# 27edo

 ← 26edo 27edo 28edo →
Prime factorization 33
Step size 44.4444¢
Fifth 16\27 (711.111¢)
Semitones (A1:m2) 4:1 (177.8¢ : 44.44¢)
Consistency limit 9
Distinct consistency limit 7
Special properties

27 equal divisions of the octave (abbreviated 27edo or 27ed2), also called 27-tone equal temperament (27tet) or 27 equal temperament (27et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 27 equal parts of about 44.4 ¢ each. Each step represents a frequency ratio of 21/27, or the 27th root of 2.

## Theory

27edo divides the octave in 27 equal parts each exactly 4449 cents in size. However, 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 octave compression. The local zeta peak around 27 is at 27.086614, which corresponds to a step size of 44.3023 cents. More generally, narrowing the steps to between 44.2 and 44.35 cents would be better in theory; 43edt, 70ed6, and 97ed12 are good options if octave compression is acceptable, and these narrow the octaves by 5.75, 3.53, and 2.55 cents, respectively.

However, assuming just octaves, 27edo's fifth and harmonic seventh are both sharp by nine cents, and the major third is the same 400 cent major third as 12edo, sharp by 13.7 cents. 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 1/3 septimal comma superpyth in the same way that 19edo is audibly indistinguishable from 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.

27edo, with its 400 cent major third, 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 allegedly Bohlen-Pierce 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.

Though 27edo's 7-limit tuning is not highly accurate, it nonetheless is the smallest equal division to represent the 7-odd-limit both consistently and distinctly – that is, everything in the 7-odd-limit 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-11s, no-17s 19-limit) temperament. It also approximates 19/10, 19/12, and 19/14, so 0 – 7 – 13 – 25 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 triad, 3:5:7, and a passable approximation of 5:7:9, making 27 the smallest edo that can simulate tritave harmony, although it rapidly becomes rough if extended to the 11 and above, unlike a true tritave based system.

Its step, as well as the octave-inverted and octave-equivalent versions of it, has some of the highest harmonic entropy possible and thus is, in theory, one of the most dissonant intervals possible, assuming the relatively common values of a = 2 and s = 1%. This property is shared with all edos between around 24 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.

### Odd harmonics

Approximation of odd harmonics in 27edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +9.2 +13.7 +9.0 +18.3 -18.0 +3.9 -21.6 -16.1 +13.6 +18.1 -6.1
Relative (%) +20.6 +30.8 +20.1 +41.2 -40.5 +8.8 -48.6 -36.1 +30.6 +40.7 -13.6
Steps
(reduced)
43
(16)
63
(9)
76
(22)
86
(5)
93
(12)
100
(19)
105
(24)
110
(2)
115
(7)
119
(11)
122
(14)

## Notation

Circle of fifths in 27edo
Cents Note
Standard
notation
Quarter tone
notation
0 C A
711.11 G E
222.22 D B  F
933.33 A C
444.44 E G
1155.55 B D
666.66 F♯ A
177.77 C♯ E
888.88 G♯ B
400 D♯ F
1111.11 A♯ C
622.22 E♯ G
133.33 B♯ F𝄫 D
844.44 F𝄪 C𝄫 A
355.56 C𝄪 G𝄫 E
1066.67 G𝄪 D𝄫 B
577.78 D𝄪 A𝄫 F
88.89 A𝄪 E𝄫 C
800 E𝄪 B𝄫 G
311.11 B𝄪 F♭ D
1022.22 C♭ A
533.33 G♭ E
44.44 D♭ B
755.56 A♭ F
266.67 E♭ C
977.78 B♭ G
488.89 F D
0 C A

The 27-note system can be notated using ups and downs notation, in which case arrows or Helmholtz–Ellis accidentals can be used, or with a variation on quarter tone accidentals. With standard circle-of-fifths notation, a sharp raises a note by 4 steps, just one step beneath the following nominal (for example C to C♯ describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that 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 notes from C to D are C, D♭, C, D , C♯, and D, with some ascending intervals appearing to be descending on the staff.

Another notational implication is that, being a Superpythagorean system, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located one major third above C must be notated as D♯ or E . Conversely, the 6/5 minor third of a 10:12:15 chord is actually reached by a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located one minor third above D must be notated as either G♭ or F . The composer can decide for themselves which additional accidental pair is appropriate if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A♯ to be higher than B♭ is not only familiar, though here very exaggerated, to those working with the Pythagorean scale (see 53edo), but also to many classically trained violinists.

 Step Offset Sharp Symbol Flat Symbol 0 1 2 3 4 5 6 7 8 9

## Intervals

# Cents Approximate Ratios* Ups and Downs Notation Walker Brightness Notation 6L 1s Notation Solfeges
0 0.00 1/1 P1 perfect unison D unison perfect unison C da do
1 44.44 28/27, 36/35, 39/38, 49/48, 50/49, 81/80 ^1, m2 up unison, minor 2nd ^D, Eb diesis aug 1sn, double-dim 2nd C#, Dbbb fra di
2 88.89 16/15, 21/20, 25/24, 19/18, 20/19 ^^1, ^m2 dup unison, upminor 2nd ^^D, ^Eb minor second double-aug 1sn, dim 2nd Cx, Dbb fru ra
3 133.33 15/14, 14/13, 13/12 vA1, ~2 downaug 1sn, mid 2nd vD#, vvE neutral second minor 2nd Db ri ru
4 177.78 10/9 A1, vM2 aug 1sn, downmajor 2nd D#, vE small major second major 2nd D ro reh
5 222.22 8/7, 9/8 M2 major 2nd E large major second aug 2nd, double-dim 3rd D#, Ebbb ra re
6 266.67 7/6 m3 minor 3rd F subminor third double-aug 2nd, dim 3rd Dx, Ebb na ma
7 311.11 6/5, 19/16 ^m3 upminor 3rd Gb minor third minor 3rd Eb nu me
8 355.56 16/13 ~3 mid 3rd ^Gb neutral third major 3rd E mi mu
9 400.00 5/4, 24/19 vM3 downmajor 3rd vF# major third aug 3rd, double-dim 4th E#, Fbbb mo mi
10 444.44 9/7, 13/10 M3 major 3rd F# supermajor third double-aug 3rd, dim 4th Ex, Fbb ma mo
11 488.89 4/3 P4 perfect 4th G fourth minor 4th Ex#, Fb fa fa
12 533.33 27/20, 48/35, 19/14, 26/19 ^4 up 4th Ab superfourth major 4th F fu/sha fih
13 577.78 7/5, 18/13 ~4, ^d5 mid 4th, updim 5th ^^G, ^Ab small tritone aug 4th, double-dim 5th F#, Gbbb fi/shu fi
14 622.22 10/7, 13/9 vA4, ~5 downaug 4th, mid 5th vG#, vvA large tritone double-aug 4th, dim 5th Fx, Gbb po/si se
15 666.67 40/27, 35/24, 19/13, 28/19 v5 down fifth G# subfifth minor 5th Fx#, Gb pa/so sih
16 711.11 3/2 P5 perfect 5th A fifth major 5th G sa so/sol
17 755.56 14/9, 20/13 m6 minor 6th Bb subminor sixth aug 5th, double-dim 6th G#, Abbb fla lo
18 800.00 8/5, 19/12 ^m6 upminor 6th ^Bb minor sixth double-aug 5th, dim 6th Gx, Abb flu le
19 844.44 13/8 ~6 mid 6th vA# neutral sixth minor 6th Ab li lu
20 888.89 5/3, 32/19 vM6 downmajor 6th A# major sixth major 6th A lo la
21 933.33 12/7 M6 major 6th B supermajor sixth aug 6th, double-dim 7th A#, Bbbb la li
22 977.78 7/4, 16/9 m7 minor 7th C harmonic seventh double-aug 6th, dim 7th Ax, Bbb tha ta
23 1022.22 9/5 ^m7 upminor 7th Db large minor seventh minor 7th Bb thu te
24 1066.67 28/15, 13/7, 24/13 ~7 mid 7th ^Db neutral seventh major 7th B ti tu
25 1111.11 15/8, 40/21, 48/25, 19/10, 36/19 vM7 downmajor 7th vC# major seventh aug 7th, double-dim 8ve B#, Cbb to ti
26 1155.56 27/14, 35/18, 96/49, 49/25, 160/81 M7 major 7th C# supermajor seventh double-aug 7th, dim 8ve Bx, Cb ta da
27 1200.00 2/1 P8 8ve D octave 8ve C da do
• based on treating 27edo as a 2.3.5.7.13.19 subgroup temperament; other approaches are possible.

### Interval quality and chord names in color notation

Combining ups and downs notation with color notation, qualities can be loosely associated with colors:

Quality Color Name Monzo Format Examples
minor zo {a, b, 0, 1} 7/6, 7/4
fourthward wa {a, b}, b < -1 32/27, 16/9
upminor gu {a, b, -1} 6/5, 9/5
mid tho {a, b, 0, 0, 0, 1} 13/12, 13/8
thu {a, b, 0, 0, 0, -1} 16/13, 24/13
downmajor yo {a, b, 1} 5/4, 5/3
major fifthward wa {a, b}, b > 1 9/8, 27/16
ru {a, b, 0, -1} 9/7, 12/7

All 27edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, ilo, yo and ru triads:

Color of the 3rd JI Chord Notes as Edosteps Notes of C Chord Written Name Spoken Name
zo 6:7:9 0–6–16 C–E♭–G Cm C minor
gu 10:12:15 0–7–16 C–F♭–G, C–E –G C^m C upminor
ilo 18:22:27 0–8–16 C–E –G C~ C mid
yo 4:5:6 0–9–16 C–D♯–G, C–E –G Cv C downmajor or C down
ru 14:18:21 0–10–16 C–E–G C C major or C

For a more complete list, see Ups and Downs Notation #Chords and Chord Progressions. See also the 22edo page.

## Approximation to JI

Selected 19-limit intervals approximated in 27edo

### Interval mappings

The following tables show how 15-odd-limit intervals are represented in 27edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 27edo (direct approximation, even if inconsistent)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
7/6, 12/7 0.204 0.5
15/11, 22/15 3.617 8.1
13/8, 16/13 3.917 8.8
5/3, 6/5 4.530 10.2
9/5, 10/9 4.626 10.4
7/5, 10/7 4.734 10.7
13/7, 14/13 5.035 11.3
13/12, 24/13 5.239 11.8
11/9, 18/11 8.148 18.3
7/4, 8/7 8.952 20.1
3/2, 4/3 9.156 20.6
9/7, 14/9 9.360 21.1
13/10, 20/13 9.770 22.0
11/10, 20/11 12.774 28.7
5/4, 8/5 13.686 30.8
15/14, 28/15 13.891 31.3
13/9, 18/13 14.395 32.4
11/6, 12/11 17.304 38.9
11/7, 14/11 17.508 39.4
11/8, 16/11 17.985 40.5
9/8, 16/9 18.312 41.2
15/13, 26/15 18.926 42.6
15/8, 16/15 21.602 48.6
13/11, 22/13 21.901 49.3
15-odd-limit intervals in 27edo (patent val mapping)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
7/6, 12/7 0.204 0.5
13/8, 16/13 3.917 8.8
5/3, 6/5 4.530 10.2
9/5, 10/9 4.626 10.4
7/5, 10/7 4.734 10.7
13/7, 14/13 5.035 11.3
13/12, 24/13 5.239 11.8
7/4, 8/7 8.952 20.1
3/2, 4/3 9.156 20.6
9/7, 14/9 9.360 21.1
13/10, 20/13 9.770 22.0
5/4, 8/5 13.686 30.8
15/14, 28/15 13.891 31.3
13/9, 18/13 14.395 32.4
11/8, 16/11 17.985 40.5
9/8, 16/9 18.312 41.2
15/13, 26/15 18.926 42.6
13/11, 22/13 21.901 49.3
15/8, 16/15 22.842 51.4
11/7, 14/11 26.936 60.6
11/6, 12/11 27.141 61.1
11/10, 20/11 31.671 71.3
11/9, 18/11 36.297 81.7
15/11, 22/15 40.827 91.9
15-odd-limit intervals by 27e val mapping
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
7/6, 12/7 0.204 0.5
15/11, 22/15 3.617 8.1
13/8, 16/13 3.917 8.8
5/3, 6/5 4.530 10.2
9/5, 10/9 4.626 10.4
7/5, 10/7 4.734 10.7
13/7, 14/13 5.035 11.3
13/12, 24/13 5.239 11.8
11/9, 18/11 8.148 18.3
7/4, 8/7 8.952 20.1
3/2, 4/3 9.156 20.6
9/7, 14/9 9.360 21.1
13/10, 20/13 9.770 22.0
11/10, 20/11 12.774 28.7
5/4, 8/5 13.686 30.8
15/14, 28/15 13.891 31.3
13/9, 18/13 14.395 32.4
11/6, 12/11 17.304 38.9
11/7, 14/11 17.508 39.4
9/8, 16/9 18.312 41.2
15/13, 26/15 18.926 42.6
13/11, 22/13 22.543 50.7
15/8, 16/15 22.842 51.4
11/8, 16/11 26.460 59.5

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [43 -27 [27 43]] −2.89 2.88 6.50
2.3.5 128/125, 20000/19683 [27 43 63]] −3.88 2.74 6.19
2.3.5.7 64/63, 126/125, 245/243 [27 43 63 76]] −3.70 2.39 5.40
2.3.5.7.13 64/63, 91/90, 126/125, 169/168 [27 43 63 76 100]] −3.18 2.39 5.39
2.3.5.7.13.19 64/63, 76/75, 91/90, 126/125, 169/168 [27 43 63 76 100 115]] −3.18 2.18 4.92
• 27et (27eg val) is lower in relative error than any previous equal temperaments in the 13-, 17-, and 19-limit. The next equal temperaments doing better in those subgroups are 31, 31, and 46, respectively.
• 27et is particularly strong in the 2.3.5.7.13.19 subgroup. The next equal temperament that does better in this subgroup is 53.

### Rank-2 temperaments

Periods
per 8ve
Generator Temperaments MOS Scales
1 1\27 Quartonic / quarto (27e) / quartz (27)
1 2\27 Octacot / octocat (27e) 1L 12s, 13L 1s
1 4\27 Tetracot (27e) / modus (27e) / wollemia (27e) 1L 5s, 6L 1s, 7L 6s, 7L 13s
1 5\27 Machine (27)
Kumonga (27e)
1L 4s, 5L 1s, 5L 6s, 11L 5s
1 7\27 Myna (27e) / coleto (27e) / myno (27)
Oolong (27e)
4L 3s, 4L 7s, 4L 11s, 4L 15s, 4L 19s
1 8\27 Beatles (27e) / ringo (27e) / beetle (27) 3L 4s, 7L 3s, 10L 7s
1 10\27 Sensi 3L 2s, 3L 5s, 8L 3s, 8L 11s
1 11\27 Superpyth (27e) 5L 2s, 5L 7s, 5L 12s, 5L 17s
1 13\27 Fervor (27e) 2L 3s, 2L 5s, 2L 7s, 2L 9s, 2L 11s, etc. … 2L 23s
3 1\27 Hemiaug (27e)
3 2\27 Augene (27e) / Eugene (27) 3L 3s, 3L 6s, 3L 9s, 12L 3s
3 4\27 Oodako (27e)
Terrain
3L 3s, 6L 3s, 6L 9s, 6L 15s
9 1\27 Niner (27e)
Ennealimmal (out of tune)
9L 9s

### Commas

27edo tempers out the following commas. (Note: This assumes the patent val, 27 43 63 76 93 100].)

Prime
Limit
Ratio[1] Monzo Cents Color Name Name
5 128/125 [7 0 -3 41.06 Trigu Augmented comma, lesser diesis
5 20000/19683 [5 -9 4 27.66 Saquadyo Tetracot comma, minimal diesis
5 78732/78125 [2 9 -7 13.40 Sepgu Sensipent comma
5 (26 digits) [1 -27 18 0.86 Satritribiyo Ennealimma
7 686/675 [1 -3 -2 3 27.99 Trizo-agugu Senga
7 64/63 [6 -2 0 -1 27.26 Ru Septimal comma
7 50421/50000 [-4 1 -5 5 14.52 Quinzogu Trimyna comma
7 245/243 [0 -5 1 2 14.19 Zozoyo Sensamagic comma
7 126/125 [1 2 -3 1 13.79 Zotrigu Starling comma
7 4000/3969 [5 -4 3 -2 13.47 Rurutriyo Octagar comma
7 1728/1715 [6 3 -1 -3 13.07 Triru-agu Orwellisma
7 (16 digits) [-11 -9 0 9 1.84 Tritrizo Septimal ennealimma
7 (12 digits) [-6 -8 2 5 1.12 Quinzo-ayoyo Wizma
7 2401/2400 [-5 -1 -2 4 0.72 Bizozogu Breedsma
7 4375/4374 [-1 -7 4 1 0.40 Zoquadyo Ragisma
7 (12 digits) [-4 6 -6 3 0.33 Trizogugu Landscape comma
11 55/54 [-1 -3 1 0 1 31.77 Loyo Undecimal diasecundal comma, telepathma
11 99/98 [-1 2 0 -2 1 17.58 Loruru Mothwellsma
11 896/891 [7 -4 0 1 -1 9.69 Saluzo Pentacircle comma
11 385/384 [-7 -1 1 1 1 4.50 Lozoyo Keenanisma
13 66/65 [1 1 -1 0 1 -1 26.43 Thulogu Winmeanma
13 91/90 [-1 -2 -1 1 0 1 19.13 Thozogu Superleap comma, biome comma
13 512/507 [9 -1 0 0 0 -2 16.99 Thuthu Tridecimal neutral thirds comma
13 325/324 [-2 -4 2 0 0 1 5.34 Thoyoyo Marveltwin comma
13 351/350 [-1 3 -2 -1 0 1 4.94 Thorugugu Ratwolfsma
13 31213/31104 [-7 -5 0 4 0 1 6.06 Thoquadzo Praveensma
17 85/84 [-2 -1 1 -1 0 0 1 20.49 Soruyo Monk comma
17 154/153 [1 -2 0 1 1 0 -1 11.28 Sulozo Augustma
19 77/76 [2 -1 -2 0 0 0 0 1 22.63 Nulozo Small undevicesimal ninth tone
19 96/95 [5 1 -1 0 0 0 0 -1 18.13 Nugu 19th Partial chroma
1. Ratios longer than 10 digits are presented by placeholders with informative hints

## Scales

### MOS scales

• Superpyth pentatonic - Superpyth[5] 2L 3s (gen = 11\27): 5 5 6 5 6
• Superpyh diatonic - Superpyth[7] 5L 2s (gen = 11\27): 5 5 1 5 5 5 1
• Superpyth chromatic - Superpyth[12] 5L 7s (gen = 11\27): 4 1 1 4 1 4 1 4 1 1 4 1
• Superpyth hyperchromatic - Superpyth[17] 5L 12s (gen = 11\27): 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1
• Augene[6] 3L 3s (period = 9\27, gen = 2\27): 7 2 7 2 7 2
• Augene[9] 3L 6s (period = 9\27, gen = 2\27): 5 2 2 5 2 2 5 2 2
• Augene[12] 3L 9s (period = 9\27, gen = 2\27): 3 2 2 2 3 2 2 2 3 2 2 2
• Augene[15] 12L 3s (period = 9\27, gen = 2\27): 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2
• Beatles[7] 3L 4s (gen = 8\27): 3 5 3 5 3 5 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
• 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[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[16] 11L 5s (gen = 5\27): 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2
• 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[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
• 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

### Other scales

• 5-limit / pental / Pinetone major pentatonic: 5 4 7 4 7
• 5-limit / pental / Pinetone minor pentatonic: 7 4 5 7 4
• enharmonic trichord octave species: 9 2 5 9 2, 2 9 5 2 9
• 5-limit / pental double harmonic hexatonic (Augmented[6] 4M): 2 7 2 7 7 2, 7 7 2 2 7 2
• 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 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
• 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
• 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 melodic minor: 5 2 4 5 4 5 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-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 / 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
• Pinetone diatonic: 4 3 4 5 4 3 4
• Pinetone major-harmonic octatonic: 4 3 4 2 3 4 3 4
• Pinetone minor-harmonic octatonic: 4 3 2 4 3 4 4 3
• Pinetone diminished octatonic / Porcusmine: 3 4 2 4 3 4 3 4
• Pinetone harmonic diminished: 3 4 2 5 2 4 3 4
• 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 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)
• Blackdye / syntonic dipentatonic (superset of Zarlino): 1 4 2 4 1 4 2 4 1 4
• Blackville / 5-limit dipentatonic (superset of Zarlino): 3 2 4 2 3 2 4 2 3 2

Direct sunlight (this is its original/default tuning; subset of Sensi[19])

• 44.444
• 133.333
• 488.889
• 711.111
• 755.555
• 1155.555
• 1200.000

Hypersakura (this is its original/default tuning; subset of Sensi[19])

• 44.444
• 488.889
• 711.111
• 755.555
• 1200.000

## Instruments

Brendan Byrnes, guitarist

While playing 27edo instruments requires significantly more frets or keys than 12edo, it is still possible to create physical instruments that can play all its notes. Probably the most notable of these is owned by Brendan Byrnes and played on some of his tracks listed in the music section.

However, the frets are very close together and playing high up the neck requires careful use of fingernails for fretting. A skip-fretted guitar would have notes only slightly closer together than 12edo and be easier to play, particularly when tuned in the configuration detailed below.

27edo can also be played on the Lumatone, with various layouts discussed here.

## Music

Abnormality
Nae Ayy
Beheld
Gregoire Blanc
Brendan Byrnes
Bryan Deister
Igliashon Jones
Peter Kosmorsky
Claudi Meneghin
NullPointerException Music
Dustin Schallert
Gene Ward Smith
Joel Taylor
Tristan Bay
Chris Vaisvil
Xotla