Chords of superpyth
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Below are listed the 11-odd-limit dyadic chords of 11-limit superpyth temperament. Typing the chords requires consideration of the fact that superpyth conflates 9/8 with 8/7, and 11/10 with 10/9. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9.
Chords essentially tempered by 64/63 are labeled archytas, by 100/99 ptolemismic, by 176/175 valinorsmic, by 245/243 sensamagic, by 540/539 swetismic. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked ares. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked octarod. Chords that require 176/175 and 540/539 tempering are marked guanyin.
Triads
| # | Transversal | Type | Complexity |
|---|---|---|---|
| 1 | 1–9/8–3/2 | ambitonal | 2 |
| 2 | 1–3/2–12/7 | utonal | 3 |
| 3 | 1–8/7–12/7 | otonal | 3 |
| 4 | 1–9/7–3/2 | utonal | 4 |
| 5 | 1–8/7–9/7 | ambitonal | 4 |
| 6 | 1–9/7–12/7 | otonal | 4 |
| 7 | 1–10/9–12/7 | sensamagic | 7 |
| 8 | 1–10/9–9/7 | sensamagic | 7 |
| 9 | 1–3/2–5/3 | otonal | 8 |
| 10 | 1–9/7–5/3 | sensamagic | 8 |
| 11 | 1–10/9–5/3 | utonal | 8 |
| 12 | 1–5/4–3/2 | otonal | 9 |
| 13 | 1–9/8–5/4 | otonal | 9 |
| 14 | 1–10/9–5/4 | utonal | 9 |
| 15 | 1–5/4–5/3 | utonal | 9 |
| 16 | 1–8/7–10/7 | ||
| 17 | 1–12/7–10/7 | ||
| 18 | 1–9/7–10/7 | ||
| 19 | 1–10/9–10/7 | ||
| 20 | 1–5/3–10/7 | ||
| 21 | 1–5/4–10/7 | ||
| 22 | 1–12/7–11/9 | ||
| 23 | 1–10/9–11/9 | ||
| 24 | 1–10/7–11/9 | ||
| 25 | 1–3/2–11/6 | ||
| 26 | 1–9/7–11/6 | ||
| 27 | 1–10/9–11/6 | ||
| 28 | 1–5/3–11/6 | ||
| 29 | 1–10/7–11/6 | ||
| 30 | 1–11/9–11/6 | ||
| 31 | 1–3/2–11/8 | otonal | |
| 32 | 1–9/8–11/8 | otonal | |
| 33 | 1–11/10–11/8 | utonal | |
| 34 | 1–5/3–11/8 | ptolemismic | |
| 35 | 1–5/4–11/8 | otonal | |
| 36 | 1–11/9–11/8 | utonal | |
| 37 | 1–11/6–11/8 | utonal | |
| 38 | 1–8/7–11/7 | ||
| 39 | 1–12/7–11/7 | ||
| 40 | 1–9/7–11/7 | ||
| 41 | 1–10/9–11/7 | ||
| 42 | 1–5/4–11/7 | ||
| 43 | 1–10/7–11/7 | ||
| 44 | 1–11/9–11/7 | ||
| 45 | 1–11/6–11/7 | ||
| 46 | 1–11/8–11/7 |
Tetrads
| # | Transversal | Type | Complexity |
|---|---|---|---|
| 1 | 1–3/2–8/7–12/7 | ||
| 2 | 1–3/2–8/7–9/7 | ||
| 3 | 1–3/2–12/7–9/7 | ||
| 4 | 1–8/7–12/7–9/7 | ||
| 5 | 1–12/7–9/7–10/9 | ||
| 6 | 1–3/2–9/7–5/3 | ||
| 7 | 1–9/7–10/9–5/3 | ||
| 8 | 1–3/2–8/7–5/4 | ||
| 9 | 1–3/2–5/3–5/4 | ||
| 10 | 1–10/9–5/3–5/4 | ||
| 11 | 1–8/7–12/7–10/7 | ||
| 12 | 1–8/7–9/7–10/7 | ||
| 13 | 1–12/7–9/7–10/7 | ||
| 14 | 1–12/7–10/9–10/7 | ||
| 15 | 1–9/7–10/9–10/7 | ||
| 16 | 1–9/7–5/3–10/7 | ||
| 17 | 1–10/9–5/3–10/7 | ||
| 18 | 1–8/7–5/4–10/7 | ||
| 19 | 1–10/9–5/4–10/7 | ||
| 20 | 1–5/3–5/4–10/7 | ||
| 21 | 1–12/7–10/9–11/9 | ||
| 22 | 1–12/7–10/7–11/9 | ||
| 23 | 1–10/9–10/7–11/9 | ||
| 24 | 1–3/2–9/7–11/6 | ||
| 25 | 1–9/7–10/9–11/6 | ||
| 26 | 1–3/2–5/3–11/6 | ||
| 27 | 1–9/7–5/3–11/6 | ||
| 28 | 1–10/9–5/3–11/6 | ||
| 29 | 1–9/7–10/7–11/6 | ||
| 30 | 1–10/9–10/7–11/6 | ||
| 31 | 1–5/3–10/7–11/6 | ||
| 32 | 1–10/9–11/9–11/6 | ||
| 33 | 1–10/7–11/9–11/6 | ||
| 34 | 1–3/2–8/7–11/8 | ||
| 35 | 1–3/2–5/3–11/8 | ||
| 36 | 1–10/9–5/3–11/8 | ||
| 37 | 1–3/2–5/4–11/8 | ||
| 38 | 1–8/7–5/4–11/8 | ||
| 39 | 1–10/9–5/4–11/8 | ||
| 40 | 1–5/3–5/4–11/8 | ||
| 41 | 1–10/9–11/9–11/8 | ||
| 42 | 1–3/2–11/6–11/8 | ||
| 43 | 1–10/9–11/6–11/8 | ||
| 44 | 1–5/3–11/6–11/8 | ||
| 45 | 1–11/9–11/6–11/8 | ||
| 46 | 1–8/7–12/7–11/7 | ||
| 47 | 1–8/7–9/7–11/7 | ||
| 48 | 1–12/7–9/7–11/7 | ||
| 49 | 1–12/7–10/9–11/7 | ||
| 50 | 1–9/7–10/9–11/7 | ||
| 51 | 1–8/7–5/4–11/7 | ||
| 52 | 1–10/9–5/4–11/7 | ||
| 53 | 1–8/7–10/7–11/7 | ||
| 54 | 1–12/7–10/7–11/7 | ||
| 55 | 1–9/7–10/7–11/7 | ||
| 56 | 1–10/9–10/7–11/7 | ||
| 57 | 1–5/4–10/7–11/7 | ||
| 58 | 1–12/7–11/9–11/7 | ||
| 59 | 1–10/9–11/9–11/7 | ||
| 60 | 1–10/7–11/9–11/7 | ||
| 61 | 1–9/7–11/6–11/7 | ||
| 62 | 1–10/9–11/6–11/7 | ||
| 63 | 1–10/7–11/6–11/7 | ||
| 64 | 1–11/9–11/6–11/7 | ||
| 65 | 1–8/7–11/8–11/7 | ||
| 66 | 1–10/9–11/8–11/7 | ||
| 67 | 1–5/4–11/8–11/7 | ||
| 68 | 1–11/9–11/8–11/7 | ||
| 69 | 1–11/6–11/8–11/7 |
Pentads
| # | Transversal | Type | Complexity |
|---|---|---|---|
| 1 | 1–3/2–8/7–12/7–9/7 | ||
| 2 | 1–8/7–12/7–9/7–10/7 | ||
| 3 | 1–12/7–9/7–10/9–10/7 | ||
| 4 | 1–9/7–10/9–5/3–10/7 | ||
| 5 | 1–10/9–5/3–5/4–10/7 | ||
| 6 | 1–12/7–10/9–10/7–11/9 | ||
| 7 | 1–3/2–9/7–5/3–11/6 | ||
| 8 | 1–9/7–10/9–5/3–11/6 | ||
| 9 | 1–9/7–10/9–10/7–11/6 | ||
| 10 | 1–9/7–5/3–10/7–11/6 | ||
| 11 | 1–10/9–5/3–10/7–11/6 | ||
| 12 | 1–10/9–10/7–11/9–11/6 | ||
| 13 | 1–3/2–8/7–5/4–11/8 | ||
| 14 | 1–3/2–5/3–5/4–11/8 | ||
| 15 | 1–10/9–5/3–5/4–11/8 | ||
| 16 | 1–3/2–5/3–11/6–11/8 | ||
| 17 | 1–10/9–5/3–11/6–11/8 | ||
| 18 | 1–10/9–11/9–11/6–11/8 | ||
| 19 | 1–8/7–12/7–9/7–11/7 | ||
| 20 | 1–12/7–9/7–10/9–11/7 | ||
| 21 | 1–8/7–12/7–10/7–11/7 | ||
| 22 | 1–8/7–9/7–10/7–11/7 | ||
| 23 | 1–12/7–9/7–10/7–11/7 | ||
| 24 | 1–12/7–10/9–10/7–11/7 | ||
| 25 | 1–9/7–10/9–10/7–11/7 | ||
| 26 | 1–8/7–5/4–10/7–11/7 | ||
| 27 | 1–10/9–5/4–10/7–11/7 | ||
| 28 | 1–12/7–10/9–11/9–11/7 | ||
| 29 | 1–12/7–10/7–11/9–11/7 | ||
| 30 | 1–10/9–10/7–11/9–11/7 | ||
| 31 | 1–9/7–10/9–11/6–11/7 | ||
| 32 | 1–9/7–10/7–11/6–11/7 | ||
| 33 | 1–10/9–10/7–11/6–11/7 | ||
| 34 | 1–10/9–11/9–11/6–11/7 | ||
| 35 | 1–10/7–11/9–11/6–11/7 | ||
| 36 | 1–8/7–5/4–11/8–11/7 | ||
| 37 | 1–10/9–5/4–11/8–11/7 | ||
| 38 | 1–10/9–11/9–11/8–11/7 | ||
| 39 | 1–10/9–11/6–11/8–11/7 | ||
| 40 | 1–11/9–11/6–11/8–11/7 |
Hexads
| # | Transversal | Type | Complexity |
|---|---|---|---|
| 1 | 1–9/7–10/9–5/3–10/7–11/6 | 15 | |
| 2 | 1–8/7–9/7–10/7–11/7–12/7 | otonal | 18 |
| 3 | 1–12/7–9/7–10/9–10/7–11/7 | 18 | |
| 4 | 1–12/7–10/9–10/7–11/9–11/7 | 18 | |
| 5 | 1–9/7–10/9–10/7–11/6–11/7 | 18 | |
| 6 | 1–10/9–10/7–11/9–11/6–11/7 | 18 | |
| 7 | 1–11/10–11/9–11/8–11/7–11/6 | utonal | 18 |