List of just intonation intervals: Difference between revisions

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Created page with " This is a list of just ratios, similar to the list of EDOs and the list of regular temperaments. It exists to compile information on a number of just ratios. '''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. {{Adv|The formula for "good edos" is the edos that satisfy, for interval x in cents and edo n: <br> abs(round(xn/1200)-xn/1200)*..."
 
m →2.3.7: standardize precision
 
(6 intermediate revisions by one other user not shown)
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This is a list of just intervals, similar to the list of [[EDO|EDOs]] and the [[list of regular temperaments]]. It exists to compile information on a number of just intonation intervals.
This is a list of just ratios, similar to the list of [[EDO|EDOs]] and the [[list of regular temperaments]]. It exists to compile information on a number of just ratios.


'''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.
'''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.
Line 39: Line 38:
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
|[[Diatonic semitone]]
|[[Diatonic semitone]]
|Small step of the diatonic scale.
|Small step of the diatonic scale. See [[Blackwood]] temperament.
|-
|-
| -4
| -4
Line 123: Line 122:
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
|[[Chromatic semitone]]
|[[Chromatic semitone]]
|Chroma of the diatonic scale.
|Chroma of the diatonic scale. See [[Whitewood]] temperament.
|}
|}


Line 138: Line 137:
|27, 28, 29, 30, 31, 32, 58, 59, 117, 146, 292
|27, 28, 29, 30, 31, 32, 58, 59, 117, 146, 292
|augmented diesis
|augmented diesis
|
|See [[Augmented]] temperament.
|-
|-
|25/24
|25/24
|70.7
|70.7
|16, 17, 18, 33, 34, 35, 51, 68, 85, 102
|16, 17, 18, 33, 34, 35, 51, 68, 85, 102
|
|classical chromatic semitone
|
|See [[Interclassical]] temperament.
|-
|-
|135/128
|135/128
Line 150: Line 149:
|13, 25, 26, 27, 39, 52, 65, 78, 91, 104
|13, 25, 26, 27, 39, 52, 65, 78, 91, 104
|major chroma
|major chroma
|
|See [[Mavila]] temperament.
|-
|-
|16/15
|16/15
Line 161: Line 160:
|133.2
|133.2
|9, 18, 27, 36, 45, 54, 63, 72, 81, 90
|9, 18, 27, 36, 45, 54, 63, 72, 81, 90
|
|acute minor second
|
|
|-
|-
Line 245: Line 244:
|1017.6
|1017.6
|13, 20, 26, 33, 46, 79, 125, 250
|13, 20, 26, 33, 46, 79, 125, 250
|
|acute minor seventh
|
|
|}
|}
Line 263: Line 262:
|31, 32, 33, 34, 35, 36, 67, 101, 168
|31, 32, 33, 34, 35, 36, 67, 101, 168
|interseptimal diesis
|interseptimal diesis
|
|See [[Semaphore]] temperament.
|-
|-
|28/27
|28/27
|63
|63.0
|18, 19, 20, 37, 38, 39, 57, 76
|18, 19, 20, 37, 38, 39, 57, 76
|
|septimal subminor second
|
|See [[Trienstonic]] temperament.
|-
|-
|8/7
|8/7
Line 320: Line 319:
|-
|-
|27/14
|27/14
|1137
|1137.0
|18, 19, 20, 37, 38, 39, 57, 76
|18, 19, 20, 37, 38, 39, 57, 76
|
|septimal supermajor seventh
|
|
|}
|}


=== 2.3.5.7 ===
=== 2...7 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
Line 333: Line 332:
!Name
!Name
!Notes
!Notes
|-
|50/49
|35
|31, 32, 33, 34, 35, 36, 68, 69, 103, 137, 240
|jubilisma
|
|-
|-
|36/35
|36/35
|48.8
|48.8
|23, 24, 25, 26, 49, 50, 74, 123
|23, 24, 25, 26, 49, 50, 74, 123
|
|famity, septimal quartertone
|
|See [[Mint]] temperament
|-
|-
|21/20
|21/20
|84.5
|84.5
|14, 15, 28, 29, 42, 43, 57, 71, 142, 213
|14, 15, 28, 29, 42, 43, 57, 71, 142, 213
|
|septimal narrow limma
|
|
|-
|-
Line 355: Line 348:
|119.4
|119.4
|10, 20, 30, 31, 40, 50, 201
|10, 20, 30, 31, 40, 50, 201
|septimal major semitone
|septimal wide chroma
|
|
|-
|-
Line 367: Line 360:
|196.2
|196.2
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|
|septimal narrow whole tone
|
|
|-
|-
Line 385: Line 378:
|400.1
|400.1
|6, 9, 12, 15, 18, ... 99, 102, 105
|6, 9, 12, 15, 18, ... 99, 102, 105
|
|septimal narrow major third
|
|
|-
|-
Line 397: Line 390:
|462.3
|462.3
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|
|septimal tendo third
|
|
|-
|-
Line 427: Line 420:
|737.7
|737.7
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|
|septimal arto sixth
|
|
|-
|-
Line 439: Line 432:
|799.9
|799.9
|6, 9, 12, 15, 18, ... 99, 102, 105
|6, 9, 12, 15, 18, ... 99, 102, 105
|
|septimal wide minor sixth
|
|
|-
|-
Line 445: Line 438:
|1003.8
|1003.8
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|
|septimal wide minor seventh
|
|
|-
|-
Line 457: Line 450:
|1151.2
|1151.2
|23, 24, 25, 26, 49, 50, 74, 123
|23, 24, 25, 26, 49, 50, 74, 123
|
|septimal ultramajor seventh
|
|
|}
|}
Line 471: Line 464:
!Notes
!Notes
|-
|-
|11/8
|'''11/8'''
|551.3
|'''551.3'''
|11, 13, 24, 26, 35, 37, 50, 61, 74, 111
|'''11, 13, 24, 26, 35, 37, 50, 61, 74, 111'''
|
|undecimal ultrafourth
|
|
|-
|-
Line 480: Line 473:
|347.4
|347.4
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|
|undecimal artoneutral third
|
|
|-
|-
Line 486: Line 479:
|165
|165
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|
|undecimal submajor second
|
|
|-
|-
Line 492: Line 485:
|1049.4
|1049.4
|8, 16, 24, 32, 40, 48, 56, 247
|8, 16, 24, 32, 40, 48, 56, 247
|
|undecimal neutral seventh
|
|
|-
|-
Line 498: Line 491:
|150.6
|150.6
|8, 16, 24, 32, 40, 48, 56, 247
|8, 16, 24, 32, 40, 48, 56, 247
|
|undecimal neutral second
|
|
|-
|-
Line 504: Line 497:
|648.7
|648.7
|11, 13, 24, 26, 35, 37, 50, 61, 74, 111
|11, 13, 24, 26, 35, 37, 50, 61, 74, 111
|
|undecimal infrafifth
|
|
|-
|-
Line 510: Line 503:
|852.6
|852.6
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|
|undecimal tendoneutral sixth
|
|
|-
|-
Line 516: Line 509:
|1035
|1035
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|
|undecimal supraminor seventh
|
|
|-
|-
Line 522: Line 515:
|354.5
|354.5
|10, 17, 27, 34, 37, 44, 61, 88, 132
|10, 17, 27, 34, 37, 44, 61, 88, 132
|
|undecimal neutral third
|
|
|-
|-
Line 528: Line 521:
|663
|663
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|
|undecimal subfifth
|
|
|-
|-
Line 534: Line 527:
|537
|537
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|
|undecimal superfourth
|
|
|-
|-
Line 540: Line 533:
|53.3
|53.3
|21, 22, 23, 24, 44, 45, 46, 68, 90, 135
|21, 22, 23, 24, 44, 45, 46, 68, 90, 135
|
|undecimal quartertone
|
|
|-
|-
Line 546: Line 539:
|480.6
|480.6
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|
|undecimal subfourth
|
|
|-
|-
Line 552: Line 545:
|867
|867
|11, 18, 25, 29, 36, 47, 54, 191
|11, 18, 25, 29, 36, 47, 54, 191
|
|undecimal submajor sixth
|
|
|-
|-
Line 558: Line 551:
|845.5
|845.5
|10, 17, 27, 34, 37, 44, 61, 88, 132
|10, 17, 27, 34, 37, 44, 61, 88, 132
|
|undecimal artoneutral sixth
|
|
|-
|-
Line 564: Line 557:
|221.3
|221.3
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|
|undecimal supermajor second
|
|
|-
|-
Line 570: Line 563:
|978.7
|978.7
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|
|undecimal subminor seventh
|
|
|-
|-
Line 576: Line 569:
|31.8
|31.8
|35, 36, 37, 38, 39, 40, 75, 76, 113, 151
|35, 36, 37, 38, 39, 40, 75, 76, 113, 151
|
|undecimal diesis
|
|See [[Eleventyfive]] temperament.
|}
|}


=== 2.3.5.7.11 ===
=== 2...11 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
Line 591: Line 584:
|396.2
|396.2
|6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106
|6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106
|
|valinorsmic narrow major third
|
|
|-
|-
Line 597: Line 590:
|1098.1
|1098.1
|12, 23, 24, 35, 36, 47, 59, 106
|12, 23, 24, 35, 36, 47, 59, 106
|
|undecimal major seventh
|
|
|-
|-
Line 603: Line 596:
|101.9
|101.9
|12, 23, 24, 35, 36, 47, 59, 106
|12, 23, 24, 35, 36, 47, 59, 106
|
|undecimal semitone
|
|
|-
|-
Line 609: Line 602:
|284.4
|284.4
|17, 21, 25, 34, 38, 42, 59, 76, 135, 173
|17, 21, 25, 34, 38, 42, 59, 76, 135, 173
|
|undecimal neominor third
|
|
|-
|-
Line 615: Line 608:
|1119.5
|1119.5
|14, 15, 29, 30, 31, 44, 45, 60, 149, 164
|14, 15, 29, 30, 31, 44, 45, 60, 149, 164
|
|undecimal neomajor seventh
|
|
|-
|-
Line 621: Line 614:
|80.5
|80.5
|14, 15, 29, 30, 31, 44, 45, 60, 149, 164
|14, 15, 29, 30, 31, 44, 45, 60, 149, 164
|
|undecimal neominor second
|
|
|-
|-
Line 627: Line 620:
|417.5
|417.5
|20, 23, 26, 29, 43, 46, 69, 92
|20, 23, 26, 29, 43, 46, 69, 92
|
|undecimal neomajor third
|
|
|-
|-
Line 633: Line 626:
|782.5
|782.5
|20, 23, 26, 29, 43, 46, 69, 92
|20, 23, 26, 29, 43, 46, 69, 92
|
|undecimal neominor sixth
|
|
|}
|}
Line 639: Line 632:
== 13-limit ==
== 13-limit ==


=== 2.3.5.7.13 ===
=== 2...7.13 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
Line 647: Line 640:
!Notes
!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
|
|
|}
|}


=== 2.3.5.7.11.13 ===
=== 2...13 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
Line 662: Line 817:
!Notes
!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 ==
== Higher limits ==
=== 2...17 ===
{| class="wikitable"
!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 ===
{| class="wikitable"
!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 ===
{| class="wikitable"
!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 ===
{| class="wikitable"
!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 ===
{| class="wikitable"
!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 ===
{| class="wikitable"
!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
|
|
|}

Latest revision as of 04:45, 15 February 2026

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 63.0 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 1137.0 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
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