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 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. Triples describe 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 are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample (tbc)
[[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. Triples describe 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 are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes]]Click the triad for an audio sample
{| class="wikitable"
{| class="wikitable"
|+
|+
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|-
|2
|2
|[https://www.dropbox.com/s/gw3zd7teif6klo6/3.aif?dl=0 <nowiki>[0,4,13]</nowiki>]
|[https://www.dropbox.com/s/gw3zd7teif6klo6/2.aif?dl=0 <nowiki>[0,4,13]</nowiki>]
|Suspended triad
|Suspended triad
|491
|491
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|-
|3
|3
|[https://www.dropbox.com/s/rw9vbpsbrcveak0/2.aif?dl=0 <nowiki>[0,8,13]</nowiki>]
|[https://www.dropbox.com/s/rw9vbpsbrcveak0/3.aif?dl=0 <nowiki>[0,8,13]</nowiki>]
|Supermajor triad
|Supermajor triad
|436
|436
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|Classic major seventh (no fifth)
|Classic major seventh (no fifth)
|382
|382
1082
1091
|5/4, 3/2, 15/14, 8:10:15
|5/4, 3/2, 15/14, 8:10:15
|0.78
|0.78
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|-
|11
|11
|[https://www.dropbox.com/sh/5fg5v76hsvhmbr3/AAB4Ww-MlDTw__FcmE5_9XXEa?dl=0 <nowiki>[0,4,7]</nowiki>]
|[https://www.dropbox.com/s/0tk5wn3ac4gjv7f/11.aif?dl=0 <nowiki>[0,4,7]</nowiki>]
|Classic major add 9 (no fifth)
|Classic major add 9 (no fifth)
|218
|218
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|-
|-
|12
|12
|[https://www.dropbox.com/s/z6ck2n622w0s0mt/11.aif?dl=0 <nowiki>[0,5,13]</nowiki>]
|[https://www.dropbox.com/s/z6ck2n622w0s0mt/12.aif?dl=0 <nowiki>[0,5,13]</nowiki>]
|Subminor triad
|Subminor triad
|273
|273
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|-
|-
|13
|13
|[0,7,11]
|[https://www.dropbox.com/s/e0skc9cg2ilmk7h/triad13.aif?dl=0 <nowiki>[0,7,11]</nowiki>]
|Classic major flat 5
|Classic major flat 5
|382
|382
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|-
|-
|14
|14
|[https://www.dropbox.com/s/48w3q0poo3v2ylo/13.aif?dl=0 <nowiki>[0,7,14]</nowiki>]
|[https://www.dropbox.com/s/48w3q0poo3v2ylo/14.aif?dl=0 <nowiki>[0,7,14]</nowiki>]
|Classic augmented triad
|Classic augmented triad
|382
|382
765
764
|5/4, 5/4, 9/7, 16:20:25
|5/4, 5/4, 9/7, 16:20:25
|1.08
|1.08
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|-
|16
|16
|[0,7,9]
|[https://www.dropbox.com/s/f31k6asri0qqec1/triad16.aif?dl=0 <nowiki>[0,7,9]</nowiki>]
|Classic major seventh (no third)
|Classic major seventh (no third)
|709
|709
1082
1091
|3/2, 5/4, 15/14, 8:12:15
|3/2, 5/4, 15/14, 8:12:15
|1.10
|1.10

Latest revision as of 01:07, 20 August 2025

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. Triples describe 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 are notated in root position [Note: The inversion of triads are notated in does not always match the inversion their normal form most immediately describes

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

1091

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

764

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

1091

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