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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.
27edo, with its 400{{c}} major third, [[tempering out|tempers out]] the lesser diesis, [[128/125]], and the septimal comma, [[64/63]], and hence [[126/125]] as well. These it shares with 12edo, making some relationships familiar, and they both support the [[augene]] temperament. It shares with [[22edo]] tempering out the sensamagic comma [[245/243]] as well as 64/63, so that they both support the [[superpyth]] temperament, with four quite sharp "superpythagorean" fifths giving a sharp [[9/7]] in place of meantone's 5/4.


Its step of 44.4{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very high [[harmonic entropy]]. In other words, there is a general perception of quartertones as being the most dissonant intervals. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
Its step of 44.4{{c}}, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having very high [[harmonic entropy]]. In other words, there is a general perception of quartertones as being the most dissonant intervals. This property is shared with all edos between around 20 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.
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=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|27}}
{{Harmonics in equal|27}}
=== As a tuning of other temperaments ===
27edo, with its 400{{c}} major third, [[tempering out|tempers out]] the lesser diesis, [[128/125]], and the septimal comma, [[64/63]], and hence [[126/125]] as well. These it shares with 12edo, making some relationships familiar, and they both [[support]] the [[augene]] temperament. It shares with [[22edo]] tempering out the sensamagic comma [[245/243]] as well as 64/63, so that they both support the [[superpyth]] temperament, with four quite sharp "superpythagorean" fifths giving a sharp [[9/7]] in place of meantone's 5/4. The sharp 9/7 befits a [[generator]] for [[sensi]], which 27edo also supports, but a much better tuning is found in [[46edo]]. Another notable temperament 27edo supports is [[myna]], which divides the category of thirds into five different intervals: subminor, minor, neutral, major, and supermajor, representing 7/6, 6/5, 11/9~16/13, 5/4, and 9/7, respectively.


=== Subsets and supersets ===
=== Subsets and supersets ===
Line 20: 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 41: 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 51: 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 61: 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 71: 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 81: 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 91: 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 101: 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 111: 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 121: 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 131: 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 141: Line 304:
| 11
| 11
| 488.9
| 488.9
| [[4/3]]
| P4
| P4
| perfect 4th
| perfect 4th
| G
| G
| fourth
| fa
| fa
| fa
| fa
Line 151: 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 161: 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 171: 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 181: 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 191: 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 201: 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 211: 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 221: 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 231: 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 241: 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 251: 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 261: 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 271: 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 281: 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 291: 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 301: 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 411: 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 543: 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-sharp4a}}
{{Sharpness-sharp4-szg}}
[[Alternative symbols for ups and downs notation|Alternatively,]] sharps and flats with arrows can be used, borrowed from extended [[Helmholtz–Ellis notation]]:
 
{{Sharpness-sharp4}}
=== 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}}


=== Sagittal notation ===
=== Sagittal notation ===
Line 894: 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 904: 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 1,133: Line 1,265:


== Octave stretch or compression ==
== Octave stretch or compression ==
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]], and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively.
Since the harmonics whose intervals it approximates well (3, 5, 7, 13, and 19) are all tuned sharp of just, 27edo is a prime candidate for [[stretched and compressed tuning|octave compression]]. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023{{c}}. More generally, narrowing the steps to between 44.2 and 44.35{{c}} would be better in theory; [[43edt]], [[70ed6]], [[90ed10]], and [[97ed12]] are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, 4.11, and 2.55{{c}}, respectively. [[ZPI|106zpi]] is another possible choice.
 
What follows is a comparison of compressed-octave 27edo tunings.
 
; 27edo
* Step size: 44.444{{c}}, octave size: 1200.000{{c}}
Pure-octaves 27edo approximates all harmonics up to 16 within 22.8{{c}}, with the greatest error occurring at 15/8 and 16/15, mapped inconsistently to 25\27 and 2\27, respectively.
{{Harmonics in equal|27|2|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 27edo}}
{{Harmonics in equal|27|2|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 27edo (continued)}}
 
; [[97ed12]]
* Step size: 44.350{{c}}, octave size: 1197.451{{c}}
Compressing the octave of 27edo by around 2.5{{c}} results in substantially improved primes 3, 5 and 7 at little cost. This approximates all harmonics up to 16 but 11 within 12.8{{c}}. The tuning 97ed12 does this.
{{Harmonics in equal|97|12|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 97ed12}}
{{Harmonics in equal|97|12|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 97ed12 (continued)}}
 
; [[WE|27et, 2.3.5.7.13-subgroup WE tuning]]
* Step size: 44.326{{c}}, octave size: 1196.796{{c}}
Compressing the octave of 27edo by around 3.2{{c}} results in substantially improved primes 3, 5 and 7 at little cost. This approximates all harmonics up to 16 but 11 within 12.8{{c}}. Both the 2.3.5.7.13-subgroup [[TE]] and WE tunings do this.
{{Harmonics in cet|44.325787|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, 2.3.5.7.13-subgroup WE tuning}}
{{Harmonics in cet|44.325787|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 27et, 2.3.5.7.13-subgroup WE tuning (continued)}}
 
; [[ZPI|106zpi]] / [[WE|27et, 7-limit WE tuning]] / [[70ed6]]
* Step size (70ed6): 44.314, octave size (70ed6): 1196.468{{c}}
* Step size (7-limit WE): 44.306, octave size (7-limit WE): 1196.273{{c}}
* Step size (106zpi): 44.302{{c}}, octave size (106zpi): 1196.163{{c}}
Compressing the octave of 27edo by around 3.5 to 3.8{{c}} results in even more improvement to primes 3, 5 and 7 than the 2.3.5.7.13 tuning, but now at the cost of moderate damage to 2 and 13. This approximates all harmonics up to 16 within 15.4{{c}}. Its 7-limit WE tuning and 7-limit [[TE]] tuning both do this. So do the tunings 106zpi and 70ed6.
{{Harmonics in cet|44.302326|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 106zpi}}
{{Harmonics in cet|44.302326|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 106zpi (continued)}}
 
; [[90ed10]]
* Step size: 44.292{{c}}, octave size: 1195.894{{c}}
Compressing the octave of 27edo by around 4.1{{c}} results in improved primes 3, 5, 7 and 11, using the 27e val, but a worse prime 2 and much worse 13. This approximates all harmonics up to 16 within 16.4{{c}}. The tuning 90ed10 does this.
{{Harmonics in equal|90|10|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 90ed10}}
{{Harmonics in equal|90|10|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 90ed10 (continued)}}
 
; [[43edt]]
* Step size: 44.232{{c}}, octave size: 1194.251{{c}}
Compressing the octave of 27edo by around 5.8{{c}} results in the same benefits and drawbacks as 90ed10, but amplified. This approximates all harmonics up to 16 within 21.2{{c}}. The tuning 43edt does this.
{{Harmonics in equal|43|3|1|intervals=integer|columns=11|collapsed=true|title=Approximation of harmonics in 43edt}}
{{Harmonics in equal|43|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 43edt (continued)}}


== Scales ==
== Scales ==
Line 1,189: 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
=== JI chords ===
* Myna[7] [[4L 3s]] (gen = 7\27): 6 1 6 1 6 1 6
These are those [[overtone scale]]s 27edo approximates with neat-looking [[horogram]]s, which preserves their [[mapping]] well when rotated:
* Myna[11] [[4L 7s]] (gen = 7\27): 5 1 1 5 1 1 5 1 1 5 1
* [[5afdo]] (rotated): 6 5 5 4 7
* Myna[15] [[4L 11s]] (gen = 7\27): 4 1 1 1 4 1 1 1 4 1 1 1 4 1 1
* [[6afdo]]: 6 5 5 4 4 3
* 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
* [[7afdo]] (rotated): 3 3 5 5 4 4 3
* [[9afdo]] (rotated): 3 3 3 2 3 2 4 4 3
* [[15afdo]] (rotated): 2 2 2 2 2 1 2 1 2 1 2 1 3 2 2
* [[18afdo]]: 2 2 2 2 2 1 2 1 2 1 2 1 1 1 2 1 1 1
* [[21afdo]]: 2 2 1 2 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1
 
These are other [[JI]] chords that 27edo approximates well:
 
; [[12afdo]] without 17/12
* (11 tones)
* JI - 12:13:14:15:16:18:19:20:21:22:23:24
* Included edosteps - 0, 3, 6, 9, 11, 16, 18, 20, 22, 24, 25, 27
 
; an over-13 chord
* (9 tones)
* JI - 13:14:16:18:19:20:21:23:24:26
* Included edosteps - 0, 3, 8, 13, 15, 17, 19, 22, 24, 27
 
; an over-14 chord
* (9 tones)
* JI - 14:16:18:19:20:21:23:24:26:28
* Included edosteps - 0, 5, 10, 12, 14, 16, 19, 21, 24, 27


=== Other scales ===
=== Other scales ===
; [[Pinetone]]
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone major pentatonic]]: 5 4 7 4 7
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone major pentatonic]]: 5 4 7 4 7
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone minor pentatonic]]: 7 4 5 7 4
* 5-limit / pental / [[The Pinetone System#Pinetone pentatonic|Pinetone minor pentatonic]]: 7 4 5 7 4
* enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
* [[The Pinetone System #The Pinetone diatonic|Pinetone diatonic]]: 4 3 4 5 4 3 4
* 5-limit / pental double harmonic hexatonic (Augmented[6] [[4M]]): 2 7 2 7 7 2, 7 7 2 2 7 2
* [[The Pinetone System #Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 4 3 4 2 3 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 4 3 2 4 3 4 4 3
* [[The Pinetone System #Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 3 4 2 4 3 4 3 4
* [[The Pinetone System #Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 3 4 2 5 2 4 3 4
* [[The Pinetone System #Pinetone chromatic|Pinetone chromatic]] / pinechrome: 1 3 3 1 3 2 3 1 3 3 1 3
 
; [[Superpyth]]
* Superpyth melodic minor – Superpyth 2|4 #6 #7 or 5|1 b3: 5 1 5 5 5 5 1
* Superpyth melodic minor – Superpyth 2|4 #6 #7 or 5|1 b3: 5 1 5 5 5 5 1
* Superpyth harmonic minor – Superpyth 2|4 #7: 5 1 5 5 1 9 1
* Superpyth harmonic minor – Superpyth 2|4 #7: 5 1 5 5 1 9 1
* Superpyth harmonic major – Superpyth 5|1 b6: 5 5 1 5 1 9 1
* Superpyth harmonic major – Superpyth 5|1 b6: 5 5 1 5 1 9 1
* Superpyth double harmonic major – Superpyth 5|1 b2 b6: 1 9 1 5 1 9 1
* Superpyth double harmonic major – Superpyth 5|1 b2 b6: 1 9 1 5 1 9 1
* [[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
; [[Tonality diamond]]s
* 5-odd limit tonality diamond: 7 2 2 5 2 2 7
* 7-odd limit tonality diamond: 5 1 1 2 2 2 1 2 2 2 1 1 5
* 9-odd limit tonality diamond: 4 1 1 1 2 1 1 2 1 2 1 1 2 1 1 1 4  
 
; [[5-limit]] scales:
* 5-limit / pental double harmonic  hexatonic (Augmented[6] [[4M]]): 2 7 2 7 7 2, 7 7 2 2 7 2
* 5-limit / pental tetrachordal major: 5 4 2 5 5 4 2
* 5-limit / pental tetrachordal major: 5 4 2 5 5 4 2
* 5-limit / pental tetrachordal minor: 5 2 4 5 5 2 4
* 5-limit / pental tetrachordal minor: 5 2 4 5 5 2 4
Line 1,223: Line 1,356:
* 5-limit / pental harmonic minor: 5 2 4 5 2 7 2
* 5-limit / pental harmonic minor: 5 2 4 5 2 7 2
* 5-limit / pental harmonic major: 5 4 2 5 2 7 2
* 5-limit / pental harmonic major: 5 4 2 5 2 7 2
* 5-odd limit tonality diamond: 7 2 2 5 2 2 7
* 7-odd limit tonality diamond: 5 1 1 2 2 2 1 2 2 2 1 1 5
* 9-odd limit tonality diamond: 4 1 1 1 2 1 1 2 1 2 1 1 2 1 1 1 4
* [[SNS (2/1, 3/2, 5/4)-7|5-limit / pental double harmonic major]]: 2 7 2 5 2 7 2
* [[SNS (2/1, 3/2, 5/4)-7|5-limit / pental double harmonic major]]: 2 7 2 5 2 7 2
* 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
* [[The Pinetone System #The Pinetone diatonic|Pinetone diatonic]]: 4 3 4 5 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 4 3 4 2 3 4 3 4
* [[The Pinetone System #Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 4 3 2 4 3 4 4 3
* [[The Pinetone System #Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 3 4 2 4 3 4 3 4
* [[The Pinetone System #Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 3 4 2 5 2 4 3 4
* [[The Pinetone System #Pinetone chromatic|Pinetone chromatic]] / pinechrome: 1 3 3 1 3 2 3 1 3 3 1 3
* 5-limit / pental double harmonic nonatonic (subset of Augene[12]): 2 5 2 2 5 2 5 2 2, 2 2 5 2 5 2 2 5 2 (Augene[9] [[4M]])
* 5-limit / pental double harmonic nonatonic (subset of Augene[12]): 2 5 2 2 5 2 5 2 2, 2 2 5 2 5 2 2 5 2 (Augene[9] [[4M]])
* 5-limit / pental double harmonic decatonic (subset of Augene[12]): 2 5 2 2 3 2 2 5 2 2
* 5-limit / pental double harmonic decatonic (subset of Augene[12]): 2 5 2 2 3 2 2 5 2 2
* 5-limit / pental double harmonic chromatic: 2 2 3 2 2 3 2 2 2 3 2 2, 2 2 3 2 2 2 3 2 2 3 2 2 (Augene[12] [[4M]])
* 5-limit / pental double harmonic chromatic: 2 2 3 2 2 3 2 2 2 3 2 2, 2 2 3 2 2 2 3 2 2 3 2 2 (Augene[12] [[4M]])
; Miscellaneous
* [[Blackdye]] / [[syntonic dipentatonic]] (superset of [[Zarlino]]): 1 4 2 4 1 4 2 4 1 4
* [[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
* [[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
* Direct sunlight (original/default tuning; subset of [[Sensi]][19]): 1 2 8 5 1 9 1 ((1, 3, 11, 16, 17, 26, 27)\27)
* enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
* Hypersakura (original/default tuning; subset of Sensi[19]): 1 10 5 1 10 ((1 11 16 17 27)\27)
* 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
* "Just" minor (inverse of "just" major): 5 2 4 5 2 5 49
* 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
* [[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 ==
Line 1,257: Line 1,389:
{{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)
Line 1,267: Line 1,404:


; [[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)
 
; [[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)
* ''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 1,286: Line 1,444:
; [[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]]
Line 1,297: Line 1,459:


; [[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}}


Line 1,307: Line 1,469:
; [[Joel Taylor]]
; [[Joel Taylor]]
* [https://web.archive.org/web/20201127012922/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 ''Galticeran Sonatina''] – in Augene[12] tuned to 27edo
* [https://web.archive.org/web/20201127012922/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 ''Galticeran Sonatina''] – in Augene[12] tuned to 27edo
; [[The Evil Doings Of An Intergalactic Skeleton]]
* [https://soundcloud.com/unfaced-bones/the-taste-of-pure-saccharin-27edo ''the taste of pure saccharine''] (2025)


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


; [[Uncreative Name]]
; [[Uncreative Name]]
Line 1,315: Line 1,480:


; [[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]]
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