The 16 most stable triads of 22edo: Difference between revisions

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Line 11: Line 11:
!Size in cents
!Size in cents
!Ratios approximated
!Ratios approximated
!Stability
|-
|-
|1
|1
Line 17: Line 18:
|382-709
|382-709
|5/4, 6/5, 4/3, 4:5:6
|5/4, 6/5, 4/3, 4:5:6
|0
|-
|-
|2
|2
Line 23: Line 25:
|491-709
|491-709
|4/3, 8/7, 4/3, 6:8:9
|4/3, 8/7, 4/3, 6:8:9
|
|-0.34
|-0.34
|-
|-
Line 30: Line 33:
|436-709
|436-709
|9/7, 7/6, 4/3, 14:18:21
|9/7, 7/6, 4/3, 14:18:21
|
|-0.40
|-0.40
|-
|-
Line 37: Line 41:
|327-709
|327-709
|6/5, 5/4, 4/3, 10:12:15
|6/5, 5/4, 4/3, 10:12:15
|
|-0.53
|-0.53
|-
|-
Line 44: Line 49:
|709-982
|709-982
|3/2, 7/6, 8/7, 4:6:7
|3/2, 7/6, 8/7, 4:6:7
|
|-0.53
|-0.53
|-
|-
Line 51: Line 57:
|273-982
|273-982
|7/6, 3/2, 8/7, 12:14:21
|7/6, 3/2, 8/7, 12:14:21
|
|-0.71
|-0.71
|-
|-
Line 58: Line 65:
|382-1082
|382-1082
|5/4, 3/2, 15/14, 8:10:15
|5/4, 3/2, 15/14, 8:10:15
|
|-0.78
|-0.78
|-
|-
Line 65: Line 73:
|382-655
|382-655
|5/4, 7/6, 11/8, 24:30:35
|5/4, 7/6, 11/8, 24:30:35
|
|-0.84
|-0.84
|-
|-
Line 72: Line 81:
|327-600
|327-600
|6/5, 7/6, 7/5, 5:6:7
|6/5, 7/6, 7/5, 5:6:7
|
|-0.86
|-0.86
|-
|-
Line 79: Line 89:
|382-982
|382-982
|5/4, 7/5, 8/7, 4:5:7
|5/4, 7/5, 8/7, 4:5:7
|
|-0.96
|-0.96
|-
|-
Line 86: Line 97:
|218-382
|218-382
|8/7, 10/9, 8/5,  8:9:10
|8/7, 10/9, 8/5,  8:9:10
|
|-0.99
|-0.99
|-
|-
Line 93: Line 105:
|273-709
|273-709
|7/6, 9/7, 4/3, 6:7:9
|7/6, 9/7, 4/3, 6:7:9
|
|-1.03
|-1.03
|-
|-
Line 100: Line 113:
|382-600
|382-600
|5/4, 8/7, 7/5, 12:15:17
|5/4, 8/7, 7/5, 12:15:17
|
|-1.06
|-1.06
|-
|-
Line 107: Line 121:
|382-765
|382-765
|5/4, 5/4, 9/7, 16:20:25
|5/4, 5/4, 9/7, 16:20:25
|
|-1.08
|-1.08
|-
|-
Line 114: Line 129:
|327-1036
|327-1036
|6/5, 3/2, 10/9, 5:6:9
|6/5, 3/2, 10/9, 5:6:9
|
|-1.09
|-1.09
|-
|-
Line 121: Line 137:
|709-1082
|709-1082
|3/2, 5/4, 15/14, 8:12:15
|3/2, 5/4, 15/14, 8:12:15
|
|-1.10}
|-1.10}
|}

Revision as of 12:11, 31 January 2021

The 16 most stable triads of 22-TET, from an empirical experiment, notated in Ups and Downs

Triads represent inversional equivalence classes and are written in normal form, with a root of zero. The second and third numbers in the triple represent the lower and outer intervals in degrees of 22-TET respectively. Triads are written in the inversion for which the outer interval is the smallest, and, in the case that two inversion have the same sized outer interval, that the lower interval is the smallest.

Click the triad for an audio sample

Rank Triad Name Size in cents Ratios approximated Stability
1 [0,7,13] Classic major triad 382-709 5/4, 6/5, 4/3, 4:5:6 0
2 [0,4,13] Suspended triad 491-709 4/3, 8/7, 4/3, 6:8:9
3 [0,8,13] Supermajor triad 436-709 9/7, 7/6, 4/3, 14:18:21
4 [0,6,13] Classic minor triad 327-709 6/5, 5/4, 4/3, 10:12:15
5 [0,5,9] Subminor seventh (no third) 709-982 3/2, 7/6, 8/7, 4:6:7
6 [0,4,9] Subminor seventh (no fifth) 273-982 7/6, 3/2, 8/7, 12:14:21
7 [0,2,9] Classic major seventh (no fifth) 382-1082 5/4, 3/2, 15/14, 8:10:15
8 [0,7,12] "Squished" major triad 382-655 5/4, 7/6, 11/8, 24:30:35
9 [0,6,11] Harmonic diminished triad 327-600 6/5, 7/6, 7/5, 5:6:7
10 [0,4,11] Harmonic dominant seventh (no fifth) 382-982 5/4, 7/5, 8/7, 4:5:7
11 [0,4,7] Classic major add 9 (no fifth) 218-382 8/7, 10/9, 8/5, 8:9:10
12 [0,5,13] Subminor triad 273-709 7/6, 9/7, 4/3, 6:7:9
13 [0,7,11] Classic major flat 5 382-600 5/4, 8/7, 7/5, 12:15:17
14 [0,7,14] Classic augmented triad 382-765 5/4, 5/4, 9/7, 16:20:25
15 [0,3,9] Classic minor seventh (no fifth) 327-1036 6/5, 3/2, 10/9, 5:6:9
16 [0,7,9] Classic major seventh (no third) 709-1082 3/2, 5/4, 15/14, 8:12:15
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