List of just intonation intervals

From XenReference
(Redirected from List of just ratios)

This is a list of just intervals, similar to the list of EDOs and the list of regular temperaments. It exists to compile information on a number of just intonation intervals.

Commas should not redirect here! They should instead redirect to their corresponding entry on the temperament page, or if present, a page for the temperament itself.

The formula for "good edos" is the edos that satisfy, for interval x in cents and edo n:
abs(round(xn/1200)-xn/1200)*sqrt(12/n)<(1/16) for n < or equal to 31
abs(round(xn/1200)-xn/1200)*((n^2)/1024)*sqrt(12/31)<(1/16) for n > 31

EDOs below 5 are excluded.

3-limit

(MOS) diatonic intervals
Fifthspan Ratio Cents Good edos Name Notes
-7 4096/2187 1086.3 10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190 Diatonic diminished octave
-6 1024/729 588.3 47, 49, 51, 53, 102 Diatonic diminished fifth Found in a diminished triad. A stack of two diatonic minor thirds
-5 256/243 90.2 13, 14, 26, 27, 40, 53, 80, 93, 133, 306 Diatonic semitone Small step of the diatonic scale. See Blackwood temperament.
-4 128/81 792.2 6, 44, 47, 50, 53, 56, 103 Diatonic minor sixth
-3 32/27 294.1 8, 12, 33, 37, 41, 45, 49, 53, 57, 102 Diatonic minor third Middle interval in a Pythagorean minor chord
-2 16/9 996.1 6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153 Diatonic minor seventh
-1 4/3 498 12, 17, 24, 29, 36, 41, 53, 94, 200 Perfect fourth
0 1/1 0 (All) Perfect unison Represents a multiplication by 1, i.e. no change in pitch
+1 3/2 702 12, 17, 24, 29, 36, 41, 53, 94, 200 Perfect fifth Generator of Pythagorean tuning, most consonant interval within the octave after 2/1 itself
+2 9/8 203.9 6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153 Diatonic major second Large step of the diatonic scale.
+3 27/16 905.9 8, 12, 33, 37, 41, 45, 49, 53, 57, 102 Diatonic major sixth
+4 81/64 407.8 6, 44, 47, 50, 53, 56, 103 Diatonic major third Middle interval in a Pythagorean major chord
+5 243/128 1109.8 13, 14, 26, 27, 40, 53, 80, 93, 133, 306 Diatonic major seventh
+6 729/512 611.7 47, 49, 51, 53, 102 Diatonic augmented fourth Stack of 3 tones (tritone)
+7 2187/2048 113.7 10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190 Chromatic semitone Chroma of the diatonic scale. See Whitewood temperament.

5-limit

Ratio Cents Good edos Name Notes
128/125 41.1 27, 28, 29, 30, 31, 32, 58, 59, 117, 146, 292 augmented diesis See Augmented temperament.
25/24 70.7 16, 17, 18, 33, 34, 35, 51, 68, 85, 102 classical chromatic semitone See Interclassical temperament.
135/128 92.2 13, 25, 26, 27, 39, 52, 65, 78, 91, 104 major chroma See Mavila temperament.
16/15 111.7 11, 21, 22, 32, 33, 43, 54, 86 classical diatonic semitone
27/25 133.2 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 acute minor second
10/9 182.4 13, 20, 26, 33, 46, 79, 125, 250 grave whole tone
75/64 274.6 13, 22, 26, 31, 35, 48, 70, 83, 118 classical subminor third Also an augmented second.
6/5 315.6 15, 19, 23, 34, 38, 42, 57, 76 classical minor third
5/4 386.3 22, 25, 28, 31, 34, 56, 59, 87, 146, 292 classical major third
32/25 427.4 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 classical supermajor third Also a diminished fourth.
27/20 519.6 7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194 acute fourth
45/32 590.2 59, 61, 63, 122 classical narrow tritone
64/45 609.8 59, 61, 63, 122 classical wide tritone
40/27 680.4 7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194 grave fifth
25/16 772.6 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 classical subminor sixth
8/5 813.7 22, 25, 28, 31, 34, 56, 59, 87, 146, 292 classical minor sixth
5/3 884.4 15, 19, 23, 34, 38, 42, 57, 76 classical major sixth
128/75 925.4 13, 22, 26, 31, 35, 48, 70, 83, 118 classical supermajor sixth
9/5 1017.6 13, 20, 26, 33, 46, 79, 125, 250 acute minor seventh

7-limit

2.3.7

Ratio Cents Good edos Name Notes
49/48 35.7 31, 32, 33, 34, 35, 36, 67, 101, 168 interseptimal diesis See Semaphore temperament.
28/27 63 18, 19, 20, 37, 38, 39, 57, 76 septimal subminor second See Trienstonic temperament.
8/7 231.2 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 septimal supermajor second
7/6 266.9 9, 18, 27, 36, 45, 54, 63, 72 septimal subminor third
9/7 435.1 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal supermajor third
21/16 470.8 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal subfourth
32/21 729.2 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal superfifth
14/9 764.9 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal subminor sixth
12/7 933.1 9, 18, 27, 36, 45, 54, 63, 72 septimal supermajor sixth
7/4 968.8 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 harmonic seventh
27/14 1137 18, 19, 20, 37, 38, 39, 57, 76 septimal supermajor seventh

2...7

Ratio Cents Good edos Name Notes
36/35 48.8 23, 24, 25, 26, 49, 50, 74, 123 famity, septimal quartertone See Mint temperament
21/20 84.5 14, 15, 28, 29, 42, 43, 57, 71, 142, 213 septimal narrow limma
15/14 119.4 10, 20, 30, 31, 40, 50, 201 septimal wide chroma
35/32 155.1 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 septimal neutral second
28/25 196.2 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 septimal narrow whole tone
60/49 350.6 7, 17, 24, 31, 34, 41, 48, 65, 89 septimal artoneutral third
49/40 351.3 17, 24, 31, 34, 41, 58, 82 septimal tendoneutral third
63/50 400.1 6, 9, 12, 15, 18, ... 99, 102, 105 septimal narrow major third
35/27 449.3 8, 16, 24, 32, 40, 48, 56, 211 septimal ultramajor third
64/49 462.3 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 septimal tendo third
48/35 546.8 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 septimal neutral fourth
7/5 582.5 29, 31, 33, 35, 37, 68, 70, 103 septimal narrow tritone
10/7 617.5 29, 31, 33, 35, 37, 68, 70, 103 septimal wide tritone
35/24 653.2 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 septimal neutral fifth
49/32 737.7 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 septimal arto sixth
54/35 750.7 8, 16, 24, 32, 40, 48, 56, 211 septimal inframinor sixth
100/63 799.9 6, 9, 12, 15, 18, ... 99, 102, 105 septimal wide minor sixth
25/14 1003.8 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 septimal wide minor seventh
64/35 1044.9 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 septimal neutral seventh
35/18 1151.2 23, 24, 25, 26, 49, 50, 74, 123 septimal ultramajor seventh

11-limit

2.3.5.11

Ratio Cents Good edos Name Notes
11/8 551.3 11, 13, 24, 26, 35, 37, 50, 61, 74, 111 undecimal ultrafourth
11/9 347.4 7, 14, 21, 24, 31, 38, 45, 76, 114, 152 undecimal artoneutral third
11/10 165 7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240 undecimal submajor second
11/6 1049.4 8, 16, 24, 32, 40, 48, 56, 247 undecimal neutral seventh
12/11 150.6 8, 16, 24, 32, 40, 48, 56, 247 undecimal neutral second
16/11 648.7 11, 13, 24, 26, 35, 37, 50, 61, 74, 111 undecimal infrafifth
18/11 852.6 7, 14, 21, 24, 31, 38, 45, 76, 114, 152 undecimal tendoneutral sixth
20/11 1035 7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240 undecimal supraminor seventh
27/22 354.5 10, 17, 27, 34, 37, 44, 61, 88, 132 undecimal neutral third
22/15 663 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 undecimal subfifth
15/11 537 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 undecimal superfourth
33/32 53.3 21, 22, 23, 24, 44, 45, 46, 68, 90, 135 undecimal quartertone
33/25 480.6 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 undecimal subfourth
33/20 867 11, 18, 25, 29, 36, 47, 54, 191 undecimal submajor sixth
44/27 845.5 10, 17, 27, 34, 37, 44, 61, 88, 132 undecimal artoneutral sixth
25/22 221.3 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 undecimal supermajor second
44/25 978.7 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 undecimal subminor seventh
55/54 31.8 35, 36, 37, 38, 39, 40, 75, 76, 113, 151 undecimal diesis See Eleventyfive temperament.

2...11

Ratio Cents Good edos Name Notes
44/35 396.2 6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106 valinorsmic narrow major third
66/35 1098.1 12, 23, 24, 35, 36, 47, 59, 106 undecimal major seventh
35/33 101.9 12, 23, 24, 35, 36, 47, 59, 106 undecimal semitone
33/28 284.4 17, 21, 25, 34, 38, 42, 59, 76, 135, 173 undecimal neominor third
21/11 1119.5 14, 15, 29, 30, 31, 44, 45, 60, 149, 164 undecimal neomajor seventh
22/21 80.5 14, 15, 29, 30, 31, 44, 45, 60, 149, 164 undecimal neominor second
14/11 417.5 20, 23, 26, 29, 43, 46, 69, 92 undecimal neomajor third
11/7 782.5 20, 23, 26, 29, 43, 46, 69, 92 undecimal neominor sixth

13-limit

2...7.13

Ratio Cents Good edos Name Notes
27/26 65.3 18, 19, 36, 37, 38, 55, 92, 147 small tridecimal subminor second
26/25 67.9 17, 18, 19, 34, 35, 36, 53, 71, 106, 159 large tridecimal subminor second
14/13 128.3 9, 18, 19, 28, 37, 38, 47, 56, 159 small tridecimal supraminor second
13/12 138.6 9, 17, 26, 34, 35, 43, 52, 78 large tridecimal supraminor second
39/35 187.3 13, 19, 26, 32, 38, 45, 64, 173 tridecimal major second
224/195 240 5, 10, 15 ... 150, 155, 160 tridecimal supermajor second
15/13 247.7 5, 19, 24, 29, 34, 39, 58, 63, 92, 218 tridecimal inframinor third
39/32 342.5 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal artoneutral third
16/13 359.5 10, 20, 27, 30, 40, 50, 60, 237 tridecimal tendoneutral third
26/21 369.7 13, 16, 23, 26, 29, 39, 52, 198 tridecimal submajor third
13/10 454.2 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 tridecimal ultramajor third
35/26 514.6 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal wide fourth
18/13 563.4 15, 17, 30, 32, 34, 49, 66, 115, 164 tridecimal ultrafourth
128/91 590.6 61, 63, 65, 128 tridecimal narrow tritone
91/64 609.4 61, 63, 65, 128 tridecimal wide tritone
13/9 636.6 15, 17, 30, 32, 34, 49, 66, 115, 164 tridecimal infrafifth
52/35 685.4 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal narrow fifth
20/13 745.8 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 tridecimal inframinor sixth
21/13 830.3 13, 16, 23, 26, 29, 39, 52, 198 tridecimal supraminor sixth
13/8 840.5 10, 20, 27, 30, 40, 50, 60, 237 tridecimal artoneutral sixth
64/39 857.5 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal tendoneutral sixth
26/15 952.3 5, 19, 24, 29, 34, 39, 58, 63, 92, 218 tridecimal ultramajor sixth
195/112 960 5, 10, 15 ... 150, 155, 160 tridecimal subminor seventh
70/39 1012.7 13, 19, 26, 32, 38, 45, 64, 173 tridecimal minor seventh
24/13 1061.4 9, 17, 26, 34, 35, 43, 52, 78 small tridecimal submajor seventh
13/7 1071.7 9, 18, 19, 28, 37, 38, 47, 56, 159 large tridecimal submajor seventh
25/13 1132.1 17, 18, 19, 34, 35, 36, 53, 71, 106, 159 small tridecimal supermajor seventh
52/27 1134.7 18, 19, 36, 37, 38, 55, 92, 147 large tridecimal supermajor seventh

2...13

Ratio Cents Good edos Name Notes
13/11 289.2 21, 25, 29, 33, 54, 58, 83, 112 tridecimal neominor third
33/26 412.7 26, 29, 32, 35, 38, 61, 64, 189 tridecimal neomajor third
117/88 493.1 17, 22, 29, 34, 39, 56, 73 small tridecimal narrow fourth
121/91 493.3 17, 22, 29, 34, 39, 51, 56, 73, 90 large tridecimal narrow fourth
55/39 595.1 6, 8, 10, 12, 14, 16, 18, 121, 123 small gassormic tritone
78/55 604.9 6, 8, 10, 12, 14, 16, 18, 121, 123 large gassormic tritone
182/121 706.7 17, 22, 29, 34, 39, 51, 56, 73, 90 small tridecimal wide fifth
176/117 706.9 17, 22, 29, 34, 39, 56, 73 large tridecimal wide fifth
52/33 787.3 26, 29, 32, 35, 38, 61, 64, 189 tridecimal neominor sixth
22/13 910.8 21, 25, 29, 33, 54, 58, 83, 112 tridecimal neomajor sixth

Higher limits

2...17

Ratio Cents Good edos Name Notes
34/33 51.7 22, 23, 24, 25, 46, 47, 70, 93, 116 large septendecimal quartertone
68/65 78.1 15, 16, 30, 31, 32, 46, 77, 123, 169 septendecimal third-tone
18/17 99 12, 24, 25, 36, 37, 48, 49, 85, 97, 109 small septendecimal semitone
17/16 105 11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240 large septendecimal semitone
17/15 216.7 11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144 septendecimal neomajor second
20/17 281.4 13, 17, 21, 30, 34, 47, 64, 81, 145 septendecimal neominor third
289/243 300.1 8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104 septendecimal minor third
17/14 336.1 7, 18, 25, 32, 43, 50, 75, 100 septendecimal supraminor third
21/17 365.8 10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269 septendecimal submajor third
34/27 399.1 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51 septendecimal major third
22/17 446.4 8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250 septendecimal ultramajor third
17/13 464.4 13, 18, 26, 31, 36, 44, 49, 62, 93 septendecimal subfourth
85/64 491.3 17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276 septendecimal narrow fourth
34/25 532.3 9, 18, 25, 27, 34, 36, 45, 124, 133, 257 septendecimal superfourth
24/17 597 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201 small septendecimal tritone
17/12 603 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201 large septendecimal tritone
25/17 667.7 9, 18, 25, 27, 34, 36, 45, 124, 133, 257 septendecimal subfifth
128/85 708.7 17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276 septendecimal wide fifth
26/17 735.6 13, 18, 26, 31, 36, 44, 49, 62, 93 septendecimal superfifth
17/11 753.6 8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250 septendecimal inframinor sixth
27/17 800.9 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51 septendecimal minor sixth
34/21 834.2 10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269 septendecimal supraminor sixth
28/17 863.9 7, 18, 25, 32, 43, 50, 75, 100 septendecimal submajor sixth
486/289 899.9 8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104 septendecimal major sixth
17/10 918.6 13, 17, 21, 30, 34, 47, 64, 81, 145 septendecimal neomajor sixth
30/17 983.3 11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144 septendecimal neominor seventh
32/17 1095 11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240 small septendecimal major seventh
17/9 1101 12, 24, 25, 36, 37, 48, 49, 85, 97, 109 large septendecimal major seventh
65/34 1121.9 15, 16, 30, 31, 32, 46, 77, 123, 169 septendecimal supermajor seventh
33/17 1148.3 22, 23, 24, 25, 46, 47, 70, 93, 116 small septendecimal ultramajor seventh

2...19

Ratio Cents Good edos Name Notes
20/19 88.8 13, 14, 26, 27, 28, 40, 41, 54, 81, 108
19/18 93.6 13, 25, 26, 38, 39, 51, 64, 77, 141
21/19 173.3 7, 14, 21, 28, 35, 83, 90, 97
19/17 192.6 6, 19, 25, 31, 37, 50, 56, 81, 162, 243
64/57 200.5 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
57/50 226.8 16, 21, 26, 32, 37, 53, 74, 90, 127, 291
22/19 253.8 14, 19, 24, 28, 33, 38, 52, 71, 104
45/38 292.7 8, 29, 33, 37, 41, 45, 82, 123, 164 small undevicesimal minor third
19/16 297.5 8, 12, 16, 20, 24, 28, 32, 36, 117, 121 large undevicesimal minor third
24/19 404.4 6, 9, 12, 15, 18, 21, 24, 89, 92, 181, 273 small undevicesimal major third
19/15 409.2 32, 35, 38, 41, 44, 47, 88, 261 large undevicesimal major third
25/19 475.1 5, 10, 15, 28, 33, 38, 43, 48, 53, 96, 245
95/72 479.9 5, 10, 15 ... 90, 95, 100, 105
171/128 501.4 12, 19, 24, 31, 36, 43, 55, 67, 79, 146, 213
432/323 503.4 12, 19, 24, 31, 38, 43, 50, 62
128/95 516.2 7, 14, 21, 28, 30, 35, 86, 93, 179
19/14 528.7 9, 16, 18, 25, 32, 34, 43, 50, 59, 84, 143, 202
26/19 543 11, 20, 22, 31, 33, 42, 53, 84, 179
38/27 591.6 6, 69, 71, 73
27/19 608.4 6, 69, 71, 73
19/13 657 11, 20, 22, 31, 33, 42, 53, 84, 179
28/19 671.3 9, 16, 18, 25, 32, 34, 43, 50, 59, 84, 143, 202
95/64 683.8 7, 14, 21, 28, 30, 35, 86, 93, 179
323/216 696.6 12, 19, 24, 31, 38, 43, 50, 62
256/171 698.6 12, 19, 24, 31, 36, 43, 55, 67, 79, 146, 213
144/95 720.1 5, 10, 15 ... 90, 95, 100, 105
38/25 724.9 5, 10, 15, 28, 33, 38, 43, 48, 53, 96, 245
30/19 790.8 32, 35, 38, 41, 44, 47, 88, 261
19/12 795.6 6, 9, 12, 15, 18, 21, 24, 89, 92, 181, 273
32/19 902.5 8, 12, 16, 20, 24, 28, 32, 36, 117, 121
76/45 907.3 8, 29, 33, 37, 41, 45, 82, 123, 164
19/11 946.2 14, 19, 24, 28, 33, 38, 52, 71, 104
100/57 973.2 16, 21, 26, 32, 37, 53, 74, 90, 127, 291
57/32 999.5 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
34/19 1007.4 6, 19, 25, 31, 37, 50, 56, 81, 162, 243
38/21 1026.7 7, 14, 21, 28, 35, 83, 90, 97
36/19 1106.4 13, 25, 26, 38, 39, 51, 64, 77, 141
19/10 1111.2 13, 14, 26, 27, 28, 40, 41, 54, 81, 108

2...23

Ratio Cents Good edos Name Notes
24/23 73.7 16, 17, 31, 32, 33, 34, 49, 65, 114
23/22 77 15, 16, 30, 31, 32, 46, 47, 62, 78, 109, 187
25/23 144.4 8, 17, 25, 33, 42, 50, 58, 83, 108, 133, 241
23/21 157.5 8, 15, 23, 30, 31, 38, 46, 61, 99, 160
26/23 212.3 11, 17, 23, 28, 34, 45, 51, 130
23/20 242 5, 10, 15, 20, 25, 30, 35, 119, 124
27/23 277.6 13, 17, 26, 30, 39, 43, 52, 134
23/19 330.8 11, 18, 22, 29, 36, 40, 47, 58, 69, 156, 185
28/23 340.6 7, 14, 21, 28, 32, 35, 67, 74, 81
161/128 397.1 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 136, 139
23/18 424.4 14, 17, 20, 31, 34, 48, 51, 65, 82, 164
30/23 460 13, 21, 26, 34, 39, 47, 60, 73, 120, 180, 240, 300
23/17 523.3 16, 23, 30, 32, 39, 55, 78, 94, 133
32/23 571.7 19, 21, 23, 25, 40, 42, 44, 63, 212
23/16 628.3 19, 21, 23, 25, 40, 42, 44, 63, 212
34/23 676.7 16, 23, 30, 32, 39, 55, 78, 94, 133
23/15 740 13, 21, 26, 34, 39, 47, 60, 73, 120, 180, 240, 300
36/23 775.6 14, 17, 20, 31, 34, 48, 51, 65, 82, 164
256/161 802.9 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 136, 139
23/14 859.4 7, 14, 21, 28, 32, 35, 67, 74, 81
38/23 869.2 11, 18, 22, 29, 36, 40, 47, 58, 69, 156, 185
46/27 922.4 13, 17, 26, 30, 39, 43, 52, 134
40/23 958 5, 10, 15, 20, 25, 30, 35, 119, 124
23/13 987.7 11, 17, 23, 28, 34, 45, 51, 130
42/23 1042.5 8, 15, 23, 30, 31, 38, 46, 61, 99, 160
46/25 1055.6 8, 17, 25, 33, 42, 50, 58, 83, 108, 133, 241
44/23 1123 15, 16, 30, 31, 32, 46, 47, 62, 78, 109, 187
23/12 1126.3 16, 17, 31, 32, 33, 34, 49, 65, 114

2...29

Ratio Cents Good edos Name Notes
32/29 170.4 7, 14, 21, 28, 35, 42, 49, 169
35/29 325.6 11, 22, 26, 33, 37, 48, 59, 70, 129
58/35 874.4 11, 22, 26, 33, 37, 48, 59, 70, 129
29/16 1029.6 7, 14, 21, 28, 35, 42, 49, 169

2...31

Ratio Cents Good edos Name Notes
32/31 55 21, 22, 23, 43, 44, 65, 87, 109, 131, 240
31/24 443.1 8, 19, 27, 30, 35, 38, 46, 65, 130
48/31 756.9 8, 19, 27, 30, 35, 38, 46, 65, 130
31/16 1145 21, 22, 23, 43, 44, 65, 87, 109, 131, 240

Miscellaneous

Ratio Cents Good edos Name Notes
100/97 52.7 21, 22, 23, 24, 45, 46, 68, 91, 114, 296
64/61 83.1 14, 15, 28, 29, 30, 43, 44, 58, 72, 101, 130
78/71 162.8 15, 22, 29, 30, 37, 44, 59, 81, 199
80/71 206.6 6, 17, 23, 29, 35, 41, 58, 64, 93, 122, 151
112/97 248.9 5, 19, 24, 29, 34, 48, 53, 58, 82, 135
97/84 249.1 5, 19, 24, 29, 34, 48, 53, 77, 106
62/53 271.5 9, 13, 18, 22, 31, 35, 40, 44, 53, 84, 137, 221
61/51 310 23, 27, 31, 35, 58, 62, 89, 120, 240
73/60 339.5 7, 14, 21, 25, 28, 32, 39, 46, 53, 60, 99, 152, 205
51/41 377.8 16, 19, 22, 32, 35, 38, 54, 73, 108, 162
71/57 380.2 16, 19, 22, 25, 38, 41, 60, 101, 202, 303
76/61 380.6 19, 22, 25, 38, 41, 44, 63, 82, 268
83/64 450.05 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128
128/97 480.1 5, 10, 15 ... 90, 95, 100, 105
97/64 719.9 5, 10, 15 ... 90, 95, 100, 105
128/83 749.95 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128
122/76 819.4 19, 22, 25, 38, 41, 44, 63, 82, 268
114/71 819.8 16, 19, 22, 25, 38, 41, 60, 101, 202, 303
82/51 822.2 16, 19, 22, 32, 35, 38, 54, 73, 108, 162
120/73 860.5 7, 14, 21, 25, 28, 32, 39, 46, 53, 60, 99, 152, 205
102/61 890 23, 27, 31, 35, 58, 62, 89, 120, 240
53/31 928.5 9, 13, 18, 22, 31, 35, 40, 44, 53, 84, 137, 221
168/97 950.9 5, 19, 24, 29, 34, 48, 53, 77, 106
97/56 951.1 5, 19, 24, 29, 34, 48, 53, 58, 82, 135
71/40 993.4 6, 17, 23, 29, 35, 41, 58, 64, 93, 122, 151
71/39 1037.2 15, 22, 29, 30, 37, 44, 59, 81, 199
61/32 1116.9 14, 15, 28, 29, 30, 43, 44, 58, 72, 101, 130
97/50 1147.3 21, 22, 23, 24, 45, 46, 68, 91, 114, 296
Retrieved from "https://xenreference.com/wiki/index.php?title=List_of_just_intonation_intervals&oldid=2208"