List of just intonation intervals: Difference between revisions

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Line 14: Line 14:
!Fifthspan
!Fifthspan
!Ratio
!Ratio
!12edo
!Cents
!Cents
!Good edos
!Good edos
Line 21: Line 22:
| -7
| -7
|4096/2187
|4096/2187
|11
|{{Cents from ratio|ratio=4096/2187}}
|{{Cents from ratio|ratio=4096/2187}}
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
Line 28: Line 30:
| -6
| -6
|1024/729
|1024/729
|6
|{{Cents from ratio|ratio=1024/729}}
|{{Cents from ratio|ratio=1024/729}}
|47, 49, 51, 53, 102
|47, 49, 51, 53, 102
Line 35: Line 38:
| -5
| -5
|256/243
|256/243
|1
|{{Cents from ratio|ratio=256/243}}
|{{Cents from ratio|ratio=256/243}}
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
Line 42: Line 46:
| -4
| -4
|128/81
|128/81
|8
|{{Cents from ratio|ratio=128/81}}
|{{Cents from ratio|ratio=128/81}}
|6, 44, 47, 50, 53, 56, 103
|6, 44, 47, 50, 53, 56, 103
Line 49: Line 54:
| -3
| -3
|32/27
|32/27
|3
|{{Cents from ratio|ratio=32/27}}
|{{Cents from ratio|ratio=32/27}}
|8, 12, 33, 37, 41, 45, 49, 53, 57, 102
|8, 12, 33, 37, 41, 45, 49, 53, 57, 102
Line 56: Line 62:
| -2
| -2
|16/9
|16/9
|10
|{{Cents from ratio|ratio=16/9}}
|{{Cents from ratio|ratio=16/9}}
|6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153
|6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153
Line 63: Line 70:
| -1
| -1
|4/3
|4/3
|5
|{{Cents from ratio|ratio=4/3}}
|{{Cents from ratio|ratio=4/3}}
|12, 17, 24, 29, 36, 41, 53, 94, 200
|12, 17, 24, 29, 36, 41, 53, 94, 200
Line 70: Line 78:
|0
|0
|1/1
|1/1
|0
|{{Cents from ratio|ratio=1/1}}
|{{Cents from ratio|ratio=1/1}}
|(All)
|(All)
Line 77: Line 86:
|'''+1'''
|'''+1'''
|'''3/2'''
|'''3/2'''
|7
|'''{{Cents from ratio|ratio=3/2}}'''
|'''{{Cents from ratio|ratio=3/2}}'''
|'''12, 17, 24, 29, 36, 41, 53, 94, 200'''
|'''12, 17, 24, 29, 36, 41, 53, 94, 200'''
Line 84: Line 94:
| +2
| +2
|9/8
|9/8
|2
|{{Cents from ratio|ratio=9/8}}
|{{Cents from ratio|ratio=9/8}}
|6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153
|6, 12, 18, 24, 29, 30, 35, 41, 47, 53, 59, 100, 153
Line 91: Line 102:
| +3
| +3
|27/16
|27/16
|9
|{{Cents from ratio|ratio=27/16}}
|{{Cents from ratio|ratio=27/16}}
|8, 12, 33, 37, 41, 45, 49, 53, 57, 102
|8, 12, 33, 37, 41, 45, 49, 53, 57, 102
Line 98: Line 110:
| +4
| +4
|81/64
|81/64
|4
|{{Cents from ratio|ratio=81/64}}
|{{Cents from ratio|ratio=81/64}}
|6, 44, 47, 50, 53, 56, 103
|6, 44, 47, 50, 53, 56, 103
Line 105: Line 118:
| +5
| +5
|243/128
|243/128
|11
|{{Cents from ratio|ratio=243/128}}
|{{Cents from ratio|ratio=243/128}}
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
|13, 14, 26, 27, 40, 53, 80, 93, 133, 306
Line 112: Line 126:
| +6
| +6
|729/512
|729/512
|6
|{{Cents from ratio|ratio=729/512}}
|{{Cents from ratio|ratio=729/512}}
|47, 49, 51, 53, 102
|47, 49, 51, 53, 102
Line 119: Line 134:
| +7
| +7
|2187/2048
|2187/2048
|1
|{{Cents from ratio|ratio=2187/2048}}
|{{Cents from ratio|ratio=2187/2048}}
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
|10, 11, 21, 22, 31, 32, 42, 53, 74, 95, 190
Line 126: Line 142:


== 5-limit ==
== 5-limit ==
=== 5 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
!7edo
!Cents
!Cents
!Good edos
!Good edos
!Name
!Name
!Notes
!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
|135/128
|0
|92.2
|92.2
|13, 25, 26, 27, 39, 52, 65, 78, 91, 104
|13, 25, 26, 27, 39, 52, 65, 78, 91, 104
Line 152: Line 160:
|-
|-
|16/15
|16/15
|1
|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
|
|-
|27/25
|133.2
|9, 18, 27, 36, 45, 54, 63, 72, 81, 90
|acute minor second
|
|
|-
|-
|10/9
|10/9
|1
|182.4
|182.4
|13, 20, 26, 33, 46, 79, 125, 250
|13, 20, 26, 33, 46, 79, 125, 250
|grave whole tone
|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
|6/5
|2
|315.6
|315.6
|15, 19, 23, 34, 38, 42, 57, 76
|15, 19, 23, 34, 38, 42, 57, 76
Line 182: Line 181:
|-
|-
|'''5/4'''
|'''5/4'''
|2
|'''386.3'''
|'''386.3'''
|'''22, 25, 28, 31, 34, 56, 59, 87, 146, 292'''
|'''22, 25, 28, 31, 34, 56, 59, 87, 146, 292'''
Line 187: Line 187:
|
|
|-
|-
|32/25
|27/20
|427.4
|3
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|classical supermajor third
|Also a diminished fourth.
|-
|27/20
|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
Line 200: Line 195:
|-
|-
|45/32
|45/32
|3
|590.2
|590.2
|59, 61, 63, 122
|59, 61, 63, 122
Line 206: Line 202:
|-
|-
|64/45
|64/45
|4
|609.8
|609.8
|59, 61, 63, 122
|59, 61, 63, 122
Line 212: Line 209:
|-
|-
|40/27
|40/27
|4
|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
|grave fifth
|
|-
|25/16
|772.6
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|classical subminor sixth
|
|
|-
|-
|8/5
|8/5
|5
|813.7
|813.7
|22, 25, 28, 31, 34, 56, 59, 87, 146, 292
|22, 25, 28, 31, 34, 56, 59, 87, 146, 292
Line 230: Line 223:
|-
|-
|5/3
|5/3
|5
|884.4
|884.4
|15, 19, 23, 34, 38, 42, 57, 76
|15, 19, 23, 34, 38, 42, 57, 76
|classical major sixth
|classical major sixth
|
|-
|128/75
|925.4
|13, 22, 26, 31, 35, 48, 70, 83, 118
|classical supermajor sixth
|
|
|-
|-
|9/5
|9/5
|6
|1017.6
|1017.6
|13, 20, 26, 33, 46, 79, 125, 250
|13, 20, 26, 33, 46, 79, 125, 250
Line 248: Line 237:
|}
|}


== 7-limit ==
=== 25 ===
 
=== 2.3.7 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
!7edo
!Cents
!Cents
!Good edos
!Good edos
Line 258: Line 246:
!Notes
!Notes
|-
|-
|49/48
|25/24
|35.7
|0
|31, 32, 33, 34, 35, 36, 67, 101, 168
|70.7
|interseptimal diesis
|16, 17, 18, 33, 34, 35, 51, 68, 85, 102
|See [[Semaphore]] temperament.
|classical chromatic semitone
|See [[Interclassical]] temperament.
|-
|-
|28/27
|27/25
|63.0
|1
|18, 19, 20, 37, 38, 39, 57, 76
|133.2
|septimal subminor second
|9, 18, 27, 36, 45, 54, 63, 72, 81, 90
|See [[Trienstonic]] temperament.
|acute minor second
|-
|8/7
|231.2
|5, 21, 26, 31, 36, 52, 57, 83, 109, 218
|septimal supermajor second
|
|
|-
|-
|7/6
|75/64
|266.9
|1
|9, 18, 27, 36, 45, 54, 63, 72
|274.6
|septimal subminor third
|13, 22, 26, 31, 35, 48, 70, 83, 118
|
|classical subminor third
|Also an augmented second.
|-
|-
|9/7
|32/25
|435.1
|3
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|427.4
|septimal supermajor third
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|
|classical supermajor third
|Also a diminished fourth.
|-
|-
|21/16
|25/16
|470.8
|4
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|772.6
|septimal subfourth
|14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292
|classical subminor sixth
|
|
|-
|-
|32/21
|128/75
|729.2
|6
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|925.4
|septimal superfifth
|13, 22, 26, 31, 35, 48, 70, 83, 118
|classical supermajor sixth
|
|
|-
|}
|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 ===
=== 125 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
!7edo
!Cents
!Cents
!Good edos
!Good edos
Line 333: Line 298:
!Notes
!Notes
|-
|-
|36/35
|128/125
|48.8
|1
|23, 24, 25, 26, 49, 50, 74, 123
|41.1
|famity, septimal quartertone
|27, 28, 29, 30, 31, 32, 58, 59, 117, 146, 292
|See [[Mint]] temperament
|augmented diesis
|See [[Augmented]] temperament.
|}
 
== 7-limit ==
 
=== 2.3.7 ===
{| class="wikitable"
!Ratio
!5edo
!Cents
!Good edos
!Name
!Notes
|-
|-
|21/20
|49/48
|84.5
|0
|14, 15, 28, 29, 42, 43, 57, 71, 142, 213
|35.7
|septimal narrow limma
|31, 32, 33, 34, 35, 36, 67, 101, 168
|
|interseptimal diesis
|See [[Semaphore]] temperament.
|-
|28/27
|0
|63.0
|18, 19, 20, 37, 38, 39, 57, 76
|septimal subminor second
|See [[Trienstonic]] temperament.
|-
|-
|15/14
|8/7
|119.4
|1
|10, 20, 30, 31, 40, 50, 201
|231.2
|septimal wide chroma
|5, 21, 26, 31, 36, 52, 57, 83, 109, 218
|septimal supermajor second
|
|
|-
|-
|35/32
|7/6
|155.1
|1
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|266.9
|septimal neutral second
|9, 18, 27, 36, 45, 54, 63, 72
|septimal subminor third
|
|
|-
|-
|28/25
|9/7
|196.2
|2
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|435.1
|septimal narrow whole tone
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|septimal supermajor third
|
|
|-
|-
|60/49
|21/16
|350.6
|2
|7, 17, 24, 31, 34, 41, 48, 65, 89
|470.8
|septimal artoneutral third
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|septimal subfourth
|
|
|-
|-
|49/40
|32/21
|351.3
|3
|17, 24, 31, 34, 41, 58, 82
|729.2
|septimal tendoneutral third
|5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209
|septimal superfifth
|
|
|-
|-
|63/50
|14/9
|400.1
|3
|6, 9, 12, 15, 18, ... 99, 102, 105
|764.9
|septimal narrow major third
|11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171
|septimal subminor sixth
|
|
|-
|-
|35/27
|12/7
|449.3
|4
|8, 16, 24, 32, 40, 48, 56, 211
|933.1
|septimal ultramajor third
|9, 18, 27, 36, 45, 54, 63, 72
|septimal supermajor sixth
|
|
|-
|-
|64/49
|'''7/4'''
|462.3
|4
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|'''968.8'''
|septimal tendo third
|'''5, 21, 26, 31, 36, 52, 57, 83, 109, 218'''
|'''[[harmonic seventh]]'''
|
|
|-
|-
|48/35
|27/14
|546.8
|5
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|1137.0
|septimal neutral fourth
|18, 19, 20, 37, 38, 39, 57, 76
|
|septimal supermajor seventh
|-
|7/5
|582.5
|29, 31, 33, 35, 37, 68, 70, 103
|septimal narrow tritone
|
|
|}
=== 2...7 ===
{| class="wikitable"
!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
|-
|-
|10/7
|21/20
|617.5
|1
|29, 31, 33, 35, 37, 68, 70, 103
|84.5
|septimal wide tritone
|14, 15, 28, 29, 42, 43, 57, 71, 142, 213
|septimal narrow limma
|
|
|-
|-
|35/24
|15/14
|653.2
|1
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|119.4
|septimal neutral fifth
|10, 20, 30, 31, 40, 50, 201
|septimal wide chroma
|
|
|-
|-
|49/32
|35/32
|737.7
|1
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|155.1
|septimal arto sixth
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|septimal neutral second
|
|
|-
|-
|54/35
|28/25
|750.7
|2
|8, 16, 24, 32, 40, 48, 56, 211
|196.2
|septimal inframinor sixth
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|septimal narrow whole tone
|
|
|-
|-
|100/63
|60/49
|799.9
|3
|6, 9, 12, 15, 18, ... 99, 102, 105
|350.6
|septimal wide minor sixth
|7, 17, 24, 31, 34, 41, 48, 65, 89
|septimal artoneutral third
|
|
|-
|-
|25/14
|49/40
|1003.8
|3
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|351.3
|septimal wide minor seventh
|17, 24, 31, 34, 41, 58, 82
|septimal tendoneutral third
|
|
|-
|-
|64/35
|63/50
|1044.9
|4
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|400.1
|septimal neutral seventh
|6, 9, 12, 15, 18, ... 99, 102, 105
|septimal narrow major third
|
|
|-
|-
|35/18
|35/27
|1151.2
|3
|23, 24, 25, 26, 49, 50, 74, 123
|449.3
|septimal ultramajor seventh
|8, 16, 24, 32, 40, 48, 56, 211
|septimal ultramajor third
|
|
|}
|-
 
|64/49
== 11-limit ==
|4
 
|462.3
=== 2.3.5.11 ===
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
{| class="wikitable"
|septimal tendo third
!Ratio
!Cents
!Good edos
!Name
!Notes
|-
|'''11/8'''
|'''551.3'''
|'''11, 13, 24, 26, 35, 37, 50, 61, 74, 111'''
|undecimal ultrafourth
|
|
|-
|-
|11/9
|48/35
|347.4
|5
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|546.8
|undecimal artoneutral third
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|septimal neutral fourth
|
|
|-
|-
|11/10
|7/5
|165
|5
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|582.5
|undecimal submajor second
|29, 31, 33, 35, 37, 68, 70, 103
|septimal narrow tritone
|
|
|-
|-
|11/6
|10/7
|1049.4
|5
|8, 16, 24, 32, 40, 48, 56, 247
|617.5
|undecimal neutral seventh
|29, 31, 33, 35, 37, 68, 70, 103
|septimal wide tritone
|
|
|-
|-
|12/11
|35/24
|150.6
|5
|8, 16, 24, 32, 40, 48, 56, 247
|653.2
|undecimal neutral second
|11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90
|septimal neutral fifth
|
|
|-
|-
|16/11
|49/32
|648.7
|6
|11, 13, 24, 26, 35, 37, 50, 61, 74, 111
|737.7
|undecimal infrafifth
|13, 18, 26, 31, 39, 44, 52, 109, 122, 244
|septimal arto sixth
|
|
|-
|-
|18/11
|54/35
|852.6
|7
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|750.7
|undecimal tendoneutral sixth
|8, 16, 24, 32, 40, 48, 56, 211
|septimal inframinor sixth
|
|
|-
|-
|20/11
|100/63
|1035
|6
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|799.9
|undecimal supraminor seventh
|6, 9, 12, 15, 18, ... 99, 102, 105
|septimal wide minor sixth
|
|
|-
|-
|27/22
|25/14
|354.5
|8
|10, 17, 27, 34, 37, 44, 61, 88, 132
|1003.8
|undecimal neutral third
|6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263
|septimal wide minor seventh
|
|
|-
|-
|22/15
|64/35
|663
|9
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|1044.9
|undecimal subfifth
|8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294
|septimal neutral seventh
|
|
|-
|-
|15/11
|35/18
|537
|9
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|1151.2
|undecimal superfourth
|23, 24, 25, 26, 49, 50, 74, 123
|septimal ultramajor seventh
|
|
|}
== 11-limit ==
=== 2.3.11 ===
{| class="wikitable"
!Ratio
!17edo
!Cents
!Good edos
!Name
!Notes
|-
|-
|33/32
|33/32
|1
|53.3
|53.3
|21, 22, 23, 24, 44, 45, 46, 68, 90, 135
|21, 22, 23, 24, 44, 45, 46, 68, 90, 135
Line 536: Line 563:
|
|
|-
|-
|33/25
|12/11
|480.6
|2
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|150.6
|undecimal subfourth
|8, 16, 24, 32, 40, 48, 56, 247
|undecimal neutral second
|
|
|-
|-
|33/20
|11/9
|867
|5
|11, 18, 25, 29, 36, 47, 54, 191
|347.4
|undecimal submajor sixth
|7, 14, 21, 24, 31, 38, 45, 76, 114, 152
|undecimal artoneutral third
|
|
|-
|-
|44/27
|27/22
|845.5
|5
|354.5
|10, 17, 27, 34, 37, 44, 61, 88, 132
|10, 17, 27, 34, 37, 44, 61, 88, 132
|undecimal artoneutral sixth
|undecimal tendoneutral third
|
|
|-
|-
|25/22
|'''11/8'''
|221.3
|8
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|'''551.3'''
|undecimal supermajor second
|'''11, 13, 24, 26, 35, 37, 50, 61, 74, 111'''
|undecimal ultrafourth
|
|
|-
|-
|44/25
|16/11
|978.7
|9
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|648.7
|undecimal subminor seventh
|11, 13, 24, 26, 35, 37, 50, 61, 74, 111
|undecimal infrafifth
|
|-
|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
|
|
|-
|-
|55/54
|11/6
|31.8
|15
|35, 36, 37, 38, 39, 40, 75, 76, 113, 151
|1049.4
|undecimal diesis
|8, 16, 24, 32, 40, 48, 56, 247
|See [[Eleventyfive]] temperament.
|undecimal neutral seventh
|
|}
|}


=== 2...11 ===
=== 2.3.5.11 ===
{| class="wikitable"
{| class="wikitable"
!Ratio
!Ratio
!15edo
!Cents
!Cents
!Good edos
!Good edos
Line 581: Line 629:
!Notes
!Notes
|-
|-
|44/35
|55/54
|396.2
|0
|6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106
|31.8
|valinorsmic narrow major third
|35, 36, 37, 38, 39, 40, 75, 76, 113, 151
|
|undecimal diesis
|See [[Eleventyfive]] temperament.
|-
|-
|66/35
|11/10
|1098.1
|2
|12, 23, 24, 35, 36, 47, 59, 106
|165
|undecimal major seventh
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|undecimal submajor second
|
|
|-
|-
|35/33
|25/22
|101.9
|3
|12, 23, 24, 35, 36, 47, 59, 106
|221.3
|undecimal semitone
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|undecimal supermajor second
|
|
|-
|-
|33/28
|33/25
|284.4
|6
|17, 21, 25, 34, 38, 42, 59, 76, 135, 173
|480.6
|undecimal neominor third
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|undecimal subfourth
|
|-
|15/11
|7
|537
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|undecimal superfourth
|
|-
|22/15
|8
|663
|9, 18, 20, 27, 29, 38, 47, 67, 76, 181
|undecimal subfifth
|
|-
|50/33
|9
|719.4
|5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
|undecimal superfifth
|
|
|-
|-
|21/11
|33/20
|1119.5
|11
|867
|11, 18, 25, 29, 36, 47, 54, 191
|undecimal submajor sixth
|
|-
|44/25
|12
|978.7
|11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141
|undecimal subminor seventh
|
|-
|20/11
|13
|1035
|7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240
|undecimal supraminor seventh
|
|}
 
=== 2...11 ===
{| class="wikitable"
!Ratio
!Cents
!Good edos
!Name
!Notes
|-
|22/21
|80.5
|14, 15, 29, 30, 31, 44, 45, 60, 149, 164
|undecimal neominor second
|
|-
|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
|
|-
|44/35
|396.2
|6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106
|valinorsmic narrow major third
|
|-
|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
|
|-
|66/35
|1098.1
|12, 23, 24, 35, 36, 47, 59, 106
|undecimal major seventh
|
|-
|21/11
|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
|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 ==
== 13-limit ==
 
=== 2.3.13 ===
{| class="wikitable"
!Ratio
!17edo
!Cents
!Good edos
!Name
!Notes
|-
|27/26
|1
|65.3
|18, 19, 36, 37, 38, 55, 92, 147
|small tridecimal subminor second
|
|-
|13/12
|2
|138.6
|9, 17, 26, 34, 35, 43, 52, 78
|large tridecimal supraminor 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 ultrafourth
|
|-
|13/9
|9
|636.6
|15, 17, 30, 32, 34, 49, 66, 115, 164
|tridecimal infrafifth
|
|-
|'''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
|small tridecimal submajor seventh
|
|-
|52/27
|16
|1134.7
|18, 19, 36, 37, 38, 55, 92, 147
|large tridecimal supermajor seventh
|
|}
 
=== 2.3.13/5 ===
{| class="wikitable"
!Ratio
!19edo
!Cents
!Good edos
!Name
!Notes
|-
|15/13
|4
|247.7
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|tridecimal inframinor third
|
|-
|13/10
|7
|454.2
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|tridecimal ultramajor third
|
|-
|20/13
|12
|745.8
|8, 16, 21, 24, 29, 37, 45, 66, 74, 214
|tridecimal inframinor sixth
|
|-
|26/15
|15
|952.3
|5, 19, 24, 29, 34, 39, 58, 63, 92, 218
|tridecimal ultramajor sixth
|
|}
 
=== 2.3.7.13 ===
{| class="wikitable"
!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 ===
=== 2...7.13 ===
Line 639: Line 929:
!Name
!Name
!Notes
!Notes
|-
|27/26
|65.3
|18, 19, 36, 37, 38, 55, 92, 147
|small tridecimal subminor second
|
|-
|-
|26/25
|26/25
Line 650: Line 934:
|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
|
|-
|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
|
|
|-
|-
Line 674: Line 946:
|5, 10, 15 ... 150, 155, 160
|5, 10, 15 ... 150, 155, 160
|tridecimal supermajor second
|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
|
|
|-
|-
Line 710: Line 952:
|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
|
|-
|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
|
|
|-
|-
Line 740: Line 958:
|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
|
|-
|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
|
|
|-
|-
Line 782: Line 970:
|13, 19, 26, 32, 38, 45, 64, 173
|13, 19, 26, 32, 38, 45, 64, 173
|tridecimal minor seventh
|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
|
|
|-
|-
Line 800: Line 976:
|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
|
|-
|52/27
|1134.7
|18, 19, 36, 37, 38, 55, 92, 147
|large tridecimal supermajor seventh
|
|
|}
|}
Line 1,725: Line 1,895:
|
|
|}
|}
{{Interval regions}}

Latest revision as of 10:24, 6 March 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
10/9 1 182.4 13, 20, 26, 33, 46, 79, 125, 250 grave 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 acute fourth
45/32 3 590.2 59, 61, 63, 122 classical narrow tritone
64/45 4 609.8 59, 61, 63, 122 classical wide tritone
40/27 4 680.4 7, 14, 16, 23, 30, 37, 44, 60, 67, 97, 194 grave 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 acute 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 classical chromatic semitone See Interclassical temperament.
27/25 1 133.2 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 acute minor second
75/64 1 274.6 13, 22, 26, 31, 35, 48, 70, 83, 118 classical subminor third Also an augmented second.
32/25 3 427.4 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 classical supermajor third Also a diminished fourth.
25/16 4 772.6 14, 17, 28, 31, 42, 45, 59, 73, 87, 146, 219, 292 classical subminor sixth
128/75 6 925.4 13, 22, 26, 31, 35, 48, 70, 83, 118 classical supermajor 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 See Semaphore temperament.
28/27 0 63.0 18, 19, 20, 37, 38, 39, 57, 76 septimal subminor second See Trienstonic temperament.
8/7 1 231.2 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 septimal supermajor second
7/6 1 266.9 9, 18, 27, 36, 45, 54, 63, 72 septimal subminor third
9/7 2 435.1 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal supermajor third
21/16 2 470.8 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal subfourth
32/21 3 729.2 5, 18, 23, 28, 33, 46, 51, 56, 79, 130, 209 septimal superfifth
14/9 3 764.9 11, 22, 25, 33, 36, 44, 47, 58, 69, 80, 91, 171 septimal subminor sixth
12/7 4 933.1 9, 18, 27, 36, 45, 54, 63, 72 septimal supermajor sixth
7/4 4 968.8 5, 21, 26, 31, 36, 52, 57, 83, 109, 218 harmonic seventh
27/14 5 1137.0 18, 19, 20, 37, 38, 39, 57, 76 septimal supermajor 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 septimal narrow limma
15/14 1 119.4 10, 20, 30, 31, 40, 50, 201 septimal wide chroma
35/32 1 155.1 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 septimal neutral second
28/25 2 196.2 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 septimal narrow whole tone
60/49 3 350.6 7, 17, 24, 31, 34, 41, 48, 65, 89 septimal artoneutral third
49/40 3 351.3 17, 24, 31, 34, 41, 58, 82 septimal tendoneutral third
63/50 4 400.1 6, 9, 12, 15, 18, ... 99, 102, 105 septimal narrow major third
35/27 3 449.3 8, 16, 24, 32, 40, 48, 56, 211 septimal ultramajor third
64/49 4 462.3 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 septimal tendo third
48/35 5 546.8 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 septimal neutral fourth
7/5 5 582.5 29, 31, 33, 35, 37, 68, 70, 103 septimal narrow tritone
10/7 5 617.5 29, 31, 33, 35, 37, 68, 70, 103 septimal wide tritone
35/24 5 653.2 11, 22, 24, 33, 35, 44, 46, 57, 68, 79, 90 septimal neutral fifth
49/32 6 737.7 13, 18, 26, 31, 39, 44, 52, 109, 122, 244 septimal arto sixth
54/35 7 750.7 8, 16, 24, 32, 40, 48, 56, 211 septimal inframinor sixth
100/63 6 799.9 6, 9, 12, 15, 18, ... 99, 102, 105 septimal wide minor sixth
25/14 8 1003.8 6, 12, 18, 24, 25, 30, 31, 37, 43, 49, 55, 61, 104, 159, 263 septimal wide minor seventh
64/35 9 1044.9 8, 15, 16, 23, 31, 39, 54, 62, 85, 116, 147, 294 septimal neutral seventh
35/18 9 1151.2 23, 24, 25, 26, 49, 50, 74, 123 septimal ultramajor seventh

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 neutral 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 ultrafourth
16/11 9 648.7 11, 13, 24, 26, 35, 37, 50, 61, 74, 111 undecimal infrafifth
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 neutral 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 undecimal submajor second
25/22 3 221.3 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 undecimal supermajor second
33/25 6 480.6 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 undecimal subfourth
15/11 7 537 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 undecimal superfourth
22/15 8 663 9, 18, 20, 27, 29, 38, 47, 67, 76, 181 undecimal subfifth
50/33 9 719.4 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 undecimal superfifth
33/20 11 867 11, 18, 25, 29, 36, 47, 54, 191 undecimal submajor sixth
44/25 12 978.7 11, 16, 22, 27, 32, 33, 38, 49, 65, 76, 103, 141 undecimal subminor seventh
20/11 13 1035 7, 15, 22, 29, 36, 44, 51, 58, 80, 160, 240 undecimal supraminor seventh

2...11

Ratio Cents Good edos Name Notes
22/21 80.5 14, 15, 29, 30, 31, 44, 45, 60, 149, 164 undecimal neominor second
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
44/35 396.2 6, 9, 12, 15, 18, 21, 24, 27, 30, 103, 106 valinorsmic narrow major third
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
66/35 1098.1 12, 23, 24, 35, 36, 47, 59, 106 undecimal major seventh
21/11 1119.5 14, 15, 29, 30, 31, 44, 45, 60, 149, 164 undecimal neomajor 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 small tridecimal subminor second
13/12 2 138.6 9, 17, 26, 34, 35, 43, 52, 78 large tridecimal supraminor 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 ultrafourth
13/9 9 636.6 15, 17, 30, 32, 34, 49, 66, 115, 164 tridecimal infrafifth
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 small tridecimal submajor seventh
52/27 16 1134.7 18, 19, 36, 37, 38, 55, 92, 147 large tridecimal supermajor seventh

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 tridecimal inframinor third
13/10 7 454.2 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 tridecimal ultramajor third
20/13 12 745.8 8, 16, 21, 24, 29, 37, 45, 66, 74, 214 tridecimal inframinor sixth
26/15 15 952.3 5, 19, 24, 29, 34, 39, 58, 63, 92, 218 tridecimal ultramajor 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 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
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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