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 ( | [[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) | ||
{| class="wikitable" | {| class="wikitable" | ||
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|- | |- | ||
|7 | |7 | ||
|[0,2,9] | |[https://www.dropbox.com/s/o47pctm9f36ezo5/7.aif?dl=0 <nowiki>[0,2,9]</nowiki>] | ||
|Classic major seventh (no fifth) | |Classic major seventh (no fifth) | ||
|382 | |382 | ||
| Line 66: | Line 66: | ||
|- | |- | ||
|8 | |8 | ||
|[0,7,12] | |[https://www.dropbox.com/s/bprlfpy2f5pdepf/8.aif?dl=0 <nowiki>[0,7,12]</nowiki>] | ||
|"Squished" major triad | |"Squished" major triad | ||
|382 | |382 | ||
| Line 74: | Line 74: | ||
|- | |- | ||
|9 | |9 | ||
|[0,6,11] | |[https://www.dropbox.com/s/g9jt3n34vhbpxzb/9.aif?dl=0 <nowiki>[0,6,11]</nowiki>] | ||
|Harmonic diminished triad | |Harmonic diminished triad | ||
|327 | |327 | ||
| Line 82: | Line 82: | ||
|- | |- | ||
|10 | |10 | ||
|[0,4,11] | |[https://www.dropbox.com/s/smlmcqgm8tw83qn/10.aif?dl=0 <nowiki>[0,4,11]</nowiki>] | ||
|Harmonic dominant seventh (no fifth) | |Harmonic dominant seventh (no fifth) | ||
|382 | |382 | ||
| Line 90: | Line 90: | ||
|- | |- | ||
|11 | |11 | ||
|[0,4,7] | |[https://www.dropbox.com/sh/5fg5v76hsvhmbr3/AAB4Ww-MlDTw__FcmE5_9XXEa?dl=0 <nowiki>[0,4,7]</nowiki>] | ||
|Classic major add 9 (no fifth) | |Classic major add 9 (no fifth) | ||
|218 | |218 | ||
| Line 98: | Line 98: | ||
|- | |- | ||
|12 | |12 | ||
|[0,5,13] | |[https://www.dropbox.com/s/z6ck2n622w0s0mt/11.aif?dl=0 <nowiki>[0,5,13]</nowiki>] | ||
|Subminor triad | |Subminor triad | ||
|273 | |273 | ||
| Line 114: | Line 114: | ||
|- | |- | ||
|14 | |14 | ||
|[0,7,14] | |[https://www.dropbox.com/s/48w3q0poo3v2ylo/13.aif?dl=0 <nowiki>[0,7,14]</nowiki>] | ||
|Classic augmented triad | |Classic augmented triad | ||
|382 | |382 | ||
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|- | |- | ||
|15 | |15 | ||
|[0,3,9] | |[https://www.dropbox.com/s/m6m6a1qmsj22g6z/15.aif?dl=0 <nowiki>[0,3,9]</nowiki>] | ||
|Classic minor seventh (no fifth) | |Classic minor seventh (no fifth) | ||
|327 | |327 | ||
Revision as of 09:36, 9 May 2021
Click the triad for an audio sample (tbc)
| 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 |