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| A dedecatonic (12-note) [[harm24|scale]] borrowed from the [[harmonic series]], also known as harm24:
| | #redirect [[12afdo]] |
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| 12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12, 20/12, 21/12, 22/12, 23/12, 24/12
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| which reduces to:
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| 1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1
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| in cents:
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| 0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200
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| Intervals between adjacent steps gradually get smaller, as is expected for harmonic chunks like this:
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| 13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23
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| in cents:
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| 139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74
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| ==modes==
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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).
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| {| class="wikitable"
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| |-
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| | | C-12
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| | | C#-13
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| | | D-14
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| | | D#-15
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| | | E-16
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| | | F-17
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| | | F#-18
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| | | G-19
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| | | G#-20
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| | | A-21
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| | | A#-22
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| | | B-23
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| |-
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| | | C-12
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| | | 0
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| | | 139
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| | | 267
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| | | 386
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| | | 498
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| | | 603
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| | | 702
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| | | 796
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| | | 884
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| | | 969
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| | | 1049
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| | | 1126
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| |-
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| | | C#-13
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| | | 1061
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| | | 0
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| | | 128
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| | | 248
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| | | 359
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| | | 464
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| | | 563
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| | | 657
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| | | 746
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| | | 830
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| | | 911
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| | | 988
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| |-
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| | | D-14
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| | | 933
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| | | 1072
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| | | 0
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| | | 119
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| | | 231
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| | | 336
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| | | 435
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| | | 529
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| | | 617
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| | | 702
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| | | 782
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| | | 859
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| |-
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| | | D#-15
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| | | 814
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| | | 952
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| | | 1081
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| | | 0
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| | | 112
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| | | 217
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| | | 316
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| | | 409
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| | | 498
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| | | 583
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| | | 663
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| | | 740
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| |-
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| | | E-16
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| | | 702
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| | | 841
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| | | 969
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| | | 1088
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| | | 0
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| | | 105
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| | | 204
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| | | 298
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| | | 386
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| | | 471
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| | | 551
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| | | 628
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| |-
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| | | F-17
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| | | 597
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| | | 736
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| | | 864
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| | | 983
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| | | 1095
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| | | 0
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| | | 99
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| | | 193
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| | | 281
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| | | 366
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| | | 446
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| | | 523
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| |-
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| | | F#-18
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| | | 498
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| | | 637
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| | | 765
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| | | 884
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| | | 996
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| | | 1101
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| | | 0
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| | | 94
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| | | 182
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| | | 267
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| | | 347
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| | | 424
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| |-
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| | | G-19
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| | | 404
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| | | 543
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| | | 671
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| | | 791
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| | | 902
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| | | 1007
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| | | 1106
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| | | 0
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| | | 89
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| | | 173
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| | | 254
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| | | 331
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| |-
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| | | G#-20
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| | | 316
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| | | 454
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| | | 583
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| | | 702
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| | | 814
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| | | 919
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| | | 1018
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| | | 1111
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| | | 0
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| | | 84
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| | | 165
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| | | 242
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| |-
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| | | A-21
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| | | 231
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| | | 370
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| | | 498
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| | | 617
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| | | 729
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| | | 834
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| | | 933
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| | | 1027
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| | | 1116
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| | | 0
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| | | 81
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| | | 157
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| |-
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| | | A#-22
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| | | 151
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| | | 289
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| | | 418
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| | | 537
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| | | 649
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| | | 754
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| | | 853
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| | | 946
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| | | 1035
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| | | 1119
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| | | 0
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| | | 77
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| |-
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| | | B-23
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| | | 74
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| | | 212
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| | | 341
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| | | 460
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| | | 572
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| | | 677
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| | | 776
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| | | 869
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| | | 958
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| | | 1043
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| | | 1123
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| | | 0
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| |}
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| 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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| ==Compositions==
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| [https://soundclick.com/share?songid=8839059 ant lizard dragon man], original song by Threshold of Pain, words by Scott Marshall (2006). This recording is an arrangement for otonal organ, otonal dulcimer, hand claps, and voice by Andrew Heathwaite in otones 12-24 (arranged & recorded 2010).
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| ==Inventory of intervals from 0 to 1200 cents:==
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| 0 - 1/1 - ...
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| 74 - 24/23 - B-C
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| 77 - 23/22 - A#-B
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| 81 - 22/21 - A-A#
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| 84 - 21/20 - G#-A
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| 89 - 20/19 - G-G#
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| 94 - 19/18 - F#-G
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| 99 - 18/17 - F-F#
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| 105 - 17/16 - E-F
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| 112 - 16/15 - D#-E
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| 119 - 15/14 - D-D#
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| 128 - 14/13 - C#-D
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| 139 - 13/12 - C-C#
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| 151 - 12/11 - A#-C
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| 157 - 23/21 - A-B
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| 165 - 11/10 - A#-B#
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| 173 - 21/19 - G-A
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| 182 - 10/9 - F#-G#
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| 193 - 19/17 - F-G
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| 204 - 9/8 - E-F#
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| 212 - 26/23 - B-C#
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| 217 - 17/15 - D#-F
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| 231 - 8/7 - D-E ; A-C
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| 242 - 23/20 - G#-B
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| 248 - 15/13 - C#-D#
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| 254 - 22/19 - G-A#
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| 267 - 7/6 - C-D ; F#-A
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| 281 - 20/17 - F-G#
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| 289 - 13/11 - A#-C#
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| 316 - 6/5 - D#-F# ; G#-C
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| 331 - 23/19 - G-B
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| 336 - 17/14 - D-F
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| 347 - 11/9 - F#-A#
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| 359 - 16/13 - C#-E
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| 366 - 21/17 - F-A
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| 370 - 26/21 - A-C#
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| 386 - 5/4 - C-D# ; E-G#
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| 404 - 24/19 - G-C
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| 409 - 19/15 - D#-G
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| 418 - 14/11 - A#-D
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| 424 - 23/18 - F#-B
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| 435 - 9/7 - D-F#
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| 446 - 22/17 - F-A#
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| 454 - 13/10 - G#-C#
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| 460 - 30/23 - B-D#
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| 464 - 17/13 - C#-F
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| 471 - 21/16 - E-A
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| 498 - 4/3 - C-E ; D#-G# ; F#-C ; A-D
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| 523 - 23/17 - F-B
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| 529 - 19/14 - D-G
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| 537 - 15/11 - A#-D#
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| 543 - 26/19 - G-C#
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| 551 - 11/8 - E-A
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| 563 - 18/13 - C#-F#
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| 572 - 32/23 - B-E
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| 583 - 7/5 - D#-A ; G#-D
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| 597 - 24/17 - F-C
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| 603 - 17/12 - C-F
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| 617 - 10/7 - D-G# ; A-D#
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| 628 - 23/16 - E-B
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| 637 - 13/9 - F#-C#
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| 649 - 16/11 - A-E
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| 657 - 19/13 - C#-G
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| 663 - 22/15 - D#-A#
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| 671 - 28/19 - G-D
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| 677 - 34/23 - B-F
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| ...
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| [[Category:12-tone scales]]
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| [[Category:Overtone]]
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| [[Category:Harmonic series]]
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| [[Category:AFDO]]
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| [[Category:Tables]] | |