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{{interwiki
| de = 27edo
| en = 27edo
| es =
| ja =
}}
{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}
{{ED intro}}


== Theory ==
== Theory ==
Assuming pure octaves, 27edo divides the [[octave]] in 27 equal parts each exactly 44{{frac|4|9}} [[cent]]s in size. Its fifth and harmonic seventh are both sharp by 9{{c}}, and the major third is the same 400-cent major third as [[12edo]], sharp by 13.7{{c}}. The result is that [[6/5]], [[7/5]], and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from [[superpyth|1/3-septimal-comma superpyth]] in the same way that 19edo is audibly indistinguishable from [[1/3-comma meantone|1/3-syntonic-comma meantone]], where three fifths in 19edo reach a near-perfect [[6/5]] and [[5/3]] and three fifths in 27edo reaching a near-perfect [[7/6]] and [[12/7]].
Assuming pure octaves, 27edo divides the [[octave]] in 27 equal parts each exactly 44{{frac|4|9}} [[cent]]s in size. Its fifth and harmonic seventh are both sharp by 9{{c}}, and the major third is the same 400-cent major third as [[12edo]], sharp by 13.7{{c}}. The result is that [[6/5]], [[7/5]], and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from [[superpyth|1/3-septimal-comma superpyth]] in the same way that 19edo is audibly indistinguishable from [[1/3-comma meantone|1/3-syntonic-comma meantone]]: Three fourths (C-Eb) in 19edo reach a near-perfect [[6/5]] and the same distance in 27edo reaches a near-perfect [[7/6]].


Though 27edo's [[7-limit]] tuning is not highly accurate, it nonetheless is the smallest equal division to represent the [[7-odd-limit]] both [[consistent]]ly and distinctly—that is, everything in the [[7-odd-limit]] [[tonality diamond]] is uniquely represented by a certain number of steps of 27edo. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13.19 (no-11's, no-17's 19-limit) temperament, if a highly sharp-tending one. It also approximates [[19/10]], [[19/12]], and [[19/14]], so {{dash|0, 7, 13, 25|med}} does quite well as a 10:12:14:19 chord, with the major seventh 25\27 being less than one cent off from 19/10. Octave-inverted, these also form a quite convincing approximation of the main Bohlen–Pierce triads, 3:5:7 ([0 20 33]) and 5:7:9 ([0 13 23]), via the [[BPS]] scale in [[43edt]], although approximations of the odd harmonic series rapidly become rough if extended to prime 11 and above.
Though 27edo's [[7-limit]] tuning is not highly accurate, it nonetheless is the smallest equal division to represent the [[7-odd-limit]] both [[consistent]]ly and distinctly—that is, everything in the [[7-odd-limit]] [[tonality diamond]] is uniquely represented by a certain number of steps of 27edo. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13.19 (no-11's, no-17's 19-limit) temperament, if a highly sharp-tending one. It also approximates [[19/10]], [[19/12]], and [[19/14]], so {{dash|0, 7, 13, 25|med}} does quite well as a 10:12:14:19 chord, with the major seventh 25\27 being less than one cent off from 19/10. Octave-inverted, these also form a quite convincing approximation of the main Bohlen–Pierce triads, 3:5:7 ([0 20 33]) and 5:7:9 ([0 13 23]), via the [[BPS]] scale in [[43edt]], although approximations of the odd harmonic series rapidly become rough if extended to prime 11 and above.
Line 21: Line 27:


== Intervals ==
== Intervals ==
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-1 right-2"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios<ref group="note">{{sg|27et|limit=2.3.5.7.13.19-[[subgroup]]}}</ref>
! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and vm2)
! [[Interval region]]s
! [[Interval region]]s
! colspan="2" | [[Solfege]]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]]
| {{UDnote|step=0}}
|-
| 1
| 44.4
| Diesis
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], ''[[81/80]]''
| {{UDnote|step=1}}
|-
| 2
| 88.9
| Minor second
| ''[[16/15]]'', [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| {{UDnote|step=2}}
|-
| 3
| 133.3
| Neutral second
| [[15/14]], [[14/13]], [[13/12]]
| {{UDnote|step=3}}
|-
| 4
| 177.8
| Small major second
| [[10/9]]
| {{UDnote|step=4}}
|-
| 5
| 222.2
| Large major second
| [[8/7]], [[9/8]]
| {{UDnote|step=5}}
|-
| 6
| 266.7
| Subminor third
| [[7/6]]
| {{UDnote|step=6}}
|-
| 7
| 311.1
| Minor third
| [[6/5]], [[19/16]]
| {{UDnote|step=7}}
|-
| 8
| 355.6
| Neutral third
| [[16/13]]
| {{UDnote|step=8}}
|-
| 9
| 400.0
| Major third
| [[5/4]], [[24/19]]
| {{UDnote|step=9}}
|-
| 10
| 444.4
| Supermajor third
| [[9/7]], [[13/10]]
| {{UDnote|step=10}}
|-
| 11
| 488.9
| Perfect fourth
| [[4/3]]
| {{UDnote|step=11}}
|-
| 12
| 533.3
| Superfourth
| [[19/14]], [[26/19]], [[27/20]], [[48/35]]
| {{UDnote|step=12}}
|-
| 13
| 577.8
| Small tritone
| [[7/5]], [[18/13]]
| {{UDnote|step=13}}
|-
| 14
| 622.2
| Large tritone
| [[10/7]], [[13/9]]
| {{UDnote|step=14}}
|-
| 15
| 666.7
| Subfifth
| [[19/13]], [[28/19]], [[35/24]], [[40/27]]
| {{UDnote|step=15}}
|-
| 16
| 711.1
| Perfect fifth
| [[3/2]]
| {{UDnote|step=16}}
|-
| 17
| 755.6
| Subminor sixth
| [[14/9]], [[20/13]]
| {{UDnote|step=17}}
|-
| 18
| 800.0
| Minor sixth
| [[8/5]], [[19/12]]
| {{UDnote|step=18}}
|-
| 19
| 844.4
| Neutral sixth
| [[13/8]]
| {{UDnote|step=19}}
|-
| 20
| 888.9
| Major sixth
| [[5/3]], [[32/19]]
| {{UDnote|step=20}}
|-
| 21
| 933.3
| Supermajor sixth
| [[12/7]]
| {{UDnote|step=21}}
|-
| 22
| 977.8
| Harmonic seventh
| [[7/4]], [[16/9]]
| {{UDnote|step=22}}
|-
| 23
| 1022.2
| Large minor seventh
| [[9/5]]
| {{UDnote|step=23}}
|-
| 24
| 1066.7
| Neutral seventh
| [[13/7]], [[24/13]], [[28/15]]
| {{UDnote|step=24}}
|-
| 25
| 1111.1
| Major seventh
| ''[[15/8]]'', [[19/10]], [[36/19]], [[40/21]], [[48/25]]
| {{UDnote|step=25}}
|-
| 26
| 1155.6
| Supermajor seventh
| [[27/14]], [[35/18]], [[49/25]], [[96/49]], ''[[160/81]]''
| {{UDnote|step=26}}
|-
| 27
| 1200.0
| Octave
| [[2/1]]
| {{UDnote|step=27}}
|}
<references group="note" />
=== Proposed interval names and solfèges ===
{| class="wikitable center-all right-2 left-4 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! colspan="3" | [[Kite's ups and downs notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and vm2)
! colspan="2" | [[Solfège]]s
|-
| 0
| 0.0
| P1
| P1
| perfect unison
| perfect unison
| D
| D
| unison
| da
| da
| do
| do
Line 42: Line 224:
| 1
| 1
| 44.4
| 44.4
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], ''[[81/80]]''
| ^1, m2
| ^1, m2
| up unison, minor 2nd
| up unison, minor 2nd
| ^D, Eb
| ^D, Eb
| diesis
| fra
| fra
| di
| di
Line 52: Line 232:
| 2
| 2
| 88.9
| 88.9
| ''[[16/15]]'', [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| ^^1, ^m2
| ^^1, ^m2
| dup unison, upminor 2nd
| dup unison, upminor 2nd
| ^^D, ^Eb
| ^^D, ^Eb
| minor second
| fru
| fru
| ra
| ra
Line 62: Line 240:
| 3
| 3
| 133.3
| 133.3
| [[15/14]], [[14/13]], [[13/12]]
| vA1, ~2
| vA1, ~2
| downaug 1sn, mid 2nd
| downaug 1sn, mid 2nd
| vD#, vvE
| vD#, vvE
| neutral second
| ri
| ri
| ru
| ru
Line 72: Line 248:
| 4
| 4
| 177.8
| 177.8
| [[10/9]]
| A1, vM2
| A1, vM2
| aug 1sn, downmajor 2nd
| aug 1sn, downmajor 2nd
| D#, vE
| D#, vE
| small major second
| ro
| ro
| reh
| reh
Line 82: Line 256:
| 5
| 5
| 222.2
| 222.2
| [[8/7]], [[9/8]]
| M2
| M2
| major 2nd
| major 2nd
| E
| E
| large major second
| ra
| ra
| re
| re
Line 92: Line 264:
| 6
| 6
| 266.7
| 266.7
| [[7/6]]
| m3
| m3
| minor 3rd
| minor 3rd
| F
| F
| subminor third
| na
| na
| ma
| ma
Line 102: Line 272:
| 7
| 7
| 311.1
| 311.1
| [[6/5]], [[19/16]]
| ^m3
| ^m3
| upminor 3rd
| upminor 3rd
| Gb
| Gb
| minor third
| nu
| nu
| me
| me
Line 112: Line 280:
| 8
| 8
| 355.6
| 355.6
| [[16/13]]
| ~3
| ~3
| mid 3rd
| mid 3rd
| ^Gb
| ^Gb
| neutral third
| mi
| mi
| mu
| mu
Line 122: Line 288:
| 9
| 9
| 400.0
| 400.0
| [[5/4]], [[24/19]]
| vM3
| vM3
| downmajor 3rd
| downmajor 3rd
| vF#
| vF#
| major third
| mo
| mo
| mi
| mi
Line 132: Line 296:
| 10
| 10
| 444.4
| 444.4
| [[9/7]], [[13/10]]
| M3
| M3
| major 3rd
| major 3rd
| F#
| F#
| supermajor third
| ma
| ma
| mo
| mo
Line 142: Line 304:
| 11
| 11
| 488.9
| 488.9
| [[4/3]]
| P4
| P4
| perfect 4th
| perfect 4th
| G
| G
| fourth
| fa
| fa
| fa
| fa
Line 152: Line 312:
| 12
| 12
| 533.3
| 533.3
| [[19/14]], [[26/19]], [[27/20]], [[48/35]]
| ^4
| ^4
| up 4th
| up 4th
| Ab
| Ab
| superfourth
| fu/sha
| fu/sha
| fih
| fih
Line 162: Line 320:
| 13
| 13
| 577.8
| 577.8
| [[7/5]], [[18/13]]
| ~4, ^d5
| ~4, ^d5
| mid 4th, updim 5th
| mid 4th, updim 5th
| ^^G, ^Ab
| ^^G, ^Ab
| small tritone
| fi/shu
| fi/shu
| fi
| fi
Line 172: Line 328:
| 14
| 14
| 622.2
| 622.2
| [[10/7]], [[13/9]]
| vA4, ~5
| vA4, ~5
| downaug 4th, mid 5th
| downaug 4th, mid 5th
| vG#, vvA
| vG#, vvA
| large tritone
| po/si
| po/si
| se
| se
Line 182: Line 336:
| 15
| 15
| 666.7
| 666.7
| [[19/13]], [[28/19]], [[35/24]], [[40/27]]
| v5
| v5
| down fifth
| down fifth
| G#
| G#
| subfifth
| pa/so
| pa/so
| sih
| sih
Line 192: Line 344:
| 16
| 16
| 711.1
| 711.1
| [[3/2]]
| P5
| P5
| perfect 5th
| perfect 5th
| A
| A
| fifth
| sa
| sa
| so/sol
| so/sol
Line 202: Line 352:
| 17
| 17
| 755.6
| 755.6
| [[14/9]], [[20/13]]
| m6
| m6
| minor 6th
| minor 6th
| Bb
| Bb
| subminor sixth
| fla
| fla
| lo
| lo
Line 212: Line 360:
| 18
| 18
| 800.0
| 800.0
| [[8/5]], [[19/12]]
| ^m6
| ^m6
| upminor 6th
| upminor 6th
| ^Bb
| ^Bb
| minor sixth
| flu
| flu
| le
| le
Line 222: Line 368:
| 19
| 19
| 844.4
| 844.4
| [[13/8]]
| ~6
| ~6
| mid 6th
| mid 6th
| vA#
| vA#
| neutral sixth
| li
| li
| lu
| lu
Line 232: Line 376:
| 20
| 20
| 888.9
| 888.9
| [[5/3]], [[32/19]]
| vM6
| vM6
| downmajor 6th
| downmajor 6th
| A#
| A#
| major sixth
| lo
| lo
| la
| la
Line 242: Line 384:
| 21
| 21
| 933.3
| 933.3
| [[12/7]]
| M6
| M6
| major 6th
| major 6th
| B
| B
| supermajor sixth
| la
| la
| li
| li
Line 252: Line 392:
| 22
| 22
| 977.8
| 977.8
| [[7/4]], [[16/9]]
| m7
| m7
| minor 7th
| minor 7th
| C
| C
| harmonic seventh
| tha
| tha
| ta
| ta
Line 262: Line 400:
| 23
| 23
| 1022.2
| 1022.2
| [[9/5]]
| ^m7
| ^m7
| upminor 7th
| upminor 7th
| Db
| Db
| large minor seventh
| thu
| thu
| te
| te
Line 272: Line 408:
| 24
| 24
| 1066.7
| 1066.7
| [[13/7]], [[24/13]], [[28/15]]
| ~7
| ~7
| mid 7th
| mid 7th
| ^Db
| ^Db
| neutral seventh
| ti
| ti
| tu
| tu
Line 282: Line 416:
| 25
| 25
| 1111.1
| 1111.1
| ''[[15/8]]'', [[19/10]], [[36/19]], [[40/21]], [[48/25]]
| vM7
| vM7
| downmajor 7th
| downmajor 7th
| vC#
| vC#
| major seventh
| to
| to
| ti
| ti
Line 292: Line 424:
| 26
| 26
| 1155.6
| 1155.6
| [[27/14]], [[35/18]], [[49/25]], [[96/49]], ''[[160/81]]''
| M7
| M7
| major 7th
| major 7th
| C#
| C#
| supermajor seventh
| ta
| ta
| da
| da
Line 302: Line 432:
| 27
| 27
| 1200.0
| 1200.0
| [[2/1]]
| P8
| P8
| 8ve
| 8ve
| D
| D
| octave
| da
| da
| do
| do
|}
|}
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Line 412: Line 539:
|+ 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
Line 544: Line 671:
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 ===
Line 895: Line 1,024:
| 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 905: 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 ===
Line 1,150: Line 1,281:
* Beatles[10] [[7L 3s]] (gen = 8\27): 3 3 2 3 3 2 3 3 2 3
* Beatles[10] [[7L 3s]] (gen = 8\27): 3 3 2 3 3 2 3 3 2 3
* Beatles[17] [[10L 7s]] (gen = 8\27): 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1
* Beatles[17] [[10L 7s]] (gen = 8\27): 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1
* Sensi[5] [[3L 2s]] (gen = 10\27): 7 3 7 3 7
* Sensi[8] [[3L 5s]] (gen = 10\27): 3 4 3 3 4 3 3 4
* Sensi[11] [[8L 3s]] (gen = 10\27): 3 3 1 3 3 3 1 3 3 3 1
* Machine[5] [[1L 4s]] (gen = 5\27): 5 5 5 5 7
* Machine[5] [[1L 4s]] (gen = 5\27): 5 5 5 5 7
* Machine[6] [[5L 1s]] (gen = 5\27): 5 5 5 5 5 2
* Machine[6] [[5L 1s]] (gen = 5\27): 5 5 5 5 5 2
* Machine[11] [[5L 6s]] (gen = 5\27): 2 3 2 3 2 3 2 3 2 3 2
* Machine[11] [[5L 6s]] (gen = 5\27): 2 3 2 3 2 3 2 3 2 3 2
* Machine[16] [[11L 5s]] (gen = 5\27): 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
* Machine[16] [[11L 5s]] (gen = 5\27): 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
* Myna[7] [[4L 3s]] (gen = 7\27): 6 1 6 1 6 1 6
* Myna[11] [[4L 7s]] (gen = 7\27): 5 1 1 5 1 1 5 1 1 5 1
* Myna[15] [[4L 11s]] (gen = 7\27): 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
* Myna[19] [[4L 15s]] (gen = 7\27): 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1
* Octacot[13] [[1L 12s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 3
* Octacot[14] [[13L 1s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 2 1
* Sensi[5] [[3L 2s]] (gen = 10\27): 7 3 7 3 7
* Sensi[8] [[3L 5s]] (gen = 10\27): 3 4 3 3 4 3 3 4
* Sensi[11] [[8L 3s]] (gen = 10\27): 3 3 1 3 3 3 1 3 3 3 1
* Tetracot[6] [[1L 5s]] (gen = 4\27): 4 4 4 4 4 7
* Tetracot[6] [[1L 5s]] (gen = 4\27): 4 4 4 4 4 7
* Tetracot[7] [[6L 1s]] (gen = 4\27): 4 4 4 4 4 4 3
* Tetracot[7] [[6L 1s]] (gen = 4\27): 4 4 4 4 4 4 3
* Tetracot[13] [[7L 6s]] (gen = 4\27): 3 1 3 1 3 1 3 1 3 1 3 1 3
* Tetracot[13] [[7L 6s]] (gen = 4\27): 3 1 3 1 3 1 3 1 3 1 3 1 3
* Tetracot[20] [[7L 13s]] (gen = 4\27): 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
* Tetracot[20] [[7L 13s]] (gen = 4\27): 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
* Octacot[13] [[1L 12s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 3
* Octacot[14] [[13L 1s]] (gen = 2\27): 2 2 2 2 2 2 2 2 2 2 2 2 2 1
* Myna[7] [[4L 3s]] (gen = 7\27): 6 1 6 1 6 1 6
* Myna[11] [[4L 7s]] (gen = 7\27): 5 1 1 5 1 1 5 1 1 5 1
* Myna[15] [[4L 11s]] (gen = 7\27): 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
* Myna[19] [[4L 15s]] (gen = 7\27): 3 1 1 1 1 3 1 1 1 1 3 1 1 1 1 3 1 1 1


=== JI chords ===
=== JI chords ===
Line 1,183: Line 1,314:
* (11 tones)
* (11 tones)
* JI - 12:13:14:15:16:18:19:20:21:22:23:24
* JI - 12:13:14:15:16:18:19:20:21:22:23:24
* Included edosteps - 0, 3, 6, 9, 11, 16, 18, 22, 24, 25, 27
* Included edosteps - 0, 3, 6, 9, 11, 16, 18, 20, 22, 24, 25, 27


; an over-13 chord
; an over-13 chord
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; Miscellaneous  
; Miscellaneous  
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of [[Zarlino]]): 3 2 4 2 3 2 4 2 3 2
* enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
* enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
* enharmonic tetrachord octave species: 9 1 1 5 9 1 1, 1 9 1 5 1 9 1 (also Superpyth double harmonic major), 1 1 9 5 1 1
* [[Zarlino]] / Ptolemy diatonic, "just" major: 5 4 2 5 4 5 2
* [[Zarlino]] / Ptolemy diatonic, "just" major: 5 4 2 5 4 5 2
* "Just" minor (inverse of "just" major): 5 2 4 5 2 5 4
* "Just" minor (inverse of "just" major): 5 2 4 5 2 5 49
* enharmonic tetrachord octave species: 9 1 1 5 9 1 1, 1 9 1 5 1 9 1 (also Superpyth double harmonic major), 1 1 9 5 1 1 9
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of [[Zarlino]]): 3 2 4 2 3 2 4 2 3 2
* [[Maeve Gutierrez#Gutierrez wisp scale|Gutierrez wisp scale]]{{idio}} ''(scale's [[period]] is [[nonoctave]])''
* Direct sunlight{{idio}} (original/default tuning; subset of [[Sensi]][19]): 1 2 8 5 1 9 1
* Direct sunlight{{idio}} (original/default tuning; subset of [[Sensi]][19]): 1 2 8 5 1 9 1
* Hypersakura{{idio}} (original/default tuning; subset of Sensi[19]): 1 10 5 1 10
* Hypersakura{{idio}} (original/default tuning; subset of Sensi[19]): 1 10 5 1 10
* [[Maeve Gutierrez#Gutierrez wisp scale|Gutierrez wisp scale]]{{idio}} ''(scale's [[period]] is [[nonoctave]])''
* [[Maeve Gutierrez#Will-o-wisps' scale|Lambeth will-o-wisps' scale]]{{idio}} ''(scale's [[period]] is [[nonoctave]])''
* [[User:BudjarnLambeth/Augene18 subsets in 97ed12]]


== Instruments ==
== Instruments ==
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{{Catrel| 27edo tracks }}
{{Catrel| 27edo tracks }}


=== Modern renderings ===
; {{W|Scott Joplin}}
* [https://www.youtube.com/shorts/5vRudUCuyqc ''Maple Leaf Rag''] (1899) – arranged with syntonic chroma adjustment for harpsichord and rendered by Claudi Meneghin (2025)
=== 21st century===
; [[Abnormality]]
; [[Abnormality]]
* [https://www.youtube.com/watch?v=gfGNKd8SWWc ''Boiling''] (2024)
* [https://www.youtube.com/watch?v=gfGNKd8SWWc ''Boiling''] (2024)
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; [[Gregoire Blanc]]
; [[Gregoire Blanc]]
* [https://youtu.be/a4-JhcaZSUs?feature=shared ''A microtonal teatime jam''] (2023)
* [https://www.youtube.com/watch?v=a4-JhcaZSUs ''A microtonal teatime jam''] (2023)


; [[Brendan Byrnes]]
; [[Brendan Byrnes]]
* [https://youtu.be/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)
; [[Flora Canou]]
* [https://soundcloud.com/floracanou/prelude-the-triad-challenge?in=floracanou/sets/totmc-suite "Prelude: the Triad Challenge"] from [https://soundcloud.com/floracanou/sets/totmc-suite ''TOTMC Suite''] (2023–2025) – in superpyth, 70ed6 tuning


; [[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]]
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; [[Peter Kosmorsky]]
; [[Peter Kosmorsky]]
* [https://www.youtube.com/watch?v=7QcwKlK6z4c ''miniature prelude and fugue''] (2011)
* [https://www.youtube.com/watch?v=7QcwKlK6z4c ''miniature prelude and fugue''] (2011)
; [[Budjarn Lambeth]]
* [https://www.youtube.com/watch?v=JrpcIkElKQc ''Will-O-Wisps''] (2025) – uses his "will-o-wisps' scale"{{idio}} tuned to 27edo


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [https://www.youtube.com/watch?v=nR8orkai8tQ ''Chorale in 27edo for Organ''] (2019)
* [https://www.youtube.com/watch?v=nR8orkai8tQ ''Chorale in 27edo for Organ''] (2019)
* [https://www.youtube.com/watch?v=ntnFso-3T_I ''Chaconne in 27edo, for Baroque Quartet''] (2025)


; [[Herman Miller]]
; [[Herman Miller]]
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; [[Dustin Schallert]]
; [[Dustin Schallert]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 ''Tetracot Perc-Sitar'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-perc-sitar SoundCloud]){{dead link}}
* [https://web.archive.org/web/20201127015111/http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 ''Tetracot Perc-Sitar'']
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 ''Tetracot Jam'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-jam SoundCloud]){{dead link}}
* [https://web.archive.org/web/20201129105050/http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 ''Tetracot Jam'']
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 ''Tetracot Pump'']{{dead link}} (on [https://soundcloud.com/dustin-schallert/tetracot-pump SoundCloud]){{dead link}}
* [https://web.archive.org/web/20201127012230/http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 ''Tetracot Pump''] – all in modus, 27edo tuning
* [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 ''27-EDO Guitar 1'']{{dead link}}
* [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 ''27-EDO Guitar 1'']{{dead link}}


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; [[Tristan Bay]]
; [[Tristan Bay]]
* [https://youtu.be/R30aRbNtoIY ''Pitchblende''] (2023)
* [https://www.youtube.com/watch?v=R30aRbNtoIY ''Pitchblende''] (2023)


; [[Uncreative Name]]
; [[Uncreative Name]]
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; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 ''Chicago Pile-1''] (2011)
* [https://web.archive.org/web/20231121072342/http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 ''Chicago Pile-1''] (2011)


; [[Xotla]]
; [[Xotla]]
* "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]]
Retrieved from "https://en.xen.wiki/w/27edo"