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A dedecatonic (12-note) scale borrowed from the overtone series, also known as harm24:

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

which reduces to:

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
in cents:
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200

Intervals between adjacent steps gradually get smaller, as is expected for overtone chunks like this:

13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23
in cents:
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74

modes


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).


C-12
C#-13
D-14
D#-15
E-16
F-17
F#-18
G-19
G#-20
A-21
A#-22
B-23
C-12
0
139
267
386
498
603
702
796
884
969
1049
1126
C#-13
1061
0
128
248
359
464
563
657
746
830
911
988
D-14
933
1072
0
119
231
336
435
529
617
702
782
859
D#-15
814
952
1081
0
112
217
316
409
498
583
663
740
E-16
702
841
969
1088
0
105
204
298
386
471
551
628
F-17
597
736
864
983
1095
0
99
193
281
366
446
523
F#-18
498
637
765
884
996
1101
0
94
182
267
347
424
G-19
404
543
671
791
902
1007
1106
0
89
173
254
331
G#-20
316
454
583
702
814
919
1018
1111
0
84
165
242
A-21
231
370
498
617
729
834
933
1027
1116
0
81
157
A#-22
151
289
418
537
649
754
853
946
1035
1119
0
77
B-23
74
212
341
460
572
677
776
869
958
1043
1123
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.

Compositions

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).

Inventory of intervals from 0 to 1200 cents:


0 - 1/1 - ...
74 - 24/23 - B-C
77 - 23/22 - A#-B
81 - 22/21 - A-A#
84 - 21/20 - G#-A
89 - 20/19 - G-G#
94 - 19/18 - F#-G
99 - 18/17 - F-F#
105 - 17/16 - E-F
112 - 16/15 - D#-E
119 - 15/14 - D-D#
128 - 14/13 - C#-D
139 - 13/12 - C-C#
151 - 12/11 - A#-C
157 - 23/21 - A-B
165 - 11/10 - A#-B#
173 - 21/19 - G-A
182 - 10/9 - F#-G#
193 - 19/17 - F-G
204 - 9/8 - E-F#
212 - 26/23 - B-C#
217 - 17/15 - D#-F
231 - 8/7 - D-E ; A-C
242 - 23/20 - G#-B
248 - 15/13 - C#-D#
254 - 22/19 - G-A#
267 - 7/6 - C-D ; F#-A
281 - 20/17 - F-G#
289 - 13/11 - A#-C#
316 - 6/5 - D#-F# ; G#-C
331 - 23/19 - G-B
336 - 17/14 - D-F
347 - 11/9 - F#-A#
359 - 16/13 - C#-E
366 - 21/17 - F-A
370 - 26/21 - A-C#
386 - 5/4 - C-D# ; E-G#
404 - 24/19 - G-C
409 - 19/15 - D#-G
418 - 14/11 - A#-D
424 - 23/18 - F#-B
435 - 9/7 - D-F#
446 - 22/17 - F-A#
454 - 13/10 - G#-C#
460 - 30/23 - B-D#
464 - 17/13 - C#-F
471 - 21/16 - E-A
498 - 4/3 - C-E ; D#-G# ; F#-C ; A-D
523 - 23/17 - F-B
529 - 19/14 - D-G
537 - 15/11 - A#-D#
543 - 26/19 - G-C#
551 - 11/8 - E-A
563 - 18/13 - C#-F#
572 - 32/23 - B-E
583 - 7/5 - D#-A ; G#-D
597 - 24/17 - F-C

603 - 17/12 - C-F
617 - 10/7 - D-G# ; A-D#
628 - 23/16 - E-B
637 - 13/9 - F#-C#
649 - 16/11 - A-E
657 - 19/13 - C#-G
663 - 22/15 - D#-A#
671 - 28/19 - G-D
677 - 34/23 - B-F
...