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

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[[File:16 most stable triads.png|thumb|611x611px|The 16 most stable triads of 22-TET, from an empirical experiment, notated in [[Ups and Downs Notation|Ups and Downs]]]]
[[File:16 most stable triads.png|thumb|611x611px|The 16 most stable triads of 22-TET, from empirical data, notated in [[Ups and Downs Notation|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.]]]]
 
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
Click the triad for an audio sample
Line 24: Line 22:
|[0,4,13]
|[0,4,13]
|Suspended triad
|Suspended triad
|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 38: Line 37:
|[0,6,13]
|[0,6,13]
|Classic minor triad
|Classic minor triad
|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 45: Line 45:
|[0,5,9]
|[0,5,9]
|Subminor seventh (no third)
|Subminor seventh (no third)
|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 52: Line 53:
|[0,4,9]
|[0,4,9]
|Subminor seventh (no fifth)
|Subminor seventh (no fifth)
|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 59: Line 61:
|[0,2,9]
|[0,2,9]
|Classic major seventh (no fifth)
|Classic major seventh (no fifth)
|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 66: Line 69:
|[0,7,12]
|[0,7,12]
|"Squished" major triad
|"Squished" major triad
|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 73: Line 77:
|[0,6,11]
|[0,6,11]
|Harmonic diminished triad
|Harmonic diminished triad
|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 80: Line 85:
|[0,4,11]
|[0,4,11]
|Harmonic dominant seventh (no fifth)
|Harmonic dominant seventh (no fifth)
|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 87: Line 93:
|[0,4,7]
|[0,4,7]
|Classic major add 9 (no fifth)
|Classic major add 9 (no fifth)
|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 94: Line 101:
|[0,5,13]
|[0,5,13]
|Subminor triad
|Subminor triad
|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 101: Line 109:
|[0,7,11]
|[0,7,11]
|Classic major flat 5
|Classic major flat 5
|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 108: Line 117:
|[0,7,14]
|[0,7,14]
|Classic augmented triad
|Classic augmented triad
|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 115: Line 125:
|[0,3,9]
|[0,3,9]
|Classic minor seventh (no fifth)
|Classic minor seventh (no fifth)
|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 122: Line 133:
|[0,7,9]
|[0,7,9]
|Classic major seventh (no third)
|Classic major seventh (no third)
|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 12:16, 31 January 2021

The 16 most stable triads of 22-TET, from empirical data, 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 Relative Instability
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 0.34
3 [0,8,13] Supermajor triad 436-709 9/7, 7/6, 4/3, 14:18:21 0.40
4 [0,6,13] Classic minor triad 327

709

6/5, 5/4, 4/3, 10:12:15 0.53
5 [0,5,9] Subminor seventh (no third) 709

982

3/2, 7/6, 8/7, 4:6:7 0.53
6 [0,4,9] Subminor seventh (no fifth) 273

982

7/6, 3/2, 8/7, 12:14:21 0.71
7 [0,2,9] Classic major seventh (no fifth) 382

1082

5/4, 3/2, 15/14, 8:10:15 0.78
8 [0,7,12] "Squished" major triad 382

655

5/4, 7/6, 11/8, 24:30:35 0.84
9 [0,6,11] Harmonic diminished triad 327

600

6/5, 7/6, 7/5, 5:6:7 0.86
10 [0,4,11] Harmonic dominant seventh (no fifth) 382

982

5/4, 7/5, 8/7, 4:5:7 0.96
11 [0,4,7] Classic major add 9 (no fifth) 218

382

8/7, 10/9, 8/5, 8:9:10 0.99
12 [0,5,13] Subminor triad 273

709

7/6, 9/7, 4/3, 6:7:9 1.03
13 [0,7,11] Classic major flat 5 382

600

5/4, 8/7, 7/5, 12:15:17 1.06
14 [0,7,14] Classic augmented triad 382

765

5/4, 5/4, 9/7, 16:20:25 1.08
15 [0,3,9] Classic minor seventh (no fifth) 327

1036

6/5, 3/2, 10/9, 5:6:9 1.09
16 [0,7,9] Classic major seventh (no third) 709

1082

3/2, 5/4, 15/14, 8:12:15 1.10
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