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For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. Thus, C = 1/1, C# = 13/12, etc. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, & follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2).
For your tuning pleasure, all 12 modes, arranged in a handy-dandy table. The following matrix uses a keyboard mapping that starts the scale on C. Thus, C = 1/1, C# = 13/12, etc. To find an interval, say the interval from C to F#, first find the lower pitch on the left, C, & follow it across the row to the column of the higher pitch, F# to find 702 cents. To find the name of the interval in just intonation, use the number of the higher pitch as the numerator (18) and the number of the lower pitch (12) as the denominator, then reduce (3/2).


{| class="wikitable"
{| class="wikitable right-all"
|-
|-
| |
! Note
| | C-12
! C–12
| | C#-13
! C#–13
| | D-14
! D–14
| | D#-15
! D#–15
| | E-16
! E–16
| | F-17
! F–17
| | F#-18
! F#–18
| | G-19
! G–19
| | G#-20
! G#–20
| | A-21
! A–21
| | A#-22
! A#–22
| | B-23
! B–23
|-
|-
| | C-12
! C–12
| | 0
| 0
| | 139
| 139
| | 267
| 267
| | 386
| 386
| | 498
| 498
| | 603
| 603
| | 702
| 702
| | 796
| 796
| | 884
| 884
| | 969
| 969
| | 1049
| 1049
| | 1126
| 1126
|-
|-
| | C#-13
! C#–13
| | 1061
| 1061
| | 0
| 0
| | 128
| 128
| | 248
| 248
| | 359
| 359
| | 464
| 464
| | 563
| 563
| | 657
| 657
| | 746
| 746
| | 830
| 830
| | 911
| 911
| | 988
| 988
|-
|-
| | D-14
! D–14
| | 933
| 933
| | 1072
| 1072
| | 0
| 0
| | 119
| 119
| | 231
| 231
| | 336
| 336
| | 435
| 435
| | 529
| 529
| | 617
| 617
| | 702
| 702
| | 782
| 782
| | 859
| 859
|-
|-
| | D#-15
! D#–15
| | 814
| 814
| | 952
| 952
| | 1081
| 1081
| | 0
| 0
| | 112
| 112
| | 217
| 217
| | 316
| 316
| | 409
| 409
| | 498
| 498
| | 583
| 583
| | 663
| 663
| | 740
| 740
|-
|-
| | E-16
! E–16
| | 702
| 702
| | 841
| 841
| | 969
| 969
| | 1088
| 1088
| | 0
| 0
| | 105
| 105
| | 204
| 204
| | 298
| 298
| | 386
| 386
| | 471
| 471
| | 551
| 551
| | 628
| 628
|-
|-
| | F-17
! F–17
| | 597
| 597
| | 736
| 736
| | 864
| 864
| | 983
| 983
| | 1095
| 1095
| | 0
| 0
| | 99
| 99
| | 193
| 193
| | 281
| 281
| | 366
| 366
| | 446
| 446
| | 523
| 523
|-
|-
| | F#-18
! F#–18
| | 498
| 498
| | 637
| 637
| | 765
| 765
| | 884
| 884
| | 996
| 996
| | 1101
| 1101
| | 0
| 0
| | 94
| 94
| | 182
| 182
| | 267
| 267
| | 347
| 347
| | 424
| 424
|-
|-
| | G-19
! G–19
| | 404
| 404
| | 543
| 543
| | 671
| 671
| | 791
| 791
| | 902
| 902
| | 1007
| 1007
| | 1106
| 1106
| | 0
| 0
| | 89
| 89
| | 173
| 173
| | 254
| 254
| | 331
| 331
|-
|-
| | G#-20
! G#–20
| | 316
| 316
| | 454
| 454
| | 583
| 583
| | 702
| 702
| | 814
| 814
| | 919
| 919
| | 1018
| 1018
| | 1111
| 1111
| | 0
| 0
| | 84
| 84
| | 165
| 165
| | 242
| 242
|-
|-
| | A-21
! A–21
| | 231
| 231
| | 370
| 370
| | 498
| 498
| | 617
| 617
| | 729
| 729
| | 834
| 834
| | 933
| 933
| | 1027
| 1027
| | 1116
| 1116
| | 0
| 0
| | 81
| 81
| | 157
| 157
|-
|-
| | A#-22
! A#–22
| | 151
| 151
| | 289
| 289
| | 418
| 418
| | 537
| 537
| | 649
| 649
| | 754
| 754
| | 853
| 853
| | 946
| 946
| | 1035
| 1035
| | 1119
| 1119
| | 0
| 0
| | 77
| 77
|-
|-
| | B-23
! B–23
| | 74
| 74
| | 212
| 212
| | 341
| 341
| | 460
| 460
| | 572
| 572
| | 677
| 677
| | 776
| 776
| | 869
| 869
| | 958
| 958
| | 1043
| 1043
| | 1123
| 1123
| | 0
| 0
|}
|}
You can see that, due to the varying step sizes, this relatively small scale contains a large number of unique rational intervals up to the 23-limit.
You can see that, due to the varying step sizes, this relatively small scale contains a large number of unique rational intervals up to the 23-limit.


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== Scales ==
== Scales ==
* Forrest Cahoon's Sevens [[tetrachord]]: 14/12–18/12–21/12–24/12
* 12:13:14:17:18:19:21:24 [[Lou Harrison]]'s "Kyai Gunter Sari [[pelog]]"
* Septimal minor pentatonic: 14/12-16/12-18/12-21/12-24/12
* 12:14:16:18:21:24 Septimal minor pentatonic
* [[Lou Harrison]]'s "Kyai Gunter Sari [[pelog]]": 13/12–14/12–17/12–18/12–19/12–21/12–24/12
* 12:14:18:21:24 Forrest Cahoon's Sevens [[tetrachord]]


== Music ==
== Music ==
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