List of just intonation intervals: Difference between revisions

From Xenharmonic Reference
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working on transitioning to the formalism. no sweeping changes should be needed from here
Line 163: Line 163:
|111.7
|111.7
|11, 21, 22, 32, 33, 43, 54, 86
|11, 21, 22, 32, 33, 43, 54, 86
|classical diatonic semitone
|classical diatonic semitone, schismic chromatic semitone
|
|
|-
|-
Line 170: Line 170:
|182.4
|182.4
|13, 20, 26, 33, 46, 79, 125, 250
|13, 20, 26, 33, 46, 79, 125, 250
|grave whole tone
|classical whole tone
|
|
|-
|-
Line 191: Line 191:
|519.6
|519.6
|7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194
|7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194
|acute fourth
|classical wolf fourth
|
|
|-
|-
Line 198: Line 198:
|590.2
|590.2
|59, 61, 63, 122
|59, 61, 63, 122
|classical narrow tritone
|classical augmented fourth, schismic diminished fifth
|
|
|-
|-
Line 205: Line 205:
|609.8
|609.8
|59, 61, 63, 122
|59, 61, 63, 122
|classical wide tritone
|classical diminished fifth, schismic augmented fourth
|
|
|-
|-
Line 212: Line 212:
|680.4
|680.4
|7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194
|7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194
|grave fifth
|classical wolf fifth
|
|
|-
|-
Line 233: Line 233:
|1017.6
|1017.6
|13, 20, 26, 33, 46, 79, 125, 250
|13, 20, 26, 33, 46, 79, 125, 250
|acute minor seventh
|classical minor seventh
|
|
|}
|}
Line 250: Line 250:
|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
|diptolemaic chromatic semitone, diaschismic diatonic semitone
|See [[Interclassical]] temperament.
|See [[Interclassical]] temperament.
|-
|-
Line 257: Line 257:
|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
|diptolemaic diatonic semitone
|
|
|-
|-
Line 264: Line 264:
|274.6
|274.6
|13, 22, 26, 31, 35, 48, 70, 83, 118
|13, 22, 26, 31, 35, 48, 70, 83, 118
|classical subminor third
|diaschismic minor third
|Also an augmented second.
|Also an augmented second.
|-
|-
Line 271: Line 271:
|427.4
|427.4
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|classical supermajor third
|diaschismic major third
|Also a diminished fourth.
|Also a diminished fourth.
|-
|-
Line 278: Line 278:
|772.6
|772.6
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|classical subminor sixth
|diaschismic minor sixth
|
|
|-
|-
Line 285: Line 285:
|925.4
|925.4
|13, 22, 26, 31, 35, 48, 70, 83, 118
|13, 22, 26, 31, 35, 48, 70, 83, 118
|classical supermajor sixth
|diaschismic major sixth
|
|
|}
|}
Line 321: Line 321:
|35.7
|35.7
|31, 32, 33, 34, 35, 36, 67, 101, 168
|31, 32, 33, 34, 35, 36, 67, 101, 168
|interseptimal diesis
|interseptimal diesis, diseptimal minor second
|See [[Semaphore]] temperament.
|See [[Semaphore]] temperament.
|-
|-
Line 328: Line 328:
|63.0
|63.0
|18, 19, 20, 37, 38, 39, 57, 76
|18, 19, 20, 37, 38, 39, 57, 76
|septimal subminor second
|septimal minor second
|See [[Trienstonic]] temperament.
|See [[Trienstonic]] temperament.
|-
|-
Line 335: Line 335:
|231.2
|231.2
|5, 21, 26, 31, 36, 52, 57, 83, 109, 218
|5, 21, 26, 31, 36, 52, 57, 83, 109, 218
|septimal supermajor second
|septimal major second
|
|
|-
|-
Line 342: Line 342:
|266.9
|266.9
|9, 18, 27, 36, 45, 54, 63, 72
|9, 18, 27, 36, 45, 54, 63, 72
|septimal subminor third
|septimal minor third
|
|
|-
|-
Line 349: Line 349:
|435.1
|435.1
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|septimal supermajor third
|septimal major third
|
|
|-
|-
Line 356: Line 356:
|470.8
|470.8
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|septimal subfourth
|septimal wolf fourth
|
|
|-
|-
Line 363: Line 363:
|729.2
|729.2
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|septimal superfifth
|septimal wolf fifth
|
|
|-
|-
Line 370: Line 370:
|764.9
|764.9
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|septimal subminor sixth
|septimal minor sixth
|
|
|-
|-
Line 377: Line 377:
|933.1
|933.1
|9, 18, 27, 36, 45, 54, 63, 72
|9, 18, 27, 36, 45, 54, 63, 72
|septimal supermajor sixth
|septimal major sixth
|
|
|-
|-
Line 384: Line 384:
|'''968.8'''
|'''968.8'''
|'''5, 21, 26, 31, 36, 52, 57, 83, 109, 218'''
|'''5, 21, 26, 31, 36, 52, 57, 83, 109, 218'''
|'''[[harmonic seventh]]'''
|septimal minor seventh
|
|
|-
|-
Line 391: Line 391:
|1137.0
|1137.0
|18, 19, 20, 37, 38, 39, 57, 76
|18, 19, 20, 37, 38, 39, 57, 76
|septimal supermajor seventh
|septimal major seventh
|
|
|}
|}
Line 415: Line 415:
|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
|aberschismic minor second
|
|
|-
|-
Line 422: Line 422:
|119.4
|119.4
|10, 20, 30, 31, 40, 50, 201
|10, 20, 30, 31, 40, 50, 201
|septimal wide chroma
|schismean minor second, aberschismic chromatic semitone
|
|
|-
|-
Line 429: Line 429:
|155.1
|155.1
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|septimal neutral second
|minty tendoneutral second
|
|
|-
|-
Line 436: Line 436:
|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
|marvel major second
|
|
|-
|-
Line 443: Line 443:
|350.6
|350.6
|7, 17, 24, 31, 34, 41, 48, 65, 89
|7, 17, 24, 31, 34, 41, 48, 65, 89
|septimal artoneutral third
|greenwoodmic artoneutral third
|
|
|-
|-
Line 450: Line 450:
|351.3
|351.3
|17, 24, 31, 34, 41, 58, 82
|17, 24, 31, 34, 41, 58, 82
|septimal tendoneutral third
|greenwoodmic tendoneutral third
|
|
|-
|-
Line 457: Line 457:
|400.1
|400.1
|6, 9, 12, 15, 18, ... 99, 102, 105
|6, 9, 12, 15, 18, ... 99, 102, 105
|septimal narrow major third
|marvel major third
|
|
|-
|-
Line 464: Line 464:
|449.3
|449.3
|8, 16, 24, 32, 40, 48, 56, 211
|8, 16, 24, 32, 40, 48, 56, 211
|septimal ultramajor third
|transretrominty major third
|
|
|-
|-
Line 471: Line 471:
|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
|transdiseptimal wolf fourth
|
|
|-
|-
Line 478: Line 478:
|546.8
|546.8
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|septimal neutral fourth
|minty artoneutral fourth
|
|
|-
|-
Line 485: Line 485:
|582.5
|582.5
|29, 31, 33, 35, 37, 68, 70, 103
|29, 31, 33, 35, 37, 68, 70, 103
|septimal narrow tritone
|aberschismic diminished fifth, schismean augmented fourth
|
|
|-
|-
Line 492: Line 492:
|617.5
|617.5
|29, 31, 33, 35, 37, 68, 70, 103
|29, 31, 33, 35, 37, 68, 70, 103
|septimal wide tritone
|aberschismic augmented fourth, schismean diminished fifth
|
|
|-
|-
Line 499: Line 499:
|653.2
|653.2
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|septimal neutral fifth
|minty tendoneutral fifth
|
|
|-
|-
Line 506: Line 506:
|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
|transdiseptimal wolf fifth
|
|
|-
|-
Line 513: Line 513:
|750.7
|750.7
|8, 16, 24, 32, 40, 48, 56, 211
|8, 16, 24, 32, 40, 48, 56, 211
|septimal inframinor sixth
|transretrominty minor sixth
|
|
|-
|-
Line 520: Line 520:
|799.9
|799.9
|6, 9, 12, 15, 18, ... 99, 102, 105
|6, 9, 12, 15, 18, ... 99, 102, 105
|septimal wide minor sixth
|marvel minor sixth
|
|
|-
|-
Line 527: Line 527:
|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
|marvel minor seventh
|
|
|-
|-
Line 534: Line 534:
|1044.9
|1044.9
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|septimal neutral seventh
|minty artoneutral seventh
|
|
|-
|-
Line 541: Line 541:
|1151.2
|1151.2
|23, 24, 25, 26, 49, 50, 74, 123
|23, 24, 25, 26, 49, 50, 74, 123
|septimal ultramajor seventh
|minty octave
|
|
|}
|}
Line 567: Line 567:
|150.6
|150.6
|8, 16, 24, 32, 40, 48, 56, 247
|8, 16, 24, 32, 40, 48, 56, 247
|undecimal neutral second
|undecimal tendoneutral second
|
|
|-
|-
Line 588: Line 588:
|'''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
|undecimal artoneutral fourth
|
|
|-
|-
Line 595: Line 595:
|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
|undecimal tendoneutral fifth
|
|
|-
|-
Line 616: Line 616:
|1049.4
|1049.4
|8, 16, 24, 32, 40, 48, 56, 247
|8, 16, 24, 32, 40, 48, 56, 247
|undecimal neutral seventh
|undecimal artoneutral seventh
|
|
|}
|}
Line 640: Line 640:
|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
|pine major second
|
|
|-
|-
Line 647: Line 647:
|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
|pentaretropine major second
|
|
|-
|-
Line 654: Line 654:
|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
|pentaretropine wolf fourth
|
|
|-
|-
Line 661: Line 661:
|537
|537
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|undecimal superfourth
|pine wolf fourth
|
|
|-
|-
Line 668: Line 668:
|663
|663
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|undecimal subfifth
|pine wolf fifth
|
|
|-
|-
Line 675: Line 675:
|719.4
|719.4
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|undecimal superfifth
|pentaretropine wolf fifth
|
|
|-
|-
Line 682: Line 682:
|867
|867
|11, 18, 25, 29, 36, 47, 54, 191
|11, 18, 25, 29, 36, 47, 54, 191
|undecimal submajor sixth
|pine major sixth
|
|
|-
|-
Line 689: Line 689:
|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
|pentaretropine minor seventh
|
|
|-
|-
Line 696: Line 696:
|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
|pine minor seventh
|
|
|}
|}
Line 711: Line 711:
|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
|pentacircle minor second
|
|
|-
|-
Line 717: Line 717:
|101.9
|101.9
|12, 23, 24, 35, 36, 47, 59, 106
|12, 23, 24, 35, 36, 47, 59, 106
|undecimal semitone
|schiretropentacircle minor second
|
|
|-
|-
Line 723: Line 723:
|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
|pentacircle minor third
|
|
|-
|-
Line 729: Line 729:
|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
|schiretropentacircle major third
|
|
|-
|-
Line 735: Line 735:
|417.5
|417.5
|20, 23, 26, 29, 43, 46, 69, 92
|20, 23, 26, 29, 43, 46, 69, 92
|undecimal neomajor third
|pentacircle major third
|
|
|-
|-
Line 741: Line 741:
|782.5
|782.5
|20, 23, 26, 29, 43, 46, 69, 92
|20, 23, 26, 29, 43, 46, 69, 92
|undecimal neominor sixth  
|pentacircle minor sixth  
|
|
|-
|-
Line 747: Line 747:
|1098.1
|1098.1
|12, 23, 24, 35, 36, 47, 59, 106
|12, 23, 24, 35, 36, 47, 59, 106
|undecimal major seventh
|schiretropentacircle major seventh
|
|
|-
|-
Line 753: Line 753:
|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
|pentacircle major seventh
|
|
|}
|}
Line 772: Line 772:
|65.3
|65.3
|18, 19, 36, 37, 38, 55, 92, 147
|18, 19, 36, 37, 38, 55, 92, 147
|small tridecimal subminor second
|tridecimal chromatic semitone
|
|
|-
|-
Line 779: Line 779:
|138.6
|138.6
|9, 17, 26, 34, 35, 43, 52, 78
|9, 17, 26, 34, 35, 43, 52, 78
|large tridecimal supraminor second
|tridecimal artoneutral second
|
|
|-
|-
Line 800: Line 800:
|563.4
|563.4
|15, 17, 30, 32, 34, 49, 66, 115, 164
|15, 17, 30, 32, 34, 49, 66, 115, 164
|tridecimal ultrafourth
|tridecimal tendoneutral fourth
|
|
|-
|-
Line 807: Line 807:
|636.6
|636.6
|15, 17, 30, 32, 34, 49, 66, 115, 164
|15, 17, 30, 32, 34, 49, 66, 115, 164
|tridecimal infrafifth
|tridecimal artoneutral fifth
|
|
|-
|-
Line 828: Line 828:
|1061.4
|1061.4
|9, 17, 26, 34, 35, 43, 52, 78
|9, 17, 26, 34, 35, 43, 52, 78
|small tridecimal submajor seventh
|tridecimal tendoneutral seventh
|
|
|-
|-
Line 835: Line 835:
|1134.7
|1134.7
|18, 19, 36, 37, 38, 55, 92, 147
|18, 19, 36, 37, 38, 55, 92, 147
|large tridecimal supermajor seventh
|tridecimal diminished octave
|
|
|}
|}
Line 852: Line 852:
|247.7
|247.7
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|tridecimal inframinor third
|barbados minor third
|
|
|-
|-
Line 859: Line 859:
|454.2
|454.2
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|tridecimal ultramajor third
|barbados major third
|
|
|-
|-
Line 866: Line 866:
|745.8
|745.8
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|tridecimal inframinor sixth
|barbados minor sixth
|
|
|-
|-
Line 873: Line 873:
|952.3
|952.3
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|tridecimal ultramajor sixth
|barbados major sixth
|
|
|}
|}
Line 888: Line 888:
|128.3
|128.3
|9, 18, 19, 28, 37, 38, 47, 56, 159
|9, 18, 19, 28, 37, 38, 47, 56, 159
|small tridecimal supraminor second
|''small tridecimal supraminor second''
|
|
|-
|-
Line 894: Line 894:
|369.7
|369.7
|13, 16, 23, 26, 29, 39, 52, 198
|13, 16, 23, 26, 29, 39, 52, 198
|tridecimal submajor third
|''tridecimal submajor third''
|
|
|-
|-
Line 900: Line 900:
|590.6
|590.6
|61, 63, 65, 128
|61, 63, 65, 128
|tridecimal narrow tritone
|''tridecimal narrow tritone''
|
|
|-
|-
Line 906: Line 906:
|609.4
|609.4
|61, 63, 65, 128
|61, 63, 65, 128
|tridecimal wide tritone
|''tridecimal wide tritone''
|
|
|-
|-
Line 912: Line 912:
|830.3
|830.3
|13, 16, 23, 26, 29, 39, 52, 198
|13, 16, 23, 26, 29, 39, 52, 198
|tridecimal supraminor sixth
|''tridecimal supraminor sixth''
|
|
|-
|-
Line 918: Line 918:
|1071.7
|1071.7
|9, 18, 19, 28, 37, 38, 47, 56, 159
|9, 18, 19, 28, 37, 38, 47, 56, 159
|large tridecimal submajor seventh
|''large tridecimal submajor seventh''
|
|
|}
|}
Line 933: Line 933:
|67.9
|67.9
|17, 18, 19, 34, 35, 36, 53, 71, 106, 159
|17, 18, 19, 34, 35, 36, 53, 71, 106, 159
|large tridecimal subminor second
|''large tridecimal subminor second''
|
|
|-
|-
Line 939: Line 939:
|187.3
|187.3
|13, 19, 26, 32, 38, 45, 64, 173
|13, 19, 26, 32, 38, 45, 64, 173
|tridecimal major second
|''tridecimal major second''
|
|
|-
|-
Line 945: Line 945:
|240
|240
|5, 10, 15 ... 150, 155, 160
|5, 10, 15 ... 150, 155, 160
|tridecimal supermajor second
|''tridecimal supermajor second''
|
|
|-
|-
Line 951: Line 951:
|514.6
|514.6
|7, 14, 21, 28, 35, 42, 49, 56, 63, 70
|7, 14, 21, 28, 35, 42, 49, 56, 63, 70
|tridecimal wide fourth
|''tridecimal wide fourth''
|
|
|-
|-
Line 957: Line 957:
|685.4
|685.4
|7, 14, 21, 28, 35, 42, 49, 56, 63, 70
|7, 14, 21, 28, 35, 42, 49, 56, 63, 70
|tridecimal narrow fifth
|''tridecimal narrow fifth''
|
|
|-
|-
Line 963: Line 963:
|960
|960
|5, 10, 15 ... 150, 155, 160
|5, 10, 15 ... 150, 155, 160
|tridecimal subminor seventh
|''tridecimal subminor seventh''
|
|
|-
|-
Line 969: Line 969:
|1012.7
|1012.7
|13, 19, 26, 32, 38, 45, 64, 173
|13, 19, 26, 32, 38, 45, 64, 173
|tridecimal minor seventh
|''tridecimal minor seventh''
|
|
|-
|-
Line 975: Line 975:
|1132.1
|1132.1
|17, 18, 19, 34, 35, 36, 53, 71, 106, 159
|17, 18, 19, 34, 35, 36, 53, 71, 106, 159
|small tridecimal supermajor seventh
|''small tridecimal supermajor seventh''
|
|
|}
|}
Line 990: Line 990:
|289.2
|289.2
|21, 25, 29, 33, 54, 58, 83, 112
|21, 25, 29, 33, 54, 58, 83, 112
|tridecimal neominor third
|
|
|
|-
|-
Line 996: Line 996:
|412.7
|412.7
|26, 29, 32, 35, 38, 61, 64, 189
|26, 29, 32, 35, 38, 61, 64, 189
|tridecimal neomajor third
|
|
|
|-
|-
Line 1,002: Line 1,002:
|493.1
|493.1
|17, 22, 29, 34, 39, 56, 73
|17, 22, 29, 34, 39, 56, 73
|small tridecimal narrow fourth
|''small tridecimal narrow fourth''
|
|
|-
|-
Line 1,008: Line 1,008:
|493.3
|493.3
|17, 22, 29, 34, 39, 51, 56, 73, 90
|17, 22, 29, 34, 39, 51, 56, 73, 90
|large tridecimal narrow fourth
|''large tridecimal narrow fourth''
|
|
|-
|-
Line 1,014: Line 1,014:
|595.1
|595.1
|6, 8, 10, 12, 14, 16, 18, 121, 123
|6, 8, 10, 12, 14, 16, 18, 121, 123
|small gassormic tritone
|''small gassormic tritone''
|
|
|-
|-
Line 1,020: Line 1,020:
|604.9
|604.9
|6, 8, 10, 12, 14, 16, 18, 121, 123
|6, 8, 10, 12, 14, 16, 18, 121, 123
|large gassormic tritone
|''large gassormic tritone''
|
|
|-
|-
Line 1,026: Line 1,026:
|706.7
|706.7
|17, 22, 29, 34, 39, 51, 56, 73, 90
|17, 22, 29, 34, 39, 51, 56, 73, 90
|small tridecimal wide fifth
|''small tridecimal wide fifth''
|
|
|-
|-
Line 1,032: Line 1,032:
|706.9
|706.9
|17, 22, 29, 34, 39, 56, 73
|17, 22, 29, 34, 39, 56, 73
|large tridecimal wide fifth
|''large tridecimal wide fifth''
|
|
|-
|-
Line 1,038: Line 1,038:
|787.3
|787.3
|26, 29, 32, 35, 38, 61, 64, 189
|26, 29, 32, 35, 38, 61, 64, 189
|tridecimal neominor sixth
|
|
|
|-
|-
Line 1,044: Line 1,044:
|910.8
|910.8
|21, 25, 29, 33, 54, 58, 83, 112
|21, 25, 29, 33, 54, 58, 83, 112
|tridecimal neomajor sixth
|
|
|
|}
|}
Line 1,061: Line 1,061:
|51.7
|51.7
|22, 23, 24, 25, 46, 47, 70, 93, 116
|22, 23, 24, 25, 46, 47, 70, 93, 116
|large septendecimal quartertone
|''large septendecimal quartertone''
|
|
|-
|-
Line 1,067: Line 1,067:
|78.1
|78.1
|15, 16, 30, 31, 32, 46, 77, 123, 169
|15, 16, 30, 31, 32, 46, 77, 123, 169
|septendecimal third-tone
|''septendecimal third-tone''
|
|
|-
|-
Line 1,073: Line 1,073:
|99
|99
|12, 24, 25, 36, 37, 48, 49, 85, 97, 109
|12, 24, 25, 36, 37, 48, 49, 85, 97, 109
|small septendecimal semitone
|''small septendecimal semitone''
|
|
|-
|-
Line 1,079: Line 1,079:
|'''105'''
|'''105'''
|'''11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240'''
|'''11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240'''
|large septendecimal semitone
|''large septendecimal semitone''
|
|
|-
|-
Line 1,085: Line 1,085:
|216.7
|216.7
|11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144
|11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144
|septendecimal neomajor second
|''septendecimal neomajor second''
|
|
|-
|-
Line 1,091: Line 1,091:
|281.4
|281.4
|13, 17, 21, 30, 34, 47, 64, 81, 145
|13, 17, 21, 30, 34, 47, 64, 81, 145
|septendecimal neominor third
|''septendecimal neominor third''
|
|
|-
|-
Line 1,097: Line 1,097:
|300.1
|300.1
|8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104
|8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104
|septendecimal minor third
|''septendecimal minor third''
|
|
|-
|-
Line 1,103: Line 1,103:
|336.1
|336.1
|7, 18, 25, 32, 43, 50, 75, 100
|7, 18, 25, 32, 43, 50, 75, 100
|septendecimal supraminor third
|''septendecimal supraminor third''
|
|
|-
|-
Line 1,109: Line 1,109:
|365.8
|365.8
|10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269
|10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269
|septendecimal submajor third
|''septendecimal submajor third''
|
|
|-
|-
Line 1,115: Line 1,115:
|399.1
|399.1
|6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51
|6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51
|septendecimal major third
|''septendecimal major third''
|
|
|-
|-
Line 1,121: Line 1,121:
|446.4
|446.4
|8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250
|8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250
|septendecimal ultramajor third
|''septendecimal ultramajor third''
|
|
|-
|-
Line 1,127: Line 1,127:
|464.4
|464.4
|13, 18, 26, 31, 36, 44, 49, 62, 93
|13, 18, 26, 31, 36, 44, 49, 62, 93
|septendecimal subfourth
|''septendecimal subfourth''
|
|
|-
|-
Line 1,133: Line 1,133:
|491.3
|491.3
|17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276
|17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276
|septendecimal narrow fourth
|''septendecimal narrow fourth''
|
|
|-
|-
Line 1,139: Line 1,139:
|532.3
|532.3
|9, 18, 25, 27, 34, 36, 45, 124, 133, 257
|9, 18, 25, 27, 34, 36, 45, 124, 133, 257
|septendecimal superfourth
|''septendecimal superfourth''
|
|
|-
|-
Line 1,145: Line 1,145:
|597
|597
|6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201
|6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201
|small septendecimal tritone
|''small septendecimal tritone''
|
|
|-
|-
Line 1,151: Line 1,151:
|603
|603
|6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201
|6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 199, 201
|large septendecimal tritone
|''large septendecimal tritone''
|
|
|-
|-
Line 1,157: Line 1,157:
|667.7
|667.7
|9, 18, 25, 27, 34, 36, 45, 124, 133, 257
|9, 18, 25, 27, 34, 36, 45, 124, 133, 257
|septendecimal subfifth
|''septendecimal subfifth''
|
|
|-
|-
Line 1,163: Line 1,163:
|708.7
|708.7
|17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276
|17, 22, 27, 34, 39, 44, 61, 66, 127, 149, 276
|septendecimal wide fifth
|''septendecimal wide fifth''
|
|
|-
|-
Line 1,169: Line 1,169:
|735.6
|735.6
|13, 18, 26, 31, 36, 44, 49, 62, 93
|13, 18, 26, 31, 36, 44, 49, 62, 93
|septendecimal superfifth
|''septendecimal superfifth''
|
|
|-
|-
Line 1,175: Line 1,175:
|753.6
|753.6
|8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250
|8, 16, 19, 24, 27, 32, 35, 43, 51, 78, 86, 250
|septendecimal inframinor sixth
|''septendecimal inframinor sixth''
|
|
|-
|-
Line 1,181: Line 1,181:
|800.9
|800.9
|6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51
|6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51
|septendecimal minor sixth
|''septendecimal minor sixth''
|
|
|-
|-
Line 1,187: Line 1,187:
|834.2
|834.2
|10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269
|10, 13, 23, 26, 33, 36, 46, 59, 82, 105, 269
|septendecimal supraminor sixth
|''septendecimal supraminor sixth''
|
|
|-
|-
Line 1,193: Line 1,193:
|863.9
|863.9
|7, 18, 25, 32, 43, 50, 75, 100
|7, 18, 25, 32, 43, 50, 75, 100
|septendecimal submajor sixth
|''septendecimal submajor sixth''
|
|
|-
|-
Line 1,199: Line 1,199:
|899.9
|899.9
|8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104
|8, 12, 16, 20, 24 ... 88, 92, 96, 100, 104
|septendecimal major sixth
|''septendecimal major sixth''
|
|
|-
|-
Line 1,205: Line 1,205:
|918.6
|918.6
|13, 17, 21, 30, 34, 47, 64, 81, 145
|13, 17, 21, 30, 34, 47, 64, 81, 145
|septendecimal neomajor sixth
|''septendecimal neomajor sixth''
|
|
|-
|-
Line 1,211: Line 1,211:
|983.3
|983.3
|11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144
|11, 17, 22, 28, 33, 39, 50, 61, 72, 83, 144
|septendecimal neominor seventh
|''septendecimal neominor seventh''
|
|
|-
|-
Line 1,217: Line 1,217:
|1095
|1095
|11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240
|11, 12, 22, 23, 34, 35, 46, 57, 80, 160, 240
|small septendecimal major seventh
|''small septendecimal major seventh''
|
|
|-
|-
Line 1,223: Line 1,223:
|1101
|1101
|12, 24, 25, 36, 37, 48, 49, 85, 97, 109
|12, 24, 25, 36, 37, 48, 49, 85, 97, 109
|large septendecimal major seventh
|''large septendecimal major seventh''
|
|
|-
|-
Line 1,229: Line 1,229:
|1121.9
|1121.9
|15, 16, 30, 31, 32, 46, 77, 123, 169
|15, 16, 30, 31, 32, 46, 77, 123, 169
|septendecimal supermajor seventh
|''septendecimal supermajor seventh''
|
|
|-
|-
Line 1,235: Line 1,235:
|1148.3
|1148.3
|22, 23, 24, 25, 46, 47, 70, 93, 116
|22, 23, 24, 25, 46, 47, 70, 93, 116
|small septendecimal ultramajor seventh
|''small septendecimal ultramajor seventh''
|
|
|}
|}
Line 1,292: Line 1,292:
|292.7
|292.7
|8, 29, 33, 37, 41, 45, 82, 123, 164
|8, 29, 33, 37, 41, 45, 82, 123, 164
|small undevicesimal minor third
|''small undevicesimal minor third''
|
|
|-
|-
Line 1,298: Line 1,298:
|'''297.5'''
|'''297.5'''
|'''8, 12, 16, 20, 24, 28, 32, 36, 117, 121'''
|'''8, 12, 16, 20, 24, 28, 32, 36, 117, 121'''
|'''large undevicesimal minor third'''
|'''''large undevicesimal minor third'''''
|
|
|-
|-
Line 1,304: Line 1,304:
|404.4
|404.4
|6, 9, 12, 15, 18, 21, 24, 89, 92, 181, 273
|6, 9, 12, 15, 18, 21, 24, 89, 92, 181, 273
|small undevicesimal major third
|''small undevicesimal major third''
|
|
|-
|-
Line 1,310: Line 1,310:
|409.2
|409.2
|32, 35, 38, 41, 44, 47, 88, 261
|32, 35, 38, 41, 44, 47, 88, 261
|large undevicesimal major third
|''large undevicesimal major third''
|
|
|-
|-

Revision as of 06:23, 23 April 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 12edo Cents Good edos Name Notes
-7 4096/2187 11 1086.3 10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190 Diatonic diminished octave
-6 1024/729 6 588.3 47, 49, 51, 53, 102 Diatonic diminished fifth Found in a diminished triad. A stack of two diatonic minor thirds
-5 256/243 1 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 8 792.2 6, 44, 47, 50, 53, 56, 103 Diatonic minor sixth
-3 32/27 3 294.1 8, 12, 33, 37, 41, 45, 49, 53, 57, 102 Diatonic minor third Middle interval in a Pythagorean minor chord
-2 16/9 10 996.1 6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153 Diatonic minor seventh
-1 4/3 5 498 12, 17, 24, 29, 36, 41, 53, 94, 200 Perfect fourth
0 1/1 0 0 (All) Perfect unison Represents a multiplication by 1, i.e. no change in pitch
+1 3/2 7 702 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 2 203.9 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 9 905.9 8, 12, 33, 37, 41, 45, 49, 53, 57, 102 Diatonic major sixth
+4 81/64 4 407.8 6, 44, 47, 50, 53, 56, 103 Diatonic major third Middle interval in a Pythagorean major chord
+5 243/128 11 1109.8 13, 14, 26, 27, 40, 53, 80, 93, 133, 306 Diatonic major seventh
+6 729/512 6 611.7 47, 49, 51, 53, 102 Diatonic augmented fourth Stack of 3 tones (tritone)
+7 2187/2048 1 113.7 10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190 Chromatic semitone Chroma of the diatonic scale. See Whitewood temperament.

5-limit

5

Ratio 7edo Cents Good edos Name Notes
135/128 0 92.2 13, 25, 26, 27, 39, 52, 65, 78, 91, 104 major chroma See Mavila temperament.
16/15 1 111.7 11, 21, 22, 32, 33, 43, 54, 86 classical diatonic semitone, schismic chromatic semitone
10/9 1 182.4 13, 20, 26, 33, 46, 79, 125, 250 classical whole tone
6/5 2 315.6 15, 19, 23, 34, 38, 42, 57, 76 classical minor third
5/4 2 386.3 22, 25, 28, 31, 34, 56, 59, 87, 146, 292 classical major third
27/20 3 519.6 7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194 classical wolf fourth
45/32 3 590.2 59, 61, 63, 122 classical augmented fourth, schismic diminished fifth
64/45 4 609.8 59, 61, 63, 122 classical diminished fifth, schismic augmented fourth
40/27 4 680.4 7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194 classical wolf fifth
8/5 5 813.7 22, 25, 28, 31, 34, 56, 59, 87, 146, 292 classical minor sixth
5/3 5 884.4 15, 19, 23, 34, 38, 42, 57, 76 classical major sixth
9/5 6 1017.6 13, 20, 26, 33, 46, 79, 125, 250 classical minor seventh

25

Ratio 7edo Cents Good edos Name Notes
25/24 0 70.7 16, 17, 18, 33, 34, 35, 51, 68, 85, 102 diptolemaic chromatic semitone, diaschismic diatonic semitone See Interclassical temperament.
27/25 1 133.2 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 diptolemaic diatonic semitone
75/64 1 274.6 13, 22, 26, 31, 35, 48, 70, 83, 118 diaschismic minor third Also an augmented second.
32/25 3 427.4 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 diaschismic major third Also a diminished fourth.
25/16 4 772.6 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 diaschismic minor sixth
128/75 6 925.4 13, 22, 26, 31, 35, 48, 70, 83, 118 diaschismic major sixth

125

Ratio 7edo Cents Good edos Name Notes
128/125 1 41.1 27, 28, 29, 30, 31, 32, 58, 59, 117, 146, 292 augmented diesis See Augmented temperament.

7-limit

2.3.7

Ratio 5edo Cents Good edos Name Notes
49/48 0 35.7 31, 32, 33, 34, 35, 36, 67, 101, 168 interseptimal diesis, diseptimal minor second See Semaphore temperament.
28/27 0 63.0 18, 19, 20, 37, 38, 39, 57, 76 septimal minor second See Trienstonic temperament.
8/7 1 231.2 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 septimal major second
7/6 1 266.9 9, 18, 27, 36, 45, 54, 63, 72 septimal minor third
9/7 2 435.1 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal major third
21/16 2 470.8 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal wolf fourth
32/21 3 729.2 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal wolf fifth
14/9 3 764.9 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal minor sixth
12/7 4 933.1 9, 18, 27, 36, 45, 54, 63, 72 septimal major sixth
7/4 4 968.8 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 septimal minor seventh
27/14 5 1137.0 18, 19, 20, 37, 38, 39, 57, 76 septimal major seventh

2...7

Ratio 10edo Cents Good edos Name Notes
36/35 1 48.8 23, 24, 25, 26, 49, 50, 74, 123 famity, septimal quartertone See Mint temperament
21/20 1 84.5 14, 15, 28, 29, 42, 43, 57, 71, 142, 213 aberschismic minor second
15/14 1 119.4 10, 20, 30, 31, 40, 50, 201 schismean minor second, aberschismic chromatic semitone
35/32 1 155.1 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 minty tendoneutral second
28/25 2 196.2 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 marvel major second
60/49 3 350.6 7, 17, 24, 31, 34, 41, 48, 65, 89 greenwoodmic artoneutral third
49/40 3 351.3 17, 24, 31, 34, 41, 58, 82 greenwoodmic tendoneutral third
63/50 4 400.1 6, 9, 12, 15, 18, ... 99, 102, 105 marvel major third
35/27 3 449.3 8, 16, 24, 32, 40, 48, 56, 211 transretrominty major third
64/49 4 462.3 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 transdiseptimal wolf fourth
48/35 5 546.8 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 minty artoneutral fourth
7/5 5 582.5 29, 31, 33, 35, 37, 68, 70, 103 aberschismic diminished fifth, schismean augmented fourth
10/7 5 617.5 29, 31, 33, 35, 37, 68, 70, 103 aberschismic augmented fourth, schismean diminished fifth
35/24 5 653.2 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 minty tendoneutral fifth
49/32 6 737.7 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 transdiseptimal wolf fifth
54/35 7 750.7 8, 16, 24, 32, 40, 48, 56, 211 transretrominty minor sixth
100/63 6 799.9 6, 9, 12, 15, 18, ... 99, 102, 105 marvel minor sixth
25/14 8 1003.8 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 marvel minor seventh
64/35 9 1044.9 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 minty artoneutral seventh
35/18 9 1151.2 23, 24, 25, 26, 49, 50, 74, 123 minty octave

11-limit

2.3.11

Ratio 17edo Cents Good edos Name Notes
33/32 1 53.3 21, 22, 23, 24, 44, 45, 46, 68, 90, 135 undecimal quartertone
12/11 2 150.6 8, 16, 24, 32, 40, 48, 56, 247 undecimal tendoneutral second
11/9 5 347.4 7, 14, 21, 24, 31, 38, 45, 76, 114, 152 undecimal artoneutral third
27/22 5 354.5 10, 17, 27, 34, 37, 44, 61, 88, 132 undecimal tendoneutral third
11/8 8 551.3 11, 13, 24, 26, 35, 37, 50, 61, 74, 111 undecimal artoneutral fourth
16/11 9 648.7 11, 13, 24, 26, 35, 37, 50, 61, 74, 111 undecimal tendoneutral fifth
44/27 12 845.5 10, 17, 27, 34, 37, 44, 61, 88, 132 undecimal artoneutral sixth
18/11 12 852.6 7, 14, 21, 24, 31, 38, 45, 76, 114, 152 undecimal tendoneutral sixth
11/6 15 1049.4 8, 16, 24, 32, 40, 48, 56, 247 undecimal artoneutral seventh

2.3.5.11

Ratio 15edo Cents Good edos Name Notes
55/54 0 31.8 35, 36, 37, 38, 39, 40, 75, 76, 113, 151 undecimal diesis See Eleventyfive temperament.
11/10 2 165 7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240 pine major second
25/22 3 221.3 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 pentaretropine major second
33/25 6 480.6 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 pentaretropine wolf fourth
15/11 7 537 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 pine wolf fourth
22/15 8 663 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 pine wolf fifth
50/33 9 719.4 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 pentaretropine wolf fifth
33/20 11 867 11, 18, 25, 29, 36, 47, 54, 191 pine major sixth
44/25 12 978.7 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 pentaretropine minor seventh
20/11 13 1035 7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240 pine minor seventh

2...11

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

13-limit

2.3.13

Ratio 17edo Cents Good edos Name Notes
27/26 1 65.3 18, 19, 36, 37, 38, 55, 92, 147 tridecimal chromatic semitone
13/12 2 138.6 9, 17, 26, 34, 35, 43, 52, 78 tridecimal artoneutral second
39/32 5 342.5 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal artoneutral third
16/13 5 359.5 10, 20, 27, 30, 40, 50, 60, 237 tridecimal tendoneutral third
18/13 8 563.4 15, 17, 30, 32, 34, 49, 66, 115, 164 tridecimal tendoneutral fourth
13/9 9 636.6 15, 17, 30, 32, 34, 49, 66, 115, 164 tridecimal artoneutral fifth
13/8 12 840.5 10, 20, 27, 30, 40, 50, 60, 237 tridecimal artoneutral sixth
64/39 12 857.5 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal tendoneutral sixth
24/13 15 1061.4 9, 17, 26, 34, 35, 43, 52, 78 tridecimal tendoneutral seventh
52/27 16 1134.7 18, 19, 36, 37, 38, 55, 92, 147 tridecimal diminished octave

2.3.13/5

Ratio 19edo Cents Good edos Name Notes
15/13 4 247.7 5, 19, 24, 29, 34, 39, 58, 63, 92, 218 barbados minor third
13/10 7 454.2 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 barbados major third
20/13 12 745.8 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 barbados minor sixth
26/15 15 952.3 5, 19, 24, 29, 34, 39, 58, 63, 92, 218 barbados major sixth

2.3.7.13

Ratio Cents Good edos Name Notes
14/13 128.3 9, 18, 19, 28, 37, 38, 47, 56, 159 small tridecimal supraminor second
26/21 369.7 13, 16, 23, 26, 29, 39, 52, 198 tridecimal submajor third
128/91 590.6 61, 63, 65, 128 tridecimal narrow tritone
91/64 609.4 61, 63, 65, 128 tridecimal wide tritone
21/13 830.3 13, 16, 23, 26, 29, 39, 52, 198 tridecimal supraminor sixth
13/7 1071.7 9, 18, 19, 28, 37, 38, 47, 56, 159 large tridecimal submajor seventh

2...7.13

Ratio Cents Good edos Name Notes
26/25 67.9 17, 18, 19, 34, 35, 36, 53, 71, 106, 159 large tridecimal subminor 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
35/26 514.6 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal wide fourth
52/35 685.4 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 tridecimal narrow fifth
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
25/13 1132.1 17, 18, 19, 34, 35, 36, 53, 71, 106, 159 small tridecimal supermajor seventh

2...13

Ratio Cents Good edos Name Notes
13/11 289.2 21, 25, 29, 33, 54, 58, 83, 112
33/26 412.7 26, 29, 32, 35, 38, 61, 64, 189
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
22/13 910.8 21, 25, 29, 33, 54, 58, 83, 112

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
View • Talk • EditIntervals 
Interval categories
Diatonic ordinals Unison • Second (major • neutral • minor) • Third (major • neutral • minor) • Fourth • Fifth • Sixth (major • neutral • minor) • Seventh (major • neutral • minor) • Octave
Other interval categories Diesis • Semitone • Whole tone • Interordinal intervals (chthonic • naiadic • cocytic • ouranic) • Tritone
Just intonation
Pythagorean Perfect fifth • Perfect fourth • Diatonic major second • Diatonic minor seventh • Tritave • others
5-limit 5/4 • 5/3 • 6/5 • 16/15 • 25/24 • others
7-limit 7/4 • 8/7 • 7/6 • 9/7 • 7/5 • 49/48 • others
Alpharabian 11/8 • 11/9 • 12/11 • others
Full 11-limit 11/10 • 14/11 • 11/7 • others
2.3.13/5 13/10 • 15/13 • 26/15 • 20/13 • others
Full 13-limit 16/13 • 13/8 • 13/11 • 13/9 • 13/7 • others
Higher limits 17/16 • 18/17 • 19/16 • 19/15 • 24/19 • 23/16 • others
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