm8kIkuCxtodyFCL0 Spotify] | [https://xotla.bandcamp.com/track/funkrotonal-27edo Bandcamp] | [https://www.youtube.com/watch?v=7gt1BBJuJsE YouTube]


[[Category:Augene]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Augmented]]
[[Category:Sensi]]
[[Category:Sensi]]
[[Category:Superpyth]]
[[Category:Superpyth]]
[[Category:Tetracot]]
[[Category:Tetracot]]
[[Category:Twentuning]]
[[Category:Twentuning]]
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