User:DesertFreeze/List of otonal chords
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Below is a series of justly-intonated chords represented otonally.
"With 3/2" denotes that the triads contain a 3/2 perfect fifth of ~702 ¢. In these tables, the fifth will not be explicitly listed, due to the redundancy of listing "3/2" over and over. "Tertian-based" means that the second note generally counts as a third (see Margo Schulter's interval regions). while "sus-based" denotes that the second note counts as a second or fourth, as in western sus triads.
Of course, the boundaries between second, third, and fourth are "fuzzy" as described by Margo Schulter, so subjectivity concerning interseptimal intervals such as 13/10 may arise. Editors are encouraged to add in their own viewpoints on this topic.
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Triads
| Otonal
representation |
JI ratios | ||||||
|---|---|---|---|---|---|---|---|
| Third (¢) | English triad name | Prime Limit | Steps | ||||
| 4:5:6 | 5/4 | 3/2 | 386.3 | Classic major | 5-limit | 5/4, 6/5, 4/3 | |
| 6:7:9 | 7/6 | 3/2 | 266.9 | Septimal subminor | 7-limit | 7/6, 9/7, 4/3 | |
| 10:12:15 | 6/5 | 3/2 | 315.6 | Classic minor | 5-limit | 6/5, 5/4, 4/3 | |
| 10:13:15 | 13/10 | 3/2 | 454.2 | Barbados / tridecimal ultramajor | 13-limit | 13/10, 15/13, 4/3 | |
| 14:17:21 | 17/14 | 3/2 | 336.1 | Septendecimal minor | 17-limit | 21/17, 17/14, 4/3 | |
| 14:18:21 | 9/7, | 3/2 | 435.1 | Septimal supermajor | 7-limit | 9/7, 7/6, 4/3 | |
| 16:19:24 | 19/16 | 3/2 | 297.5 | Undevicesimal minor/otonal minor | 19-limit | 19/16, 24/19, 4/3 | |
| 18:22:27 | 11/9 | 3/2 | 347.4 | Undecimal neutral/rastmic | 11-limit | 11/9, 27/22, 4/3 | |
| 18:23:27 | 23/18 | 3/2 | 424.4 | Vicesimotertial supermajor | 23-limit | 23/18, 27/23, 4/3 | |
| 20:23:30 | 23/20 | 3/2 | 242.0 | Vicesimotertial ultraminor | 23-limit | 23/20, 30/23, 4/3 | |
| 22:26:33 | 13/11 | 3/2 | 289.2 | 13-limit | 13/11, 33/26, 4/3 | ||
| 22:27:33 | 27/22 | 3/2 | 354.6 | Neutral / Rastmic | 11-limit | 27/22, 11/9, 4/3 | |
| 22:28:33 | 14/11 | 3/2 | 417.5 | 11-limit | 14/11, 33/28, 4/3 | ||
| 24:29:36 | 29/24 | 3/2 | 327.6 | 29-limit | 29/24, 36/29, 4/3 | ||
| 24:31:36 | 31/24 | 3/2 | 443.1 | 31-limit | |||
| Otonal reps. | 2nd/4th (JI) | (¢) | English triad name | Prime Limit | Steps |
|---|---|---|---|---|---|
| 6:8:9 | 4/3, 3/2 | 498.0 | Pythagorean sus4 | 3-limit | 4/3, 9/8 |
| 8:9:12 | 9/8, 3/2 | 203.9 | Pythagorean sus2 | 3-limit | 9/8, 4/3 |
| 8:11:12 | 11/8, 3/2 | 551.3 | Undecimal sus4 | 11-limit | 11/8, 12/11 |
| 10:11:15 | 11/10, 3/2 | 165.0 | Undecimal sus2 | 11-limit | 11/10, 15/11 |
| 12:13:18 | 13/12, 3/2 | 138.6 | Tridecimal sus2 | 13-limit | 13/12, 18/13 |
| 14:16:21 | 8/7, 3/2 | 231.2 | Septimal sus2 | 7-limit | |
| 14:19:21 | 19/14, 3/2 | 528.9 | Device sus4 | 19-limit |
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Todo: expand, add audios |