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54edo

← 53edo 54edo 55edo →
Prime factorization 2 × 33
Step size 22.2222 ¢ 
Fifth 32\54 (711.111 ¢) (→ 16\27)
Semitones (A1:m2) 8:2 (177.8 ¢ : 44.44 ¢)
Dual sharp fifth 32\54 (711.111 ¢) (→ 16\27)
Dual flat fifth 31\54 (688.889 ¢)
Dual major 2nd 9\54 (200 ¢) (→ 1\6)
Consistency limit 3
Distinct consistency limit 3

54 equal divisions of the octave (abbreviated 54edo or 54ed2), also called 54-tone equal temperament (54tet) or 54 equal temperament (54et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 54 equal parts of about 22.2 ¢ each. Each step represents a frequency ratio of 21/54, or the 54th root of 2.

Theory

54edo is suitable for usage as a dual-fifth tuning system, or alternatively, a no-fifth tuning system. Using the sharp fifth, it can be viewed as two rings of 27edo, which adds better approximations of the 11th and 15th harmonics. Using the flat fifth, it generates an ultrasoft diatonic scale. This scale is so soft, with L/s = 8/7, that it stops sounding like meantone or even flattone, but just sounds like a circulating temperament of 7edo.

The patent val of this edo takes the same fifth as 27edo, but the mapping for harmonic 5 is different. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. It is the highest edo in which the best mappings of the major 3rd (5/4) and harmonic 7th (7/4), 17\54 and 44\54, are exactly 600 ¢ apart, making them suitable for harmonies using tritone substitutions. In other words, this is the last edo tempering out 50/49. This means it extends quite simply to the 7- and 11-limit using the pajarous mapping and to the 13-limit using the 54f val, falling neatly between the 7- and 13-limit minimax tunings.

The 54cd val makes for an excellent tuning of 7-limit hexe temperament, while the 54bdf val does higher limit muggles about as well as it can be tuned. However, even these best temperament interpretations of 54edo are quite high in badness compared to its immediate neighbours 53- and 55edo, both of which are historically significant for different reasons, leaving it mostly unexplored so far.

Odd harmonics

Approximation of odd harmonics in 54edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +9.16 -8.54 +8.95 -3.91 +4.24 +3.92 +0.62 +6.16 -8.62 -4.11 -6.05
Relative (%) +41.2 -38.4 +40.3 -17.6 +19.1 +17.6 +2.8 +27.7 -38.8 -18.5 -27.2
Steps
(reduced) 		86
(32) 		125
(17) 		152
(44) 		171
(9) 		187
(25) 		200
(38) 		211
(49) 		221
(5) 		229
(13) 		237
(21) 		244
(28)

Subsets and supersets

Since 54 factors into 2 × 33, 54edo has subset edos 2, 3, 6, 9, 18, and 27.

Intervals

Using the sharp fifth as a generator, 54edo requires up to quadruple ups and downs to notate. But using the flat fifth as a generator, it requires up to septuple sharps and flats. Because the flat fifth generates a diatonic scale with a chroma of 1 step, ups and downs are not needed in notation if the flat fifth is used.

Table of intervals in 54edo
Degree Cents Ups and downs notation
Flat fifth (31\54) Sharp fifth (16\27)
0 0.000 D D
1 22.222 D♯, E♭♭♭♭♭♭♭ ^D, vE♭
2 44.444 D𝄪, E♭♭♭♭♭♭ ^^D, E♭
3 66.667 D♯𝄪, E♭♭♭♭♭ ^3D, ^E♭
4 88.889 D𝄪𝄪, E♭♭♭♭ ^4D, ^^E♭
5 111.111 D♯𝄪𝄪, E♭♭♭ v3D♯, ^3E♭
6 133.333 D𝄪𝄪𝄪, E♭♭ vvD♯, v4E
7 155.556 D♯𝄪𝄪𝄪, E♭ vD♯, v3E
8 177.778 E D♯, vvE
9 200.000 E♯, F♭♭♭♭♭♭ ^D♯, vE
10 222.222 E𝄪, F♭♭♭♭♭ E
11 244.444 E♯𝄪, F♭♭♭♭ ^E, vF
12 266.667 E𝄪𝄪, F♭♭♭ F
13 288.889 E♯𝄪𝄪, F♭♭ ^F, vG♭
14 311.111 E𝄪𝄪𝄪, F♭ ^^F, G♭
15 333.333 F ^3F, ^G♭
16 355.556 F♯, G♭♭♭♭♭♭♭ ^4F, ^^G♭
17 377.778 F𝄪, G♭♭♭♭♭♭ v3F♯, ^3G♭
18 400.000 F♯𝄪, G♭♭♭♭♭ vvF♯, v4G
19 422.222 F𝄪𝄪, G♭♭♭♭ vF♯, v3G
20 444.444 F♯𝄪𝄪, G♭♭♭ F♯, vvG
21 466.667 F𝄪𝄪𝄪, G♭♭ ^F♯, vG
22 488.889 F♯𝄪𝄪𝄪, G♭ G
23 511.111 G ^G, vA♭
24 533.333 G♯, A♭♭♭♭♭♭♭ ^^G, A♭
25 555.556 G𝄪, A♭♭♭♭♭♭ ^3G, ^A♭
26 577.778 G♯𝄪, A♭♭♭♭♭ ^4G, ^^A♭
27 600.000 G𝄪𝄪, A♭♭♭♭ v3G♯, ^3A♭
28 622.222 G♯𝄪𝄪, A♭♭♭ vvG♯, v4A
29 644.444 G𝄪𝄪𝄪, A♭♭ vG♯, v3A
30 666.667 G♯𝄪𝄪𝄪, A♭ G♯, vvA
31 688.889 A ^G♯, vA
32 711.111 A♯, B♭♭♭♭♭♭♭ A
33 733.333 A𝄪, B♭♭♭♭♭♭ ^A, vB♭
34 755.556 A♯𝄪, B♭♭♭♭♭ ^^A, B♭
35 777.778 A𝄪𝄪, B♭♭♭♭ ^3A, ^B♭
36 800.000 A♯𝄪𝄪, B♭♭♭ ^4A, ^^B♭
37 822.222 A𝄪𝄪𝄪, B♭♭ v3A♯, ^3B♭
38 844.444 A♯𝄪𝄪𝄪, B♭ vvA♯, v4B
39 866.667 B vA♯, v3B
40 888.889 B♯, C♭♭♭♭♭♭ A♯, vvB
41 911.111 B𝄪, C♭♭♭♭♭ ^A♯, vB
42 933.333 B♯𝄪, C♭♭♭♭ B
43 955.556 B𝄪𝄪, C♭♭♭ ^B, vC
44 977.778 B♯𝄪𝄪, C♭♭ C
45 1000.000 B𝄪𝄪𝄪, C♭ ^C, vD♭
46 1022.222 C ^^C, D♭
47 1044.444 C♯, D♭♭♭♭♭♭♭ ^3C, ^D♭
48 1066.667 C𝄪, D♭♭♭♭♭♭ ^4C, ^^D♭
49 1088.889 C♯𝄪, D♭♭♭♭♭ v3C♯, ^3D♭
50 1111.111 C𝄪𝄪, D♭♭♭♭ vvC♯, v4D
51 1133.333 C♯𝄪𝄪, D♭♭♭ vC♯, v3D
52 1155.556 C𝄪𝄪𝄪, D♭♭ C♯, vvD
53 1177.778 C♯𝄪𝄪𝄪, D♭ ^C♯, vD
54 1200.000 D D

Notation

Ups and downs notation

Using Helmholtz–Ellis accidentals, 54edo can also be notated using ups and downs notation:

Step offset 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Sharp symbol   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Flat symbol
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Here, a sharp raises by eight steps, and a flat lowers by eight steps, so single, double, and triple arrows along with Stein–Zimmerman quarter-tone accidentals can be used to fill in the gap.

Sagittal notation

This notation uses the same sagittal sequence as 61-EDO, and is a superset of the notation for 27-EDO.

Evo flavor

 Sagittal notationPeriodic table of EDOs with sagittal notation513/51281/8033/3227/26

Revo flavor

 Sagittal notationPeriodic table of EDOs with sagittal notation513/51281/8033/3227/26

Evo-SZ flavor

 Sagittal notationPeriodic table of EDOs with sagittal notation513/51281/8033/3227/26

In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's primary comma (the comma it exactly represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it approximately represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.

Octave stretch or compression

54edo’s approximations of 3/1, 5/1, 7/1, 11/1, 13/1, 17/1, 19/1 and 23/1 are all improved by 139ed6, a stretched-octave version of 54edo. The trade-off is a slightly worse 2/1 and 19/1.

If one prefers a compressed-octave tuning instead, 86edt, 126ed5 and 152ed7 are possible choices. They improve upon 54edo’s 3/1, 5/1, 7/1 and 17/1, at the cost of its 2/1, 11/1 and 13/1.

What follows is a comparison of stretched- and compressed-octave 54edo tunings.

139ed6
  • Octave size: 1205.08 ¢

Stretching the octave of 54edo by around 5 ¢ results in improved primes 3, 5, 7, 11, 13 and 17, but a worse prime 2. This approximates all harmonics up to 16 within 10.15 ¢. The tuning 139ed6 does this. So does the tuning 262zpi whose octave is identical to 139ed6 within 0.2 ¢.

Approximation of harmonics in 139ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.08 -5.08 +10.15 +3.21 +0.00 +0.92 -7.09 -10.15 +8.29 -0.50 +5.08
Relative (%) +22.7 -22.7 +45.5 +14.4 +0.0 +4.1 -31.8 -45.5 +37.1 -2.2 +22.7
Steps
(reduced) 		54
(54) 		85
(85) 		108
(108) 		125
(125) 		139
(0) 		151
(12) 		161
(22) 		170
(31) 		179
(40) 		186
(47) 		193
(54)
Approximation of harmonics in 139ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +0.40 +6.00 -1.86 -2.01 +4.61 -5.08 -9.41 -8.95 -4.15 +4.58 -5.43 +10.15
Relative (%) +1.8 +26.9 -8.3 -9.0 +20.7 -22.7 -42.2 -40.1 -18.6 +20.5 -24.3 +45.5
Steps
(reduced) 		199
(60) 		205
(66) 		210
(71) 		215
(76) 		220
(81) 		224
(85) 		228
(89) 		232
(93) 		236
(97) 		240
(101) 		243
(104) 		247
(108)
151ed7
  • Octave size: 1204.75 ¢

Stretching the octave of 54edo by around 4.5 ¢ results in improved primes 3, 5, 7, 11, 13 and 17, but a worse prime 2. This approximates all harmonics up to 16 within 11.12 ¢. The tuning 151ed7 does this.

Approximation of harmonics in 151ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.75 -5.60 +9.49 +2.45 -0.85 +0.00 -8.07 +11.12 +7.20 -1.64 +3.90
Relative (%) +21.3 -25.1 +42.5 +11.0 -3.8 +0.0 -36.2 +49.8 +32.3 -7.3 +17.5
Steps
(reduced) 		54
(54) 		85
(85) 		108
(108) 		125
(125) 		139
(139) 		151
(0) 		161
(10) 		171
(20) 		179
(28) 		186
(35) 		193
(42)
Approximation of harmonics in 151ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.82 +4.75 -3.15 -3.33 +3.27 -6.45 -10.81 -10.37 -5.60 +3.11 -6.92 +8.64
Relative (%) -3.7 +21.3 -14.1 -14.9 +14.6 -28.9 -48.4 -46.5 -25.1 +13.9 -31.0 +38.7
Steps
(reduced) 		199
(48) 		205
(54) 		210
(59) 		215
(64) 		220
(69) 		224
(73) 		228
(77) 		232
(81) 		236
(85) 		240
(89) 		243
(92) 		247
(96)
193ed12
  • Octave size: 1203.66 ¢

Stretching the octave of 54edo by around 3.5 ¢ results in improved primes 3, 5, 7, 11 and 13, but worse primes 2 and 11. This approximates all harmonics up to 16 within 10.97 ¢. The tuning 193ed12 does this.

Approximation of harmonics in 193ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.66 -7.31 +7.31 -0.07 -3.66 -3.05 +10.97 +7.67 +3.58 -5.39 +0.00
Relative (%) +16.4 -32.8 +32.8 -0.3 -16.4 -13.7 +49.2 +34.4 +16.1 -24.2 +0.0
Steps
(reduced) 		54
(54) 		85
(85) 		108
(108) 		125
(125) 		139
(139) 		151
(151) 		162
(162) 		171
(171) 		179
(179) 		186
(186) 		193
(0)
Approximation of harmonics in 193ed12 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -4.83 +0.61 -7.39 -7.67 -1.17 -10.97 +6.88 +7.24 -10.36 -1.74 +10.47 +3.66
Relative (%) -21.7 +2.7 -33.1 -34.4 -5.3 -49.2 +30.9 +32.5 -46.5 -7.8 +47.0 +16.4
Steps
(reduced) 		199
(6) 		205
(12) 		210
(17) 		215
(22) 		220
(27) 		224
(31) 		229
(36) 		233
(40) 		236
(43) 		240
(47) 		244
(51) 		247
(54)
263zpi
  • Step size: 22.243 ¢, octave size: 1201.12 ¢

Stretching the octave of 54edo by around 1 ¢ results in an improved prime 5, but worse primes 2, 3, 7, 11 and 13. This approximates all harmonics up to 16 within 10.94 ¢. The tuning 263zpi does this.

Approximation of harmonics in 263zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.12 +10.94 +2.24 -5.94 -10.18 -10.13 +3.37 -0.36 -4.82 +8.12 -9.06
Relative (%) +5.0 +49.2 +10.1 -26.7 -45.8 -45.6 +15.1 -1.6 -21.7 +36.5 -40.7
Step 54 86 108 125 139 151 162 171 179 187 193
Approximation of harmonics in 263zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +8.07 -9.01 +5.00 +4.49 +10.75 +0.76 -3.87 -3.69 +0.81 +9.25 -0.98 -7.93
Relative (%) +36.3 -40.5 +22.5 +20.2 +48.3 +3.4 -17.4 -16.6 +3.6 +41.6 -4.4 -35.7
Step 200 205 211 216 221 225 229 233 237 241 244 247
54edo
  • Step size: 22.222 ¢, octave size: 1200.00 ¢

Pure-octaves 54edo approximates all harmonics up to 16 within 9.16 ¢.

Approximation of harmonics in 54edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 +9.16 +0.00 -8.54 +9.16 +8.95 +0.00 -3.91 -8.54 +4.24 +9.16
Relative (%) +0.0 +41.2 +0.0 -38.4 +41.2 +40.3 +0.0 -17.6 -38.4 +19.1 +41.2
Steps
(reduced) 		54
(0) 		86
(32) 		108
(0) 		125
(17) 		140
(32) 		152
(44) 		162
(0) 		171
(9) 		179
(17) 		187
(25) 		194
(32)
Approximation of harmonics in 54edo (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +3.92 +8.95 +0.62 +0.00 +6.16 -3.91 -8.62 -8.54 -4.11 +4.24 -6.05 +9.16
Relative (%) +17.6 +40.3 +2.8 +0.0 +27.7 -17.6 -38.8 -38.4 -18.5 +19.1 -27.2 +41.2
Steps
(reduced) 		200
(38) 		206
(44) 		211
(49) 		216
(0) 		221
(5) 		225
(9) 		229
(13) 		233
(17) 		237
(21) 		241
(25) 		244
(28) 		248
(32)
54et, 13-limit WE tuning
  • Step size: 22.198 ¢, octave size: 1198.69 ¢

Compressing the octave of 54edo by around 1.5 ¢ results in improved primes 3, 7, 11, 13, 17 and 19, but worse primes 2 and 5. This approximates all harmonics up to 16 within 10.63 ¢. Its 13-limit WE tuning and 13-limit TE tuning both do this. So does the tuning 187ed11 whose octave is identical to 13lim WE within 0.1 ¢.

Approximation of harmonics in 54et, 13-limit WE tuning
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -1.31 +7.07 -2.62 +10.63 +5.76 +5.27 -3.92 -8.05 +9.33 -0.29 +4.46
Relative (%) -5.9 +31.9 -11.8 +47.9 +26.0 +23.7 -17.7 -36.3 +42.0 -1.3 +20.1
Step 54 86 108 126 140 152 162 171 180 187 194
Approximation of harmonics in 54et, 13-limit WE tuning (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -0.93 +3.96 -4.49 -5.23 +0.80 -9.36 +8.03 +8.02 -9.85 -1.60 +10.24 +3.15
Relative (%) -4.2 +17.8 -20.2 -23.6 +3.6 -42.2 +36.2 +36.1 -44.4 -7.2 +46.1 +14.2
Step 200 206 211 216 221 225 230 234 237 241 245 248
264zpi
  • Step size: 22.175 ¢, octave size: 1197.45 ¢

Compressing the octave of 54edo by around 2.5 ¢ results in improved primes 3, 5 and 7, but worse primes 2, 11 and 13. This approximates all harmonics up to 16 within 10.19 ¢. The tuning 264zpi does this. So does the tuning 194ed12 whose octave is identical to 264zpi within 0.01 ¢.

Approximation of harmonics in 264zpi
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -2.55 +5.09 -5.10 +7.74 +2.54 +1.77 -7.65 +10.19 +5.19 -4.59 -0.01
Relative (%) -11.5 +23.0 -23.0 +34.9 +11.5 +8.0 -34.5 +46.0 +23.4 -20.7 -0.0
Step 54 86 108 126 140 152 162 172 180 187 194
Approximation of harmonics in 264zpi (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -5.53 -0.78 -9.34 -10.20 -4.28 +7.64 +2.74 +2.64 +6.87 -7.14 +4.60 -2.56
Relative (%) -24.9 -3.5 -42.1 -46.0 -19.3 +34.5 +12.3 +11.9 +31.0 -32.2 +20.7 -11.5
Step 200 206 211 216 221 226 230 234 238 241 245 248
152ed7
  • Octave size: 1196.82 ¢

Compressing the octave of 54edo by around 3 ¢ results in improved primes 3, 5 and 7, but worse primes 2, 11 and 13. This approximates all harmonics up to 16 within 10.36 ¢. The tuning 152ed7 does this.

Approximation of harmonics in 152ed7
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.18 +4.09 -6.36 +6.27 +0.91 +0.00 -9.54 +8.18 +3.09 -6.78 -2.27
Relative (%) -14.3 +18.5 -28.7 +28.3 +4.1 +0.0 -43.0 +36.9 +13.9 -30.6 -10.2
Steps
(reduced) 		54
(54) 		86
(86) 		108
(108) 		126
(126) 		140
(140) 		152
(0) 		162
(10) 		172
(20) 		180
(28) 		187
(35) 		194
(42)
Approximation of harmonics in 152ed7 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -7.86 -3.18 +10.36 +9.44 -6.86 +5.00 +0.05 -0.09 +4.09 -9.96 +1.74 -5.45
Relative (%) -35.5 -14.3 +46.7 +42.6 -31.0 +22.6 +0.2 -0.4 +18.5 -44.9 +7.9 -24.6
Steps
(reduced) 		200
(48) 		206
(54) 		212
(60) 		217
(65) 		221
(69) 		226
(74) 		230
(78) 		234
(82) 		238
(86) 		241
(89) 		245
(93) 		248
(96)
140ed6
  • Octave size: 1196.47 ¢

Compressing the octave of 54edo by around 3.5 ¢ results in improved primes 3, 5 and 7, but worse primes 2, 11 and 13. This approximates all harmonics up to 16 within 10.59 ¢. The tuning 140ed6 does this.

Approximation of harmonics in 140ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.53 +3.53 -7.06 +5.45 +0.00 -0.99 -10.59 +7.06 +1.91 -7.99 -3.53
Relative (%) -15.9 +15.9 -31.9 +24.6 +0.0 -4.5 -47.8 +31.9 +8.6 -36.1 -15.9
Steps
(reduced) 		54
(54) 		86
(86) 		108
(108) 		126
(126) 		140
(0) 		152
(12) 		162
(22) 		172
(32) 		180
(40) 		187
(47) 		194
(54)
Approximation of harmonics in 140ed6 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) -9.16 -4.52 +8.98 +8.03 -8.30 +3.53 -1.44 -1.62 +2.54 +10.63 +0.15 -7.06
Relative (%) -41.4 -20.4 +40.5 +36.2 -37.5 +15.9 -6.5 -7.3 +11.5 +48.0 +0.7 -31.9
Steps
(reduced) 		200
(60) 		206
(66) 		212
(72) 		217
(77) 		221
(81) 		226
(86) 		230
(90) 		234
(94) 		238
(98) 		242
(102) 		245
(105) 		248
(108)
126ed5
  • Octave size: 1194.13 ¢

Compressing the octave of 54edo by around 6 ¢ results in improved primes 3, 5 and 7, but worse primes 2, 11 and 13. This approximates all harmonics up to 16 within 10.20 ¢. The tuning 126ed5 does this. So does the tuning 86edt whose octave is identical to 126ed5 within 0.1 ¢.

Approximation of harmonics in 126ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.87 -0.19 +10.38 +0.00 -6.05 -7.56 +4.52 -0.37 -5.87 +6.04 +10.20
Relative (%) -26.5 -0.8 +47.0 +0.0 -27.4 -34.2 +20.4 -1.7 -26.5 +27.3 +46.1
Steps
(reduced) 		54
(54) 		86
(86) 		109
(109) 		126
(0) 		140
(14) 		152
(26) 		163
(37) 		172
(46) 		180
(54) 		188
(62) 		195
(69)
Approximation of harmonics in 126ed5 (continued)
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +4.31 +8.69 -0.19 -1.35 +4.26 -6.24 +10.73 +10.38 -7.74 +0.17 -10.44 +4.33
Relative (%) +19.5 +39.3 -0.8 -6.1 +19.3 -28.2 +48.5 +47.0 -35.0 +0.8 -47.2 +19.6
Steps
(reduced) 		201
(75) 		207
(81) 		212
(86) 		217
(91) 		222
(96) 		226
(100) 		231
(105) 		235
(109) 		238
(112) 		242
(116) 		245
(119) 		249
(123)

Scales

  • Approximations of gamelan scales:
    • 5-tone pelog: 5 7 19 4 19
    • 7-tone pelog: 5 7 11 8 4 13 6
    • 5-tone slendro: 11 11 10 11 11

Instruments

Lumatone

See Lumatone mapping for 54edo

Music

Bryan Deister
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