Tunings (various)
General
All tunings set the absolute tuning to a' (A above middle C) equals 440Hz unless otherwise
stated.
Tunings given assume the key of C.
Whole-tone means two half-steps with different names for the notes (for example, C-D).
Diatonic half-step means a half-step (semitone) with different names for the notes (for
example, C-Db).
Chromatic half-step means a half-step (semitone) with the same name for the notes (for
example, C-C#).
There are two main types of commas: Pythagorean (ditonic) comma (531441:524288,
23.46001038¢, or 720TU) and syntonic comma (81:80, 21.5062896¢ or 660TU). Other commas are
mentioned if there are different.
EDO is an acronym for equal divisions of the octave.
TU is an acronym for temperamental unit, which is equal to 1/720 of the Pythagorean comma,
1/660 of the syntonic comma or 0.0325852873¢.
17edo
Whole-tone = 211.764706¢; diatonic half step = 70.588235¢; chromatic half step = 141.176471¢
The octave is divided into 17 equal steps. Three steps form a whole-tone, one step a diatonic
half step and two steps a chromatic half step.
19edo
Whole-tone = 189.473684¢; diatonic half step = 126.315789¢; chromatic half step = 63.157894¢
The octave is divided into 19 equal steps. Three steps form a whole-tone, two steps a diatonic
half step and one step a chromatic half step.
22edo (a/k/a Bosanquet)
Whole-tone = 218.181818¢; diatonic half step = 54.545455¢; chromatic half step = 163.636364¢
The octave is divided into 22 equal steps. Four steps form a whole-tone, one step a diatonic half
step and three steps a chromatic half step.
41edo
Whole-tone = 204.878049¢; diatonic half step = 87.804878¢; chromatic half step = 117.073171¢
The octave is divided into 41 equal steps. Seven steps form a whole-tone, three steps a diatonic
half step and four steps a chromatic half step.
53edo
Whole-tone = 203.773585¢; diatonic half step = 90.566038¢; chromatic half step = 113.207547¢
The octave is divided into 53 equal steps. Nine steps form a whole-tone, four steps a diatonic
half step and five steps a chromatic half step.
55edo (a/k/a Mozart's tuning)
Whole-tone = 196.363636¢; diatonic half step = 109.090909¢; chromatic half step = 87.272727¢
The octave is divided into 55 equal steps. Nine steps form a whole-tone, five steps a diatonic
half step and four steps a chromatic half step.
88edo
Whole-tone = 190.909091¢; diatonic half step = 122.727272¢; chromatic half step = 68.181818¢
The octave is divided into 88 equal steps. Fourteen (14) steps form a whole-tone, nine steps a
diatonic half step and five steps a chromatic half step.
1420edo
Whole-tone = 190.985915¢; diatonic half step = 122.535211¢; chromatic half step = 68.450704¢
The octave is divided into 1420 equal steps. Two hundred and twenty-six (226) steps form a
whole-tone, 145 steps a diatonic half step and 81 steps a chromatic half step. This tuning gives a
good approximation for Lucy's tuning.
1/5 syntonic comma meantone (a/k/a Holder; Rossi)
Whole-tone = 195.307486¢; diatonic half step = 111.731285¢; chromatic half step = 83.576201¢
The major sevenths are justly tuned (15:8), the fifths are too narrow by a fifth of the syntonic
comma.
5/23 syntonic comma meantone (a/k/a Holder; Rossi)
Whole-tone = 194.559441¢; diatonic half step = 113.601397¢; chromatic half step = 80.958044¢
The fifths are too narrow by 5/23 of the syntonic comma.
2/9 syntonic comma meantone (a/k/a Rossi)
Whole-tone = 194.351651¢; diatonic half step = 114.120873¢; chromatic half step = 80.230778¢
The fifths are too narrow by two-ninths of the syntonic comma.
1/3 syntonic comma meantone (a/k/a Salinas)
Whole-tone = 189.572475¢; diatonic half step = 126.068812¢; chromatic half step = 63.503664¢
The minor thirds are justly tuned (6:5), the fifths are too narrow by a third of the syntonic
comma.
½ syntonic comma meantone
Whole-tone = 182.403712¢; diatonic half step = 143.990720¢; chromatic half step = 38.412992¢
The minor sevenths are justly tuned (9:5), the fifths are too narrow by a half of the syntonic
comma.
3\37edo
C
0
97.29730
D
194.59459
291.89189
E
389.18919
F
486.48649
583.78378
G
681.08108
778.37838
A
875.67568
972.97297
B
1070.27027
C
1200
12th harmonic scale (original)
This scale is based on the number 12.
C
D
E
F
G
A
B
C
1:1 (0)
13:12 (138.57266)
7:6 (268.87091)
29:24 (327.62219)
5:4 (386.31371)
4:3 (498.045)
17:12 (603.00041)
3:2 (701.955)
19:12 (795.55802)
5:3 (884.35871)
41:24 (927.1074)
7:4 (968.82591)
2:1 (1200)
12th harmonic scale (modified)
This scale is based on the number 12.
C
D
E
F
G
A
B
C
1:1 (0)
13:12 (138.57266)
7:6 (268.87091)
29:24 (327.62219)
5:4 (386.31371)
4:3 (498.045)
17:12 (603.00041)
3:2 (701.955)
19:12 (795.55802)
5:3 (884.35871)
7:4 (968.82591)
11:6 (1049.36294)
2:1 (1200)
12-note Highschool scale #1
First 12-note Highschool scale.
C
D
E
F
G
A
B
C
1:1
21:20
9:8
6:5
5:4
4:3
7:5
3:2
8:5
5:3
7:4
15:8
2:1
12-note Highschool scale #2
Second 12-note Highschool scale.
C
D
E
F
G
A
B
C
1:1
15:14
9:8
6:5
5:4
4:3
10:7
3:2
8:5
5:3
7:4
15:8
2:1
24edl
For an intervallic system with 24 divisions, EDL is considered as equal divisions of length by
dividing string length to 24 equal divisions (so we have 12 divisions per octave).
C
D
E
F
G
A
B
C
1:1
24:23
12:11
8:7
6:5
24:19
4:3
24:17
3:2
8:5
12:7
24:13
2:1
256edl
This well-temperament is based on 256edl.
C
D
E
F
G
A
B
C
0
104.5328
200.53198
302.16858
401.5969
498.045
600
701.955
806.4878
902.48698
1004.12358
1103.5519
1200
1568edl
C
1:1 (0)
1568:1485 (94.15515)
D
28:25 (196.19848)
196:165 (298.06516)
E
49:39 (395.16915)
F
4:3 (498.04500)
196:139 (594.92253)
G
196:131 (697.54421)
784:495 (796.11015)
A
196:117 (893.21415)
98:55 (1000.02016)
B
49:26 (1097.12415)
C
2:1 (1200)
Bach (1722)
The normal layout of Bach's temperament, for solo and instrumental-ensemble work.
The fifths Eb-Bb, Bb-F, C#-G# and G#-D# are too narrow by 1/12 of the Pythagorean comma,
E-B, B-F# and F#-C# are perfect, the other fifths are one-sixth too narrow.
C
D
E
F
G
A
B
C
0
98.045
196.09
298.045
392.18
501.955
596.09
698.045
798.045
894.135
998.045
1095.135
1200
Bach R2-1 (Cammerton)
C
0
95.2136
D
198.495
299.124
E
395.505
F
499.782
593.259
G
699.637
797.169
A
896.314
999.128
B
1093.770
C
1200
Bach R2-2 (Cornet-ton)
C
0
100.628
D
197.010
301.286
E
394.763
F
501.141
598.673
G
697.818
800.633
A
895.273
1001.500
B
1096.720
C
1200
Bach seal (1722)
This tuning sets the absolute tuning at a' equals 415.88Hz, which is the equivalent of tuning the
tone scale 97.6034609394¢ lower than at 440Hz.
C
D
E
F
G
A
B
C
0
91.9662
196.15
295.876
391.05
499.786
590.011
697.303
793.921
891.872
997.831
1089.29
1200
Bach (1722), transposed to D to simulate Choryon/Cammerton
The transposed layout of Bach's temperament, for keyboards in the vocal works that were
written for a Chorton/Cammerton transposing situation. (For example, all of the Leipzig vocal music:
cantatas, masses, passions, oratorios.) Tune the organs and harpsichords using this alternate
version, for keyboard players who are reading from modern parts that have been transposed up to
the key of the orchestra.
The fifths Eb-Bb, Bb-F and F-C are too narrow by 1/12 Pythagorean comma, F#-C#, C#-G# and
G#-D# are perfect, the other fifths are one-sixth too narrow.
C
D
E
F
G
A
B
C
0
96.09
201.955
300
398.045
500
588.26999
703.91
798.045
900
1000
1096.09
1200
Barbour
A selection of harmonic intervals.
C
D
E
F
G
A
B
C
1:1
25:24
9:8
6:5
5:4
4:3
45:32
3:2
25:16
5:3
9:5
15:8
2:1
Barnes “Bach” (1979)
The fifths F-C, C-G, G-D, D-A, A-E and B-F# are too narrow by a sixth of the Pythagorean
comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
196.09
298.045
392.18
501.955
592.18
698.045
796.09
894.135
1000
1091.135
1200
Barton
Jacob Barton, tetratradic scale on 6:7:9:11.
C
D
E
F
G
A
B
C
1:1
77:72
12:11
9:8
7:6
14:11
11:8
3:2
18:11
121:72
7:4
11:6
2:1
Beat temperament
Described in the paper Bach- and Well-Temperaments for Western Classical Music, available
for free from the website http://lit.gfax.ch//tunings/BachAndWellTemperaments.pdf.
C
D
E
F
G
A
B
C
0
90.225
195.78212
294.135
387.15598
498.045
588.27
699.43891
792.18
890.22634
996.09
1086.31499
1200
Bendeler I
The fifths C-G, G-D and B-F# are too narrow by a third of the Pythagorean comma, the other
fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
188.27
294.135
392.18
498.045
588.26999
694.135
791.18
890.225
996.09
1094.135
1200
Bendeler II
The fifths C-G, D-A and F#-C# are too narrow by a third of the Pythagorean comma, the other
fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
196.09
294.135
392.18
498.045
596.09
694.135
792.18
890.225
996.09
1094.135
1200
Bendeler III
The fifths C-G, G-D, E-B and G#-D# are too narrow by a quarter of the Pythagorean comma,
the other fifths are perfect.
C
D
E
F
G
A
B
C
0
96.09
192.18
294.135
396.09
498.045
594.135
696.09
798.045
894.135
996.09
1092.18
1200
Bermuda (1555)
Near-by equal temperament.
C
D
E
F
G
A
B
C
0
100
200
294.135
400.9775
498.0445
600
701.955
801.955
901.955
996.09
1102.9325
1200
Bicycle
13-limit harmonic bicycle, George Secor, 1963.
C
D
E
F
G
A
B
C
1:1
13:12
9:8
7:6
5:4
4:3
11:8
3:2
13:8
5:3
7:4
11:6
2:1
Bifrost
This has six meantone fifths, leading to three pure thirds; on each side of the chain of
meantones we put two pure 3:2's, so we have four pure fifths in total; we then round out with two
sharp fifths of size 706.35471 cents. This leads to three sharp major thirds which are within a cent of
being pure 14:11's, being of size 416.619 cents; and two more sharp thirds of size 406.843 at E and
Ab, which are the only real problems with this temperament. http://lumma.org/tuning/gws/bifrost.html
C
D
E
F
G
A
B
C
0
86.80214
193.15686
299.51157
386.31371
503.42157
584.84714
696.57843
793.15686
889.73529
1001.46657
1082.89214
1200
Big gulp
C
1:1
33:32
D
9:8
7:6
E
5:4
F
21:16
11:8
G
3:2
99:64
A
27:16
7:4
B
15:8
C
2:1
Bihexany
Hole around [0, ½, ½, ½].
C
D
E
F
G
A
B
C
1:1
35:33
7:6
5:4
14:11
15:11
3:2
35:22
5:3
7:4
20:11
21:11
2:1
Billeter “Bach” (1979)
The fifths D-A and A-E are too narrow by a third of the syntonic comma, C-G, G-D, E-B and BF# are 1/12 too narrow, F-C is 1/11 to narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
92.17872
200.32562
296.08872
389.8981
499.99872
590.22372
700.16281
794.13372
895.11186
998.04372
1090.06091
1200
Blue-JI
John O'Sullivan and Carl Lumma.
C
D
E
F
G
A
B
C
1:1
15:14
9:8
6:5
5:4
4:3
7:5
3:2
8:5
5:3
9:5
15:8
2:1
Blues JI
Seven-limit just intonation version of Graham Breed's Blues scale.
C
D
E
F
G
A
B
C
1:1
27:25
10:9
5:4
35:27
4:3
35:24
40:27
81:50
5:3
140:81
35:18
2:1
Breedball 3
Third Breed ball around 49:40 to 7:4.
C
D
E
F
G
A
B
C
1:1
49:48
21:20
15:14
49:40
5:4
7:5
10:7
3:2
49:32
12:7
7:4
2:1
Calculus musicus
This tuning sets the absolute tuning at a' equals 458.26Hz, which is the equivalent of tuning the
tone scale 70.3954072543¢ higher than at 440Hz.
C
D
E
F
G
A
B
C
0
94.72
196.86
297.30
394.47
501.21
592.77
697.73
796.68
895.04
999.26
1093.06
1200
Calculus musicus mirror
This tuning sets the absolute tuning at a' equals 473.661Hz, which is the equivalent of tuning
the tone scale 127.6216384166¢ higher than at 440Hz.
C
D
E
F
G
A
B
C
0
94.72
196.86
297.30
394.47
501.21
592.77
697.73
796.68
895.04
999.26
1093.06
1200
Canton
A 2.3.11:7.13:7 subgroup scale.
C
D
E
F
G
A
B
C
1:1
14:13
9:8
13:11
14:11
4:3
39:28
3:2
11:7
22:13
16:9
13:7
2:1
Carlos harmonic
Carlos Harmonic & Ben Johnson's scale of 'Blues' from Suite f.micr.piano (1977) & David
Beardsley's scale of Science Friction.
C
D
E
F
G
A
B
C
1:1
17:16
9:8
19:16
5:4
21:16
11:8
3:2
13:8
27:16
7:4
15:8
2:1
Cauldron
http://lumma.org/tuning/gws/cauldron.html
C
D
E
F
G
A
B
C
0
70.31346
189.20489
291.90367
378.40979
505.39755
567.61468
694.60244
781.10856
883.80734
1002.69877
1073.01223
1200
Cent temperament
Described in the paper Bach- and Well-Temperaments for Western Classical Music, available
for free from the website http://lit.gfax.ch//tunings/BachAndWellTemperaments.pdf.
C
D
E
F
G
A
B
C
0
90.225
194.86828
294.135
388.02514
498.045
588.26999
698.28985
795.18
891.44671
996.09
1086.31499
1200
Chinese Lü scale
This scale was created by Huai-nan-dsi of the Han dynasty.
C
D
E
F
G
A
B
C
1:1
18:17
9:8
6:5
54:43
4:3
27:19
3:2
27:17
27:16
9:5
36:19
2:1
Couperin
Couperin modified meantone.
C
D
E
F
G
A
B
C
0
76.049
193.15686
289.73598
5:4
503.42157
579.47057
696.57843
25:16
889.73529
996.57878
1082.89214
1200
Courette
Michael Corrette, modified meantone temperament (1753).
C
D
E
F
G
A
B
C
0
72.62999
192.18
296.09
8192:6561
503.91
576.53999
696.09
776.53999
888.26999
1000
1080.44999
1200
CV scale #1 (epimorphic)
C
1:1
16:15
D
8:7
7:6
E
5:4
F
4:3
7:5
G
3:2
8:5
A
5:3
7:4
B
28:15
C
2:1
CV scale #3 (epimorphic = pris)
C
1:1
16:15
D
28:25
7:6
E
5:4
F
4:3
7:5
G
3:2
8:5
A
5:3
7:4
B
28:15
C
2:1
CV scale #5 (epimorphic = inverse hen12)
C
1:1
15:14
D
9:8
6:5
E
5:4
F
21:16
7:5
G
3:2
8:5
A
12:7
7:4
B
15:8
C
2:1
CV scale #7 (epimorphic)
C
1:1
21:20
D
9:8
6:5
E
9:7
F
21:16
7:5
G
3:2
8:5
A
12:7
9:5
B
15:8
C
2:1
CV scale #9 (epimorphic)
C
1:1
15:14
D
8:7
7:6
E
5:4
F
4:3
10:7
G
32:21
8:5
A
5:3
25:14
B
40:21
C
2:1
CV scale #11 (epimorphic)
C
1:1
15:14
D
9:8
6:5
E
9:7
F
21:16
7:5
G
3:2
8:5
A
12:7
9:5
B
15:8
C
2:1
CV scale #13 (epimorphic)
C
1:1
16:15
D
28:25
6:5
E
5:4
F
4:3
7:5
G
3:2
8:5
A
12:7
7:4
B
28:15
C
2:1
d'Alembert (a/k/a French ordinary temperament)
This temperament was described by a number of French documents of the period of Scarletti.
C
D
E
F
G
A
B
C
0
85.59
193.36
291.39
386.31371
498.045
584.75
696.83
787.5
888.67
994.93
1086.51
1200
Di Veroli “Bach WTC Optimal+” (2008)
The fifths Eb-Bb and F#-C# are perfect, F-C, C-G and A-E are too narrow by a sixth of the
Pythagorean comma, the other fifths are 1/12 too narrow.
C
D
E
F
G
A
B
C
0
100
196.09
300
398.045
501.955
594.135
701.955
803.91
900
1005.865
1098.045
1200
Duodene
C
1:1
16:15
D
9:8
6:5
E
5:4
F
4:3
45:32
G
3:2
8:5
A
5:3
9:5
B
15:8
C
2:1
Duodene skew
C
1:1
27:25
D
10:9
6:5
E
5:4
F
4:3
36:25
G
3:2
8:5
A
5:3
9:5
B
48:25
C
2:1
Duohex
A scale with two hexanies.
C
D
E
F
G
A
B
C
1:1
15:14
9:8
6:5
5:4
9:7
10:7
3:2
45:28
12:7
9:5
15:8
2:1
Duowell
Duowell is a well-tuning of the Ellis Duodene, where a well-tuning is a regular tuning of a just
intonation scale with an eye to making it circulate.
C
D
E
F
G
A
B
C
0
107.65973
202.1885
309.84823
391.24602
498.90575
593.42451
701.09425
808.75398
890.15177
1010.94247
1092.34026
1200
Dwarf 12/7
The seven-limit 12-note dwarf.
C
D
E
F
G
A
B
C
1:1
16:15
9:8
6:5
5:4
4:3
7:5
3:2
8:5
5:3
9:5
28:15
2:1
Dwarf 12/11
The 11-limit 12-note dwarf.
C
D
E
F
G
A
B
C
1:1
16:15
11:10
6:5
5:4
4:3
7:5
22:15
8:5
5:3
9:5
28:15
2:1
Erlich
Whole-tone = 192.037444¢; diatonic half step = 119.906389¢; chromatic half step = 72.131055¢
The fifths are too narrow by 175/634 of the syntonic comma.
Genovese 12
Danny Genovese's superposition of harmonics 8-16 and subharmonics 6-12.
C
D
E
F
G
A
B
C
1:1
12:11
9:8
6:5
5:4
4:3
11:8
3:2
13:8
12:7
7:4
15:8
2:1
Ganassi's well-temperament
This well-temperament is based on 120-edl.
C
D
E
F
G
A
B
C
1:1
20:19
10:9
20:17
5:4
4:3
24:17
3:2
30:19
5:3
30:17
15:8
2:1
Glumma
C
1:1
36:35
D
8:7
6:5
E
5:4
F
48:35
10:7
G
3:2
5:3
A
12:7
7:4
B
96:49
C
2:1
Grail
This grail-type temperament has the following attributes:
1. Near the key center, it functions as an honest meantone, with major thirds not too far off pure.
2. All fifths are usable; there are no wolf fifths.
3. All thirds in all keys are functional.
http://lumma.org/tuning/gws/grail.html
C
D
E
F
G
A
B
C
0
86.86903
195.62301
304.37699
391.24602
504.37699
578.08096
695.62301
795.62301
895.62301
1013.16506
1086.86903
1200
Hahn7
Paul Hahn's scale with 32 consonant seven-limit dyads.
C
D
E
F
G
A
B
C
1:1
21:20
7:6
6:5
5:4
4:3
7:5
3:2
8:5
5:3
7:4
28:15
2:1
Hahn12
Hahn-reduced 12-note scale.
C
D
E
F
G
A
B
C
1:1
15:14
8:7
6:5
5:4
4:3
7:5
3:2
8:5
5:3
7:4
15:8
2:1
Harrison Cinna
Lou Harrison, Incidental Music for Corneille's Cinna (1955-56).
C
D
E
F
G
A
B
C
1:1
25:24
9:8
6:5
5:4
21:16
45:32
3:2
8:5
5:3
7:4
15:8
2:1
Harrison Revelation
Michael Harrison, piano tuning for Revelation (2001).
C
D
E
F
G
A
B
C
1:1
64:63
9:8
567:512
81:64
21:16
729:512
3:2
189:128
27:16
7:4
243:128
2:1
Hexy
Maximized nine-limit harmony containing a hexany.
C
D
E
F
G
A
B
C
1:1
21:20
9:8
7:6
5:4
4:3
7:5
3:2
8:5
5:3
7:4
28:15
2:1
Jencka (2005)
The fifths F-C, C-G, G-D, D-A and A-E are too narrow by a sixth of the Pythagorean comma,
Eb-Bb, C#-G# and G#-D# are 1/18 too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
196.09
299.34833
392.18
501.955
596.09
698.045
798.69667
894.135
1000
1094.135
1200
Jira (2005) “geschlossen” (closed) temperament
The fifths C-G, G-D, D-A and A-E are too narrow by a sixth of the Pythagorean comma, Eb-Bb,
B-F, F#-C# and C#-G# are 1/12 too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
196.09
296.09
392.18
498.045
594.135
698.045
794.135
894.135
996.09
1094.135
1200
Jira (2005) “offen” (open) temperament
The fifths C-G, G-D, D-A and A-E are too narrow by a quarter of the syntonic comma, Eb-Bb,
Bb-F and G#-D# are 7/132 too wide, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
88.26999
196.09
294.135
392.18
498.045
592.18
698.045
790.225
894.135
996.09
1094.135
1200
Kafi
Selection of harmonic intervals, developed by Erv Wilson and Amiya Dasgupta in 1978.
C
D
E
F
G
A
B
C
1:1
256:243
10:9
32:27
5:4
4:3
45:32
3:2
128:81
5:3
16:9
15:8
2:1
Kelletat (1966)
The fifths C-G, G-D and D-A are too narrow by a quarter of the Pythagorean comma, F-C is
1/12 too narrow, A-E is one-sixth too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
92.18
192.18
296.09
386.31499
500
590.225
696.09
794.135
888.26999
998.045
1088.26999
1200
Kellner “Bach” (1975)
The fifths C-G, G-D, D-A and B-F# are too narrow by a fifth of the Pythagorean comma, the
other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
194.526
294.135
389.052
498.045
588.26999
697.263
792.18
891.789
996.09
1091.007
1200
Labyrinthus musicus
This tuning sets the absolute tuning at a' equals 458.13Hz, which is the equivalent of tuning the
tone scale 69.8399753343¢ higher than at 440Hz.
C
D
E
F
G
A
B
C
0
94.5765
196.854
298.486
393.206
501.211
592.621
697.725
796.531
895.034
1000.44
1091.79
1200
Labyrinthus musicus mirror
This tuning sets the absolute tuning at a' equals 474.577Hz, which is the equivalent of tuning
the tone scale 130.9663912787¢ higher than at 440Hz.
C
D
E
F
G
A
B
C
0
94.5765
196.854
298.486
393.206
501.211
592.621
697.725
796.531
895.034
1000.44
1091.79
1200
Lehman Buxtehude/Bohm
The fifths F-C, E-B and C#-G# are perfect, C-G, G-D, D-A and A-E are too narrow by 3/16 of the
Pythagorean comma, the other fifths are 1/12 too narrow.
C
D
E
F
G
A
B
C
0
92.18
195.1125
294.135
390.225
498.045
592.18
661.87748
794.135
892.66875
994.135
1092.18
1200
Lindley “Handel-style” (circa 1995)
The fifths C-G, G-D, D-A and A-E are too narrow by 15/96 of the Pythagorean comma, E-B and
F-C are 11/96 too narrow, B-F# and F#-C# are 7/96 too narrow, C#-G# is 3/96 too narrow, Ab-Eb, EbB and B-F are 1/96 too wide. (No fifths are perfect.)
C
D
E
F
G
A
B
C
0
92.91312
196.57875
296.33437
393.1575
500.73313
592.66875
698.28937
794.135
894.86812
998.53375
1092.42437
1200
Locomotive
A 2.9.11.13 subgroup scale.
C
D
E
F
G
A
B
C
1:1
88:81
9:8
11:9
16:13
11:8
13:9
16:11
13:8
18:11
16:9
81:44
2:1
Lucy tuning
Whole-tone = 190.985932¢; diatonic half step = 122.535171¢; chromatic half step = 68.450761¢
“Lucy comma” is to generate “LucyTuning” which sets the size of a whole step as 1200/2π¢.
Because LucyTuning is a regular meantone, this tuning came up with an invented comma (Lucy
comma, which equals 25.848140041¢) which generates the proper sizes of intervals.
The fifths are too narrow by a quarter of the Lucy comma.
Major third and minor third equally beating
Whole-tone = 191.458992¢; diatonic half step = 121.352520¢; chromatic half step = 70.106472¢
The fifths are too narrow by 11/38 of the syntonic comma.
Major third and perfect fifth equally beating
Whole-tone = 191.259243¢; diatonic half step = 121.851892¢; chromatic half step = 69.407351¢
The fifths are too narrow by 5/17 of the syntonic comma.
Malcolm 2
Alexander Malcolm's 1721 scale.
C
D
E
F
G
A
B
C
1:1
17:16
9:8
19:16
5:4
4:3
17:12
3:2
19:12
5:3
85:48
15:8
2:1
Marpug I
The fifth D-A is too narrow by a syntonic comma, F#-C# is too wide by a schisma (ratio
32805:32768, or 1.953720788¢), the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
203.91
294.135
386.31371
498.045
590.22372
701.955
792.18
884.35871
996.09
1088.26871
1200
Marpug II
The fifth E-B is too narrow by a sixth of the Pythagorean comma, Bb-F is 5/6 too narrow, the
other fifths are perfect.
C
D
E
F
G
A
B
C
0
109.775
203.91
313.68501
407.82
498.045
607.82
701.955
811.73001
905.865
1015.64001
1105.865
1200
Marpug III
The fifth E-B is too narrow by ¾ of the Pythagorean comma, Eb-Bb is a quarter too narrow, the
other fifths are perfect.
C
D
E
F
G
A
B
C
0
96.09
203.91
300
407.82
498.045
594.135
701.955
798.045
905.865
996.09
1092.18
1200
Marpug IV
The fifth E-B is too narrow by 2/3 of the Pythagorean comma, G#-D# is a third too narrow, the
other fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
203.91
294.135
407.82
498.045
596.09
701.955
800
905.865
996.09
1094.135
1200
Marpug V
The fifth E-B is too narrow by 5/12 of the Pythagorean comma, Bb-F is 7/12 too narrow, the
other fifths are perfect.
C
D
E
F
G
A
B
C
0
103.91
203.91
307.82
407.82
601.955
498.045
701.955
805.865
905.865
1009.775
1100
1200
Marpug VI
The fifths B-F# and Bb-F are too narrow by a half of the Pythagorean comma, the other fifths
are perfect.
C
D
E
F
G
A
B
C
0
101.955
203.91
305.865
407.82
498.045
600
701.955
803.91
905.865
1007.82
1109.775
1200
Marpug VII
The fifths C-G, E-B and C#-G# are too narrow by a third of the Pythagorean comma, the other
fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
196.09
294.135
400
498.045
596.09
694.135
792.18
898.045
996.09
1094.135
1200
Marpug VIII
The fifths C-G, E-B, C#-G# and Bb-F are too narrow by a quarter of the Pythagorean comma,
the other fifths are perfect.
C
D
E
F
G
A
B
C
0
101.955
198.045
300
401.955
498.045
600
696.09
798.045
900
1001.955
1098.045
1200
Marpug IX
The fifths B-F#, F#-C#, Bb-F and F-C are too narrow by a quarter of the Pythagorean comma,
the other fifths are perfect.
C
D
E
F
G
A
B
C
0
101.955
203.91
305.865
407.82
503.91
605.865
701.955
803.91
905.865
1007.82
1109.775
1200
Marpug X
The fifths C-G, D-A, E-B, F#-C#, G#-D# and Bb-F are too narrow by a sixth of the Pythagorean
comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
200
298.045
400
498.045
600
698.045
800
898.045
1000
1098.045
1200
Marpug XI
The fifths B-F#, F#-C#, C#-G#, G#-D#, Eb-Bb and Bb-F are too narrow by a sixth of the
Pythagorean comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
105.865
203.91
301.955
407.82
498.045
607.82
701.955
803.91
905.865
1000
1109.775
1200
Marpug XII
The fifth C-G is too wide by 1/12 of the Pythagorean comma, F-C is 1/12 too narrow, A-E is 1/6
too narrow, G#-D# is 5/6 too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
111.73001
205.865
296.09
405.865
500
609.775
703.91
813.68501
907.82
998.045
1107.82
1200
Max1
C
1:1
8:7
D
7:6
6:5
E
5:4
F
4:3
7:5
G
3:2
8:5
A
5:3
12:7
B
7:4
C
2:1
Max2
C
1:1
8:7
D
7:6
6:5
E
5:4
F
4:3
10:7
G
3:2
8:5
A
5:3
12:7
B
7:4
C
2:1
Max3
C
1:1
8:7
D
7:6
6:5
E
5:4
F
4:3
7:5
G
10:7
3:2
A
8:5
5:3
B
12:7
C
2:1
Max4
C
1:1
7:6
D
6:5
5:4
E
4:3
F
7:5
10:7
G
3:2
8:5
A
5:3
12:7
B
7:4
C
2:1
Max5
C
1:1
8:7
D
7:6
6:5
E
5:4
F
4:3
7:5
G
10:7
3:2
A
5:3
12:7
B
7:4
C
2:1
Max6
C
1:1
8:7
D
7:6
6:5
E
4:3
F
7:5
10:7
G
3:2
8:5
A
5:3
12:7
B
7:4
C
2:1
Marcel de Velde
A 2.3.5.19 subgroup scale.
C
D
E
F
G
A
B
C
1:1
19:18
9:8
19:16
5:4
4:3
45:32
3:2
19:12
27:16
16:9
15:8
2:1
Meantone scale
Equal beating 5/4 = 3/2 opposite. Almost 1/5 Pythagorean. Gottfried Keller (1707).
C
D
E
F
G
A
B
C
0
80.94883
194.55381
308.16479
389.11362
502.72160
583.67043
697.27840
778.22724
891.83521
1005.44319
1086.39202
1200
Middle Eastern/blues scale
This scale is based on the number 18.
C
D
E
F
G
A
B
C
1:1
19:18
10:9
7:6
11:9
4:3
17:12
3:2
19:12
5:3
7:4
11:6
2:1
Mohajira to Slendro
From Moharija to Aeolian and Slendros.
C
D
E
F
G
A
B
C
1:1
21:20
9:8
6:5
49:40
4:3
7:5
3:2
8:5
49:30
9:5
11:6
2:1
Neidhart (1732) Pythagorean
The fifth C-G is too narrow by a Pythagorean comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
180.44999
294.135
384.36
498.045
588.27
678.49499
792.18
882.045
996.09
1086.315
1200
Neidhart (1732) 5th circle #2
The fifths Eb-Bb, G-D and B-F# are too narrow by 1/12 of the Pythagorean comma, the other
fifths are one-sixth too narrow.
C
D
E
F
G
A
B
C
0
101.955
203.91
298.045
400
498.045
603.91
698.045
800
901.955
1003.91
1098.045
1200
Neidhart (1732) 5th circle #3
The fifths Eb-Bb, F-C, G-D, A-E, B-F# and C#-G# are too narrow by a sixth of the Pythagorean
comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
101.955
200
301.955
400
501.955
600
701.955
800
901.955
1000
1001.955
1200
Neidhart (1732) 5th circle #4
The fifths Eb-Bb, C-G, A-E and F#-C# are too narrow by a quarter of the Pythagorean comma,
the other fifths are perfect.
C
D
E
F
G
A
B
C
0
96.09
198.045
300
398.045
498.045
600
696.09
798.045
900
996.09
1098.045
1200
Neidhart (1732) 5th circle #5
The fifth G#-D# is perfect, F-C, D-A and B-F# are too narrow by 1/12 Pythagorean comma, the
other fifths are one-sixth too narrow.
C
D
E
F
G
A
B
C
0
100
200
301.955
401.955
501.955
600
700
800
898.045
1001.955
1101.955
1200
Neidhart (1732) 5th circle #6
The fifths Eb-Bb, C-G, A-E and F#-C# are too narrow by a sixth of the Pythagorean comma, BbF, G-D, E-B and C#-F# are one-quarter too narrow, F-C, D-A, B-F# and G#-D# are one-sixth too
wide.
C
D
E
F
G
A
B
C
0
100
196.09
300
400
496.09
600
700
796.09
900
1000
1096.09
1200
Neidhart (1732) 5th circle #7
The fifth G#-D# is too narrow by 1/12 of the Pythagorean comma, Eb-Bb, Bb-F, G-D, D-A, E-B
and B-F# are 1/6 too narrow, C-G is one-quarter too narrow, F-C, A-E and C#-G# are one-sixth too
wide.
C
D
E
F
G
A
B
C
0
98.045
194.135
298.045
398.045
494.135
594.135
696.09
796.09
898.045
996.09
1096.09
1200
Neidhart (1732) 5th circle #8 (Big City)
The fifths Bb-F, F-C, A-E, B-F# and F#-C# are too narrow by 1/12 of the Pythagorean comma,
C-G, G-D and D-A are one-sixth too narrow, Eb-Bb, E-B and G#-D# are perfect.
C
D
E
F
G
A
B
C
0
96.09
196.09
298.045
394.135
500
594.135
698.045
796.09
894.135
1000
1096.09
1200
Neidhart (1732) 5th circle #9
The fifths C-G, E-B and G#-D# are too narrow by 1/12 of the Pythagorean comma, Eb-Bb, G-D
and B-F# are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
196.09
300
400
500
596.09
700
800
898.045
996.09
1100
1200
Neidhart (1732) 5th circle #10
The fifths Eb-Bb, A-E and F#-C# are too narrow by a sixth of the Pythagorean comma, C-G and
D-A are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
198.045
298.045
392.18
198.045
598.045
696.09
796.09
894.135
996.09
1094.135
1200
Neidhart (1732) 5th circle #11
The fifths G-D and F#-C# are too narrow by a sixth of the Pythagorean comma, D-A and G#-D#
are one-quarter too narrow, the other fifths are 1/12 too narrow.
C
D
E
F
G
A
B
C
0
96.09
198.045
296.09
394.135
500
598.045
700
800
894.135
996.09
1098.045
1200
Neidhart (1732) 5th circle #12
The fifths C-G and F#-C# are too narrow by 1/12 of the Pythagorean comma, G-D and C#-G#
are one-sixth too narrow, Eb-Bb and A-E are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
98.045
198.045
300
396.09
498.045
600
700
798.045
900
996.09
1098.045
1200
Neidhart (1732) example #1 for chapter 7 (before 3 rd-circles)
The fifths F-C and A-E are too narrow by a Pythagorean comma, the fifth C#-G# is too wide by
a Pythagorean comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
203.91
317.59501
384.35999
521.50501
588.26999
701.95
815.64001
905.865
1019.55001
1086.31499
1200
Neidhart (1732) example #2 for chapter 7 (before 3 rd-circles)
The fifths Eb-Bb, F-C and F#-C# are too narrow by 1/12 of the Pythagorean comma, C-G is
one-sixth too narrow, G-D, D-A and A-E are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
194.135
294.135
386.31499
496.09
590.225
698.045
792.18
890.225
994.135
1088.26999
1200
Neidhart (1732) example #3 for chapter 7 (before 3 rd-circles)
The fifths Eb-Bb and F#-C# are too narrow by 1/12 of the Pythagorean comma, C-G and G-D
are one-sixth too narrow, D-A and A-E are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
92.18
196.09
292.18
388.27
498.045
592.18
698.045
788.26999
892.18
999.09
1090.225
1200
Neidhart (1732) 3rd-circle #1 (Village)
The fifths Bb-F, C-G, B-F# and C#-G# are too narrow by 1/12 of the Pythagorean comma, G-D
is one-sixth too narrow, D-A and A-E are one-quarter too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
198.045
296.09
390.225
498.045
592.18
700
788.26999
888.26999
998.045
1092.18
1200
Neidhart (1732) 3rd-circle #2 (Small City)
The fifths Eb-Bb, E-B, B-F# and G#-D# are too narrow by 1/12 of the Pythagorean comma, CG, G-D and D-A are one-sixth too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
196.09
296.09
392.18
498.045
592.18
698.045
796.09
894.135
996.09
1092.18
1200
Neidhart (1732) 3rd-circle #3
The fifths F-C, D-A, C#-G# and G#-D# are too narrow by 1/12 of the Pythagorean comma, the
other fifths are one-sixth too narrow.
C
D
E
F
G
A
B
C
0
96.09
196.09
296.09
394.135
500
598.045
698.045
796.09
896.09
1001.955
1092.18
1200
Neidhart (1732) 3rd-circle #4
The fifths Eb-Bb, F#-C# and C#-G# are too narrow by 1/12 of the Pythagorean comma, Bb-F, CG, G-D, D-A and E-B are one-sixth too narrow, F-C, A-E and B-F# are perfect.
C
D
E
F
G
A
B
C
0
96.09
196.09
296.09
396.09
498.045
596.09
698.045
796.09
894.135
1000
1094.135
1200
Neidhart (1732) 3rd-circle #5
The fifths F-C and A-E are too narrow by a sixth of the Pythagorean comma, Bb-F and F#-C#
are perfect, the other fifths are 1/12 too narrow.
C
D
E
F
G
A
B
C
0
100
200
300
398.045
501.955
598.045
700
800
900
1000
1098.045
1200
No fives
A no-fives seven-limit Fokker block, discovered by Gene Ward Smith.
C
D
E
F
G
A
B
C
1:1
28:27
9:8
7:6
9:7
4:3
49:36
3:2
14:9
12:7
7:4
49:27
2:1
Öljare
Mats Öljare, scale for Tampere (2001).
C
D
E
F
G
A
B
C
1:1
35:32
7:6
5:4
4:3
35:24
3:2
14:9
5:3
7:4
15:8
35:18
2:1
Omaha
A 2.3.11 subgroup scale.
C
D
E
F
G
A
B
C
1:1
12:11
9:8
32:27
11:9
4:3
11:8
3:2
18:11
27:16
16:9
11:6
2:1
Omaha temperament
243:242 tempered Omaha 2.3.11 scale.
C
D
E
F
G
A
B
C
0
148.42105
202.10526
296.84211
350.52632
498.94737
552.63158
701.05263
849.47368
903.15789
997.89474
1051.57895
1200
Optimal well-temperament #1
C
0
102.0
D
203.8
297.2
E
396.3
F
498.1
600
G
702
803.8
A
897.2
996.3
B
1098.1
C
1200
Optimal well-temperament #2
C
0
93.1
D
203.1
296.3
E
397.4
F
498.5
591.7
G
701.6
794.8
A
903.4
997.4
B
1091.4
C
1200
Otones 12-24 (a/k/a harm24)
A dedecatonic scale borrowed from the overtone series.
C
D
E
F
G
A
B
C
1:1
13:12
7:6
5:4
4:3
17:12
3:2
19:12
5:3
7:4
11:6
23:12
2:1
Pajara
C
0
107.04769
D
214.09538
278.85693
E
385.90462
F
492.95231
600
G
707.04769
814.09538
A
878.85693
985.90462
B
1092.95231
C
1200
PBP (procentual beating pitch) temperament
Described in the paper Bach- and Well-Temperaments for Western Classical Music, available
for free from the website http://lit.gfax.ch//tunings/BachAndWellTemperaments.pdf.
C
D
E
F
G
A
B
C
0
90.225
195.25271
294.135
386.87185
498.045
588.26999
699.44315
792.18
891.06228
996.09
1086.31499
1200
Piagui
C
0
99.02
D
198.04
297.07
E
396.09
F
498.04
600
G
699.02
798.04
A
897.07
996.09
B
1098.05
C
1200
Portsmouth
A 2.3.7.11 subgroup scale.
C
D
E
F
G
A
B
C
1:1
22:21
8:7
7:6
9:7
4:3
11:8
3:2
11:7
12:7
7:4
11:6
2:1
Pre-Arcytas
Pre-Arcytas transversal Hobbit tuning by Gene Ward Smith.
C
D
E
F
G
A
B
C
1:1
16:15
9:8
6:5
5:4
4:3
64:45
3:2
8:5
5:3
16:9
15:8
2:1
Pris
Optimized (15:14)^3 (16:15)^3 (21:20)^3 (25:24)^3 scale.
C
D
E
F
G
A
B
C
1:1
16:15
28:25
7:6
5:4
4:3
7:5
3:2
8:5
5:3
7:4
28:15
2:1
Prism
Prism by Carl Lumma.
C
D
E
F
G
A
B
C
1:1
16:15
28:25
7:6
5:4
4:3
7:5
112:75
8:5
5:3
7:4
28:15
2:1
Ptolex
John Lyle Smith's extended septimal Ptolemy.
C
D
E
F
G
A
B
C
1:1
21:20
9:8
7:6
9:7
4:3
10:7
3:2
63:40
27:16
7:4
27:14
2:1
Ratwolf (a/k/a rational wolf)
This is a version of meantone which tries its hardest to circulate.
C
D
E
F
G
A
B
C
0
70.86342
191.67526
312.48711
383.35053
504.16237
575.02579
695.83763
766.70106
887.5129
1008.32474
1079.18816
1200
Rectoo
Hahn-reduced circle of fifths scale.
C
D
E
F
G
A
B
C
1:1
10:9
8:7
6:5
5:4
4:3
3:2
25:16
8:5
5:3
7:4
9:5
2:1
Riley/Rosary
Terry Riley, tuning for Cactus Rosary (1993).
C
D
E
F
G
A
B
C
1:1
49:48
9:8
7:6
5:4
21:16
11:8
3:2
49:32
13:8
7:4
15:8
2:1
Sa-grama
This tuning sets the absolute tuning at a' equals 441Hz, which is the equivalent of tuning the
tone scale 3.9301584394¢ higher than at 440Hz.
C
D
E
F
G
A
B
C
1:1 (0)
1.5:√2 (101.955)
9:8 (203.91)
6:5 (315.64129)
5:4 (386.31371)
4:3 (498.045)
45:32 (590.22372)
3:2 (701.955)
8:5 (813.68629)
27:16 (905.865)
9:5 (1017.59629)
15:8 (1088.26871)
2:1 (1200)
Schisdia 32805:32768 2048:2025 scale
C
1:1
256:243
D
10:9
32:27
E
5:4
F
4:3
45:32
G
16384:10935
128:81
A
5:3
16:9
B
15:8
C
2:1
Secor 5/23 TX
George Secor's synchronous 5/23-comma temperament extraordinaire.
C
D
E
F
G
A
B
C
1:1
62:59
66:59
70:59
591:472
631:472
331:236
353:236
745:472
395:236
631:354
221:118
2:1
Septimal optimal well-temperament #1
C
0
42
D
206
272
E
386
F
491
543
G
704
764
A
877
977
B
1090
C
1200
Septimal optimal well-temperament #2
C
0
93
D
209
262
E
386
F
490
588
G
707
769
A
876
978
B
1093
C
1200
Serafini 11
Carlo Serafini, scale of Piano 11.
C
D
E
F
G
A
B
C
1:1
11:10
9:8
7:6
5:4
11:8
10:7
3:2
8:5
5:3
7:4
20:11
2:1
Sevish
Sean “Sevish” Archibald's Trapped in a Cycle scale.
C
D
E
F
G
A
B
C
1:1
33:32
9:8
7:6
5:4
21:16
11:8
3:2
77:48
5:3
27:16
7:4
2:1
Sonbirkez sorted
Sonbirkez Huzzam scale.
C
D
E
F
G
A
B
C
1:1
121:108
847:720
57:46
4:3
3:2
8:5
81:50
64:39
121:72
847:480
171:92
2:1
Sorge (1744)
The fifths Eb-Bb, Bb-F, B-F# and F#-C# are too narrow by 1/12 of the Pythagorean comma, CG, G-D and D-A are one-sixth too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
94.135
196.09
298.045
396.09
498.045
594.135
698.045
796.09
894.135
998.045
1094.135
1200
Sparschuh (2005) proportional beating “Bach”
The fifth Eb-Bb is too narrow by 46TU, Bb-F is 122TU too narrow, F-C is 82TU too narrow, C-G
is 55TU too narrow, G-D is 36TU too narrow, D-A is 81TU too narrow, A-E is 86TU too narrow, E-B is
58TU too narrow, B-F# is 154TU too narrow, the other fifths are perfect.
This tuning sets the absolute tuning a' equals 410Hz, which is the equivalent of tuning the tone
scale 122.2555368231¢ lower than at 440Hz.
C
D
E
F
G
A
B
C
0
100.1955
196.18775
300.48875
395.95966
501.173
599.86967
697.32817
799.96742
894.00466
1000.48875
1097.91467
1200
Sparschuh's 5-limit dodecatonics with two Kirnberger fifths
C
1:1
256:243
D
262144:234375
32:27
E
5:4
F
4:3
1024:729
G
16384:10935
128:81
A
78125:46656
16:9
B
4096:2187
C
2:1
Sparschuh-Zapf
The fifth Eb-Bb is too narrow by 46TU, Bb-F is 122TU too narrow, F-C is 82TU too narrow, C-G
is 55TU too narrow, G-D is 36TU too narrow, D-A is 81TU too narrow, A-E is 86TU too narrow, E-B is
58TU too narrow, B-F# is 154TU too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
100.1955
196.18775
300.48875
395.95966
501.173
599.86967
697.32817
799.96742
894.00466
1000.48875
1097.91467
1200
Steel
An 11-limit tuning discovered by Lou Harrison and Bill Slye.
C
D
E
F
G
A
B
C
1:1
28:27
9:8
7:6
5:4
4:3
11:8
3:2
14:9
5:3
7:4
11:6
2:1
Stelhex
Stellated two of 1 3 5 7 hexany.
C
D
E
F
G
A
B
C
1:1
21:20
7:6
6:5
5:4
21:16
7:5
3:2
8:5
42:25
7:4
9:5
2:1
Stelhex2
Stellated two of 1 3 5 9 hexany.
C
D
E
F
G
A
B
C
1:1
135:128
9:8
5:4
81:64
27:20
45:32
3:2
25:16
5:3
27:16
15:8
2:1
Stelhex5
Stellated two of 1 3 7 9 hexany, stellation is degenerate.
C
D
E
F
G
A
B
C
1:1
9:8
7:6
81:64
21:16
189:128
3:2
49:32
27:16
7:4
27:14
63:32
2:1
Superpyth
C
0
177.77778
D
222.22222
266.66667
E
444.44444
F
488.88889
666.66667
G
711.11111
755.55556
A
933.33333
977.77778
B
1155.55556
C
1200
Terrain
Just-intonation version of generation scale for 63:50 and 10:9.
C
D
E
F
G
A
B
C
1:1
50:49
10:9
500:441
63:50
9:7
7:5
10:7
100:63
81:50
441:250
9:5
2:1
Unimajor
A 2.3.11:7 subgroup scale.
C
D
E
F
G
A
B
C
1:1
22:21
9:8
32:27
14:11
4:3
63:44
3:2
11:7
27:16
16:9
21:11
2:1
Unimajor penta
Pentacircle (896:891) tempered unimajor.
C
D
E
F
G
A
B
C
0
78.76448
208.49421
287.25869
416.98842
495.7529
625.48263
704.2471
783.01158
912.74131
991.50579
1121.23352
1200
Venturino/Interbartolo
The fifths Eb-Bb, C#-G# and G#-D# are too wide by 7/132 of the syntonic comma, F-C, C-G, GD, D-A and A-E are ¼ too narrow, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
92.17953
193.15709
298.37074
386.31418
503.42146
608.77559
696.57854
804.72487
889.73563
1001.46634
1088.2693
1200
Venturino/Interbartolo (2005)
The fifths F-C, C-G, G-D, D-A and A-E are too narrow by a quarter of the syntonic comma, EbBb, C#-G# and G#-D# are 1/12 too wide, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
192.18
298.045
384.35999
503.91
588.26999
696.09
794.135
888.26999
1001.955
1086.31499
1200
Vogel
Vogel's reconstruction of Scheidermann/Praetorius.
C
D
E
F
G
A
B
C
0
86.80214
193.15686
288.75843
391.69029
498.045
584.84714
696.57843
783.38057
895.11186
996.09
1088.26871
1200
Wendy Carlos harmonic scale
C
1:1
17:16
D
9:8
19:16
E
5:4
F
21:16
11:8
G
3:2
13:8
A
27:16
7:4
B
15:8
C
2:1
Wendy Carlos super just intonation
C
1:1
17:16
D
9:8
6:5
E
5:4
F
4:3
11:8
G
3:2
13:8
A
5:3
7:4
B
15:8
C
2:1
Wilson class
C
1:1
25:24
D
28:25
7:6
E
5:4
F
4:3
7:5
G
35:24
8:5
A
5:3
7:4
B
28:15
C
2:1
Wilsonistic
Margo Schulter's Wilsonistic Pivot on C.
C
D
E
F
G
A
B
C
1:1
91:88
44:39
7:6
14:11
4:3
11:8
3:2
273:176
22:13
7:4
21:11
2:1
Young 2
The fifths C-G, G-D, D-A, A-E, E-B and B-F# are too narrow by a sixth of the Pythagorean
comma, the other fifths are perfect.
C
D
E
F
G
A
B
C
0
90.225
196.09
294.135
392.18
498.045
588.27
698.045
792.18
894.135
996.09
1090.225
1200