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{{Infobox ADO|steps=12}}
{{Infobox AFDO|steps=12}}
'''12ado''' is the [[ADO|arithmetic equal division of the octave]] into twelve parts of 1/12 each. 12ado is a subset of the esoteric [[Factor 9 grid]] temperament connected to "A = 432 Hz" conspiracy.
 
'''12afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''12odo''' ([[otonal division]] of the octave), divides the octave into twelve parts of 1/12 each. It is a superset of [[11afdo]] and a subset of [[13afdo]]. As a scale it may be known as [[Harmonic mode|mode 12 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-12]] scale.  


== Intervals ==
== Intervals ==
Line 103: Line 104:
|}
|}


[[Category:ADO]]
== 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).
 
{| class="wikitable"
|-
| |
| | 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.
 
== 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
 
…
 
== Scala file ==
Useable in [[Scala]] and any software/hardware supporting it.
<pre>
! harm24.scl
!
Harmonics 12 to 24
! Also known as otones12-24                                                           
12
!
13/12
7/6
5/4
4/3
17/12
3/2
19/12
5/3
7/4
11/6
23/12
2/1
</pre>
 
== Scales ==
* Forrest Cahoon's Sevens [[tetrachord]]: 14/12–18/12–21/12–24/12
* Septimal minor pentatonic: 14/12-16/12-18/12-21/12-24/12
* [[Lou Harrison]]'s "Kyai Gunter Sari [[pelog]]": 13/12–14/12–17/12–18/12–19/12–21/12–24/12
 
== Music ==
; [[Andrew Heathwaite]]
* [https://soundclick.com/share?songid=8839059 ''ant lizard dragon man''] (arranged & recorded 2010) – 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.
 
; [[Forrest Cahoon]]
* [https://soundcloud.com/fcahoon/the-sevens ''The Sevens''] (2012) – uses the Sevens tetrachord
 
{{Todo| cleanup }}
 
[[Category:Pages with Scala files]]
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