Chords of superpyth: Difference between revisions
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Superpyth has [[MOS]] scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18, and would thus require the 22-note mos, but even the 5- and 7-note MOSes contain enough chords to be interesting, though the 12- and 17-note MOSes are needed to properly explore full 7- and 11-limit harmonies. | Superpyth has [[MOS]] scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18, and would thus require the 22-note mos, but even the 5- and 7-note MOSes contain enough chords to be interesting, though the 12- and 17-note MOSes are needed to properly explore full 7- and 11-limit harmonies. | ||
Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords|ares]]. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked [[octarod chords|octarod | Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords|ares]]. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked [[octarod chords|octarod]]. | ||
== Triads == | == Triads == | ||
Revision as of 07:46, 15 December 2025
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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.
Superpyth has MOS scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18, and would thus require the 22-note mos, but even the 5- and 7-note MOSes contain enough chords to be interesting, though the 12- and 17-note MOSes are needed to properly explore full 7- and 11-limit harmonies.
Chords essentially tempered by 64/63 are labeled archytas, by 100/99 ptolemismic, by 176/175 valinorsmic, by 245/243 sensamagic, and 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.
Triads
| # | Generators | Transversal | Type |
|---|---|---|---|
| 1 | 0–1–2 | 1–9/8–3/2 | Ambitonal |
| 2 | 0–1–3 | 1–3/2–12/7 | Utonal |
| 3 | 0–2–3 | 1–8/7–12/7 | Otonal |
| 4 | 0–1–4 | 1–9/7–3/2 | Utonal |
| 5 | 0–2–4 | 1–8/7–9/7 | Otonal/utonal |
| 6 | 0–3–4 | 1–9/7–12/7 | Otonal |
| 7 | 0–3–7 | 1–10/9–12/7 | Sensamagic |
| 8 | 0–4–7 | 1–10/9–9/7 | Sensamagic |
| 9 | 0–1–8 | 1–3/2–5/3 | Otonal |
| 10 | 0–4–8 | 1–9/7–5/3 | Sensamagic |
| 11 | 0–7–8 | 1–10/9–5/3 | Utonal |
| 12 | 0–1–9 | 1–5/4–3/2 | Otonal |
| 13 | 0–2–9 | 1–9/8–5/4 | Otonal |
| 14 | 0–7–9 | 1–10/9–5/4 | Utonal |
| 15 | 0–8–9 | 1–5/4–5/3 | Utonal |
| 16 | 0–2–11 | 1–8/7–10/7 | Otonal |
| 17 | 0–3–11 | 1–10/7–12/7 | Otonal |
| 18 | 0–4–11 | 1–9/7–10/7 | Otonal |
| 19 | 0–7–11 | 1–10/9–10/7 | Utonal |
| 20 | 0–8–11 | 1–10/7–5/3 | Utonal |
| 21 | 0–9–11 | 1–5/4–10/7 | Utonal |
| 22 | 0–3–14 | 1–11/9–12/7 | Swetismic |
| 23 | 0–7–14 | 1–10/9–11/9 | Otonal/utonal |
| 24 | 0–11–14 | 1–11/9–10/7 | Swetismic |
| 25 | 0–1–15 | 1–3/2–11/6 | Otonal |
| 26 | 0–4–15 | 1–9/7–11/6 | Swetismic |
| 27 | 0–7–15 | 1–11/10–11/6 | Utonal |
| 28 | 0–8–15 | 1–5/3–11/6 | Otonal |
| 29 | 0–11–15 | 1–10/7–11/6 | Swetismic |
| 30 | 0–14–15 | 1–11/9–11/6 | Utonal |
| 31 | 0–1–16 | 1–11/8–3/2 | Otonal |
| 32 | 0–2–16 | 1–9/8–11/8 | Otonal |
| 33 | 0–7–16 | 1–11/10–11/8 | Utonal |
| 34 | 0–8–16 | 1–11/8–5/3 | Ptolemismic |
| 35 | 0–9–16 | 1–5/4–11/8 | Otonal |
| 36 | 0–14–16 | 1–11/9–11/8 | Utonal |
| 37 | 0–15–16 | 1–11/8–11/6 | Utonal |
| 38 | 0–2–18 | 1–8/7–11/7 | Otonal |
| 39 | 0–3–18 | 1–11/7–12/7 | Otonal |
| 40 | 0–4–18 | 1–9/7–11/7 | Otonal |
| 41 | 0–7–18 | 1–11/10–11/7 | Utonal |
| 42 | 0–9–18 | 1–5/4–11/7 | Valinorsmic |
| 43 | 0–11–18 | 1–10/7–11/7 | Otonal |
| 44 | 0–14–18 | 1–11/9–11/7 | Utonal |
| 45 | 0–15–18 | 1–11/7–11/6 | Utonal |
| 46 | 0–16–18 | 1–11/8–11/7 | Utonal |
Tetrads
| # | Generators | Transversal | Type |
|---|---|---|---|
| 1 | 0–1–2–3 | 1–8/7–3/2–12/7 | Archytas |
| 2 | 0–1–2–4 | 1–9/8–9/7–3/2 | Utonal |
| 3 | 0–1–3–4 | 1–9/7–3/2–12/7 | Ambitonal |
| 4 | 0–2–3–4 | 1–8/7–9/7–12/7 | Otonal |
| 5 | 0–3–4–7 | 1–10/9–9/7–12/7 | Sensamagic |
| 6 | 0–1–4–8 | 1–9/7–3/2–5/3 | Sensamagic |
| 7 | 0–4–7–8 | 1–9/7–10/9–5/3 | Sensamagic |
| 8 | 0–1–2–9 | 1–9/8–5/4–3/2 | Otonal |
| 9 | 0–1–8–9 | 1–5/4–3/2–5/3 | Ambitonal |
| 10 | 0–7–8–9 | 1–10/9–5/4–5/3 | Utonal |
| 11 | 0–2–3–11 | 1–8/7–10/7–12/7 | Otonal |
| 12 | 0–2–4–11 | 1–8/7–9/7–10/7 | Otonal |
| 13 | 0–3–4–11 | 1–9/7–10/7–12/7 | Otonal |
| 14 | 0–3–7–11 | 1–10/9–10/7–12/7 | Sensamagic |
| 15 | 0–4–7–11 | 1–10/9–9/7–10/7 | Sensamagic |
| 16 | 0–4–8–11 | 1–9/7–10/7–5/3 | Sensamagic |
| 17 | 0–7–8–11 | 1–10/9–10/7–5/3 | Utonal |
| 18 | 0–2–9–11 | 1–8/7–5/4–10/7 | Archytas/valinorsmic |
| 19 | 0–7–9–11 | 1–10/9–5/4–10/7 | Utonal |
| 20 | 0–8–9–11 | 1–5/4–10/7–5/3 | Utonal |
| 21 | 0–3–7–14 | 1–10/9–11/9–12/7 | Swetismic |
| 22 | 0–3–11–14 | 1–11/9–10/7–12/7 | Swetismic |
| 23 | 0–7–11–14 | 1–10/9–11/9–10/7 | Swetismic |
| 24 | 0–1–4–15 | 1–9/7–3/2–11/6 | Swetismic |
| 25 | 0–4–7–15 | 1–10/9–9/7–11/6 | Octarod |
| 26 | 0–1–8–15 | 1–3/2–5/3–11/6 | Otonal |
| 27 | 0–4–8–15 | 1–9/7–5/3–11/6 | Octarod |
| 28 | 0–7–8–15 | 1–10/9–5/3–11/6 | Ptolemismic |
| 29 | 0–4–11–15 | 1–9/7–10/7–11/6 | Swetismic |
| 30 | 0–7–11–15 | 1–10/9–10/7–11/6 | Octarod |
| 31 | 0–8–11–15 | 1–10/7–5/3–11/6 | Octarod |
| 32 | 0–7–14–15 | 1–11/10–11/9–11/6 | Utonal |
| 33 | 0–11–14–15 | 1–11/9–10/7–11/6 | Swetismic |
| 34 | 0–1–2–16 | 1–9/8–11/8–3/2 | Otonal |
| 35 | 0–1–8–16 | 1–11/8–3/2–5/3 | Ptolemismic |
| 36 | 0–7–8–16 | 1–10/9–5/3–11/8 | Ptolemismic |
| 37 | 0–1–9–16 | 1–5/4–11/8–3/2 | Otonal |
| 38 | 0–2–9–16 | 1–9/8–5/4–11/8 | Otonal |
| 39 | 0–7–9–16 | 1–10/9–5/4–11/8 | Ptolemismic |
| 40 | 0–8–9–16 | 1–5/4–11/8–5/3 | Ptolemismic |
| 41 | 0–9–14–16 | 1–11/10–11/9–11/8 | Utonal |
| 42 | 0–1–15–16 | 1–11/8–3/2–11/6 | Ambitonal |
| 43 | 0–7–15–16 | 1–11/10–11/8–11/6 | Utonal |
| 44 | 0–8–15–16 | 1–11/8–5/3–11/6 | Ptolemismic |
| 45 | 0–14–15–16 | 1–11/9–11/8–11/6 | Utonal |
| 46 | 0–2–3–18 | 1–8/7–11/7–12/7 | Otonal |
| 47 | 0–2–4–18 | 1–8/7–9/7–11/7 | Otonal |
| 48 | 0–3–4–18 | 1–9/7–11/7–12/7 | Otonal |
| 49 | 0–3–7–18 | 1–10/9–11/7–12/7 | Octarod |
| 50 | 0–4–7–18 | 1–10/9–9/7–11/7 | Swetismic |
| 51 | 0–2–9–18 | 1–8/7–5/4–11/7 | Valinorsmic |
| 52 | 0–7–9–18 | 1–10/9–5/4–11/7 | Valinorsmic |
| 53 | 0–2–11–18 | 1–8/7–10/7–11/7 | Otonal |
| 54 | 0–3–11–18 | 1–10/7–11/7–12/7 | Otonal |
| 55 | 0–4–11–18 | 1–9/7–10/7–11/7 | Otonal |
| 56 | 0–7–11–18 | 1–10/9–10/7–11/7 | Ptolemismic |
| 57 | 0–9–11–18 | 1–5/4–10/7–11/7 | Valinorsmic |
| 58 | 0–3–14–18 | 1–11/9–11/7–12/7 | Swetismic |
| 59 | 0–7–14–18 | 1–11/10–11/9–11/7 | Utonal |
| 60 | 0–11–14–18 | 1–11/9–10/7–11/7 | Swetismic |
| 61 | 0–4–15–18 | 1–9/7–11/7–11/6 | Swetismic |
| 62 | 0–7–15–18 | 1–11/10–11/7–11/6 | Utonal |
| 63 | 0–11–15–18 | 1–10/7–11/7–11/6 | Swetismic |
| 64 | 0–14–15–18 | 1–11/9–11/7–11/6 | Utonal |
| 65 | 0–2–16–18 | 1–8/7–11/8–11/7 | Archytas |
| 66 | 0–7–16–18 | 1–11/10–11/8–11/7 | Utonal |
| 67 | 0–9–16–18 | 1–5/4–11/8–11/7 | Valinorsmic |
| 68 | 0–14–16–18 | 1–11/9–11/8–11/7 | Utonal |
| 69 | 0–15–16–18 | 1–11/8–11/7–11/6 | Utonal |
Pentads
| # | Generators | Transversal | Type |
|---|---|---|---|
| 1 | 0–1–2–3–4 | 1–8/7–9/7–3/2–12/7 | Archytas |
| 2 | 0–2–3–4–11 | 1–8/7–9/7–10/7–12/7 | Otonal |
| 3 | 0–3–4–7–11 | 1–10/9–9/7–10/7–12/7 | Sensamagic |
| 4 | 0–4–7–8–11 | 1–10/9–9/7–10/7–5/3 | Sensamagic |
| 5 | 0–7–8–9–11 | 1–10/9–5/4–10/7–5/3 | Utonal |
| 6 | 0–3–7–11–14 | 1–10/9–11/9–10/7–12/7 | Octarod |
| 7 | 0–1–4–8–15 | 1–9/7–3/2–5/3–11/6 | Octarod |
| 8 | 0–4–7–8–15 | 1–10/9–9/7–5/3–11/6 | Octarod |
| 9 | 0–4–7–11–15 | 1–9/7–10/9–10/7–11/6 | Octarod |
| 10 | 0–4–8–11–15 | 1–9/7–5/3–10/7–11/6 | Octarod |
| 11 | 0–7–8–11–15 | 1–10/9–5/3–10/7–11/6 | Octarod |
| 12 | 0–7–11–14–15 | 1–10/9–11/9–10/7–11/6 | Octarod |
| 13 | 0–1–2–9–16 | 1–9/8–5/4–11/8–3/2 | Otonal |
| 14 | 0–1–8–9–16 | 1–5/4–11/8–3/2–5/3 | Ptolemismic |
| 15 | 0–7–8–9–16 | 1–10/9–5/3–5/4–11/8 | Ptolemismic |
| 16 | 0–1–8–15–16 | 1–11/8–3/2–5/3–11/6 | Ptolemismic |
| 17 | 0–7–8–15–16 | 1–10/9–11/8–5/3–11/6 | Ptolemismic |
| 18 | 0–7–14–15–16 | 1–11/10–11/9–11/8–11/6 | Utonal |
| 19 | 0–2–3–4–18 | 1–8/7–9/7–11/7–12/7 | Otonal |
| 20 | 0–3–4–7–18 | 1–10/9–9/7–11/7–12/7 | Octarod |
| 21 | 0–2–3–11–18 | 1–8/7–10/7–11/7–12/7 | Otonal |
| 22 | 0–2–4–11–18 | 1–8/7–9/7–10/7–11/7 | Otonal |
| 23 | 0–3–4–11–18 | 1–9/7–10/7–11/7–12/7 | Otonal |
| 24 | 0–3–7–11–18 | 1–12/7–10/9–10/7–11/7 | Octarod |
| 25 | 0–4–7–11–18 | 1–10/9–9/7–10/7–11/7 | Octarod |
| 26 | 0–2–9–11–18 | 1–8/7–5/4–10/7–11/7 | Valinorsmic |
| 27 | 0–7–9–11–18 | 1–10/9–5/4–10/7–11/7 | Ares |
| 28 | 0–3–7–14–18 | 1–10/9–11/9–11/7–12/7 | Octarod |
| 29 | 0–3–11–14–18 | 1–11/9–10/7–11/7–12/7 | Swetismic |
| 30 | 0–7–11–14–18 | 1–10/9–11/9–10/7–11/7 | Octarod |
| 31 | 0–4–7–15–18 | 1–10/9–9/7–11/7–11/6 | Octarod |
| 32 | 0–4–11–15–18 | 1–9/7–10/7–11/7–11/6 | Octarod |
| 33 | 0–7–11–15–18 | 1–10/9–10/7–11/7–11/6 | Octarod |
| 34 | 0–7–14–15–18 | 1–11/10–11/9–11/7–11/6 | Utonal |
| 35 | 0–11–14–15–18 | 1–11/9–10/7–11/7–11/6 | Octarod |
| 36 | 0–2–9–16–18 | 1–8/7–5/4–11/8–11/7 | Ares |
| 37 | 0–7–9–16–18 | 1–11/10–5/4–11/8–11/7 | Valinorsmic |
| 38 | 0–7–14–16–18 | 1–11/10–11/9–11/8–11/7 | Utonal |
| 39 | 0–7–15–16–18 | 1–11/10–11/8–11/7–11/6 | Utonal |
| 40 | 0–14–15–16–18 | 1–11/9–11/8–11/7–11/6 | Utonal |
Hexads
| # | Generators | Transversal | Type |
|---|---|---|---|
| 1 | 0–4–7–8–11–15 | 1–10/9–9/7–10/7–5/3–11/6 | Octarod |
| 2 | 0–2–3–4–11–18 | 1–8/7–9/7–10/7–11/7–12/7 | Otonal |
| 3 | 0–3–4–7–11–18 | 1–10/9–9/7–10/7–11/7–12/7 | Octarod |
| 4 | 0–3–7–11–14–18 | 1–10/9–11/9–10/7–11/7–12/7 | Octarod |
| 5 | 0–4–7–11–15–18 | 1–10/9–9/7–10/7–11/7–11/6 | Octarod |
| 6 | 0–7–11–14–15–18 | 1–10/9–10/7–11/9–11/6–11/7 | Octarod |
| 7 | 0–7–14–15–16–18 | 1–11/10–11/9–11/8–11/7–11/6 | Utonal |