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{{Editable user page| Please complete the description and tables. This page is planned to be moved to main space once completed.}}
{{Breadcrumb|Superpyth}}
Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[superpyth|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.
Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s in [[11-limit]] [[superpyth|superpyth temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of perfect fifth [[generator]]s above the root.


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]], 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 that require 176/175 and 540/539 tempering are marked [[guanyin chords|guanyin]].  
If a chord is [[dyadic chord #Essentially tempered dyadic chord|essentially just]], it is classified as [[otonal]] if it is best analyzed in terms of the [[harmonic series]], [[utonal]] if best analyzed in terms of the [[subharmonic series]], and [[ambitonal]] if equally well analyzed by either. If a chord is [[dyadic chord #Essentially tempered dyadic chord|essentially tempered]], it is classified based on which [[comma]]s are needed to define the chord. 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 to vanish are labeled [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 to vanish are labeled [[octarod chords|octarod]].  
 
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. However, sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 8/7 or 10/9 above the root.
 
Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.{{Overline|09}}[[{{c}}]]) and [[27edo|16\27]] (711.{{Overline|11}}{{c}}), and generates [[mos]] scales of the patterns [[2L 3s]] (pentic), [[5L 2s]] (diatonic), [[5L 7s]] (p-chromatic), [[5L 12s]], [[5L 17s]], and [[22L 5s]]. The pentic and diatonic scales contain some chords in the [[2.3.7 subgroup|2.3.7]] [[subgroup]], though the 12-note chromatic scale is needed to properly utilize intervals of [[5/1|5]], and intervals of [[11/1|11]] don't become common until the 17- and 22-note scales. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth has not been explored much either, so these mos scales would be a great place to start such explorations.


== Triads ==
== Triads ==
{| class="wikitable"
{| class="wikitable sortable center-1"
|-
|-
! #
! #
! Generators
! class="unsortable" | Generators
! Transversal
! class="unsortable" | Transversal
! Type
! Type
! class="unsortable" | Comments
|-
|-
| 1
| 1
| 0–1–2
| 0–1–2
| 1–9/8–3/2
| 1–9/8–3/2
| ambitonal
| Ambitonal
| [[6:8:9]], [[8:9:12]]
|-
|-
| 2
| 2
| 0–1–3
| 0–1–3
| 1–3/2–12/7
| 1–3/2–12/7
| utonal
| Utonal
| [[14:21:24|1/(12:8:7)]]
|-
|-
| 3
| 3
| 0–2–3
| 0–2–3
| 1–8/7–12/7
| 1–8/7–12/7
| otonal
| Otonal
| [[4:6:7]]
|-
|-
| 4
| 4
| 0–1–4
| 0–1–4
| 1–9/7–3/2
| 1–9/7–3/2
| utonal
| Utonal
| [[14:18:21|1/(9:7:6)]]
|-
|-
| 5
| 5
| 0–2–4
| 0–2–4
| 1–8/7–9/7
| 1–8/7–9/7
| ambitonal
| Otonal/utonal
| 7:8:9~1/(9:8:7)
|-
|-
| 6
| 6
| 0–3–4
| 0–3–4
| 1–9/7–12/7
| 1–9/7–12/7
| otonal
| Otonal
| [[6:7:9]]
|-
|-
| 7
| 7
| 0–3–7
| 0–3–7
| 1–10/9–12/7
| 1–10/9–12/7
| sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
| 0–4–7
| 0–4–7
| 1–10/9–9/7
| 1–10/9–9/7
| sensamagic
| Sensamagic
|
|-
|-
| 9
| 9
| 0–1–8
| 0–1–8
| 1–3/2–5/3
| 1–3/2–5/3
| otonal
| Otonal
| [[6:9:10]]
|-
|-
| 10
| 10
| 0–4–8
| 0–4–8
| 1–9/7–5/3
| 1–9/7–5/3
| sensamagic
| Sensamagic
|
|-
|-
| 11
| 11
| 0–7–8
| 0–7–8
| 1–10/9–5/3
| 1–10/9–5/3
| utonal
| Utonal
| [[10:15:18|1/(9:6:5)]]
|-
|-
| 12
| 12
| 0–1–9
| 0–1–9
| 1–5/4–3/2
| 1–5/4–3/2
| otonal
| Otonal
| [[4:5:6]]
|-
|-
| 13
| 13
| 0–2–9
| 0–2–9
| 1–9/8–5/4
| 1–9/8–5/4
| otonal
| Otonal
|
|-
|-
| 14
| 14
| 0–7–9
| 0–7–9
| 1–10/9–5/4
| 1–10/9–5/4
| utonal
| Utonal
|
|-
|-
| 15
| 15
| 0–8–9
| 0–8–9
| 1–5/4–5/3
| 1–5/4–5/3
| utonal
| Utonal
| [[10:12:15|1/(6:5:4)]]
|-
|-
| 16
| 16
| 0–2–11
| 0–2–11
| 1–8/7–10/7
| 1–8/7–10/7
|  
| Otonal
| [[4:5:7]]
|-
|-
| 17
| 17
| 0–3–11
| 0–3–11
| 1–12/7–10/7
| 1–10/7–12/7
|  
| Otonal
| [[5:6:7]]
|-
|-
| 18
| 18
| 0–4–11
| 0–4–11
| 1–9/7–10/7
| 1–9/7–10/7
| Otonal
|  
|  
|-
|-
Line 105: Line 128:
| 0–7–11
| 0–7–11
| 1–10/9–10/7
| 1–10/9–10/7
| Utonal
|  
|  
|-
|-
| 20
| 20
| 0–8–11
| 0–8–11
| 1–5/3–10/7
| 1–10/7–5/3
|  
| Utonal
| [[30:35:42|1/(7:6:5)]]
|-
|-
| 21
| 21
| 0–9–11
| 0–9–11
| 1–5/4–10/7
| 1–5/4–10/7
|  
| Utonal
| [[28:35:40|1/(10:8:7)]]
|-
|-
| 22
| 22
| 0–3–14
| 0–3–14
| 1–12/7–11/9
| 1–11/9–12/7
| Swetismic
|  
|  
|-
|-
Line 125: Line 152:
| 0–7–14
| 0–7–14
| 1–10/9–11/9
| 1–10/9–11/9
|  
| Otonal/utonal
| 9:10:11~1/(11:10:9)
|-
|-
| 24
| 24
| 0–11–14
| 0–11–14
| 1–10/7–11/9
| 1–11/9–10/7
| Swetismic
|  
|  
|-
|-
Line 135: Line 164:
| 0–1–15
| 0–1–15
| 1–3/2–11/6
| 1–3/2–11/6
| Otonal
|  
|  
|-
|-
Line 140: Line 170:
| 0–4–15
| 0–4–15
| 1–9/7–11/6
| 1–9/7–11/6
| Swetismic
|  
|  
|-
|-
| 27
| 27
| 0–7–15
| 0–7–15
| 1–10/9–11/6
| 1–11/10–11/6
| Utonal
|  
|  
|-
|-
Line 150: Line 182:
| 0–8–15
| 0–8–15
| 1–5/3–11/6
| 1–5/3–11/6
| Otonal
|  
|  
|-
|-
Line 155: Line 188:
| 0–11–15
| 0–11–15
| 1–10/7–11/6
| 1–10/7–11/6
| Swetismic
|  
|  
|-
|-
Line 160: Line 194:
| 0–14–15
| 0–14–15
| 1–11/9–11/6
| 1–11/9–11/6
| Utonal
|  
|  
|-
|-
| 31
| 31
| 0–1–16
| 0–1–16
| 1–3/2–11/8
| 1–11/8–3/2
| otonal
| Otonal
|  
|-
|-
| 32
| 32
| 0–2–16
| 0–2–16
| 1–9/8–11/8
| 1–9/8–11/8
| otonal
| Otonal
|
|-
|-
| 33
| 33
| 0–7–16
| 0–7–16
| 1–11/10–11/8
| 1–11/10–11/8
| utonal
| Utonal
|
|-
|-
| 34
| 34
| 0–8–16
| 0–8–16
| 1–5/3–11/8
| 1–11/8–5/3
| ptolemismic
| Ptolemismic
|  
|-
|-
| 35
| 35
| 0–9–16
| 0–9–16
| 1–5/4–11/8
| 1–5/4–11/8
| otonal
| Otonal
|
|-
|-
| 36
| 36
| 0–14–16
| 0–14–16
| 1–11/9–11/8
| 1–11/9–11/8
| utonal
| Utonal
|
|-
|-
| 37
| 37
| 0–15–16
| 0–15–16
| 1–11/6–11/8
| 1–11/8–11/6
| utonal
| Utonal
|  
|-
|-
| 38
| 38
| 0–2–18
| 0–2–18
| 1–8/7–11/7
| 1–8/7–11/7
| Otonal
|  
|  
|-
|-
| 39
| 39
| 0–3–18
| 0–3–18
| 1–12/7–11/7
| 1–11/7–12/7
| Otonal
|  
|  
|-
|-
Line 210: Line 254:
| 0–4–18
| 0–4–18
| 1–9/7–11/7
| 1–9/7–11/7
| Otonal
|  
|  
|-
|-
| 41
| 41
| 0–7–18
| 0–7–18
| 1–10/9–11/7
| 1–11/10–11/7
| Utonal
|  
|  
|-
|-
Line 220: Line 266:
| 0–9–18
| 0–9–18
| 1–5/4–11/7
| 1–5/4–11/7
| Valinorsmic
|  
|  
|-
|-
Line 225: Line 272:
| 0–11–18
| 0–11–18
| 1–10/7–11/7
| 1–10/7–11/7
| Otonal
|  
|  
|-
|-
Line 230: Line 278:
| 0–14–18
| 0–14–18
| 1–11/9–11/7
| 1–11/9–11/7
| Utonal
|  
|  
|-
|-
| 45
| 45
| 0–15–18
| 0–15–18
| 1–11/6–11/7
| 1–11/7–11/6
| Utonal
|  
|  
|-
|-
Line 240: Line 290:
| 0–16–18
| 0–16–18
| 1–11/8–11/7
| 1–11/8–11/7
| Utonal
|  
|  
|}
|}


== Tetrads ==
== Tetrads ==
{| class="wikitable"
{| class="wikitable sortable center-1"
|-
|-
! #
! #
! Generators
! class="unsortable" | Generators
! Transversal
! class="unsortable" | Transversal
! Type
! Type
! class="unsortable" | Comments
|-
|-
| 1
| 1
|  
| 0–1–2–3
| 1–3/2–8/7–12/7
| 1–8/7–3/2–12/7
| Archytas
|  
|  
|-
|-
| 2
| 2
|  
| 0–1–2–4
| 1–3/2–8/7–9/7
| 1–9/8–9/7–3/2
|  
| Utonal
| [[28:36:42:63|1/(9:7:6:4)]]
|-
|-
| 3
| 3
|  
| 0–1–3–4
| 1–3/2–12/7–9/7
| 1–9/7–3/2–12/7
|  
| Ambitonal
| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]]
|-
|-
| 4
| 4
|  
| 0–2–3–4
| 1–8/7–12/7–9/7
| 1–8/7–9/7–12/7
|  
| Otonal
| [[4:6:7:9]]
|-
|-
| 5
| 5
|  
| 0–3–4–7
| 1–12/7–9/7–10/9
| 1–10/9–9/7–12/7
| Sensamagic
|  
|  
|-
|-
| 6
| 6
|  
| 0–1–4–8
| 1–3/2–9/7–5/3
| 1–9/7–3/2–5/3
| Sensamagic
|  
|  
|-
|-
| 7
| 7
|  
| 0–4–7–8
| 1–9/7–10/9–5/3
| 1–9/7–10/9–5/3
| Sensamagic
|  
|  
|-
|-
| 8
| 8
|  
| 0–1–2–9
| 1–3/2–8/7–5/4
| 1–9/8–5/4–3/2
|  
| Otonal
| [[4:5:6:9]]
|-
|-
| 9
| 9
|  
| 0–1–8–9
| 1–3/2–5/3–5/4
| 1–5/4–3/2–5/3
|  
| Ambitonal
| [[10:12:15:18]], [[12:15:18:20]]<br>9-odd-limit ASS
|-
|-
| 10
| 10
|  
| 0–7–8–9
| 1–10/9–5/3–5/4
| 1–10/9–5/4–5/3
|  
| Utonal
| [[20:30:36:45|1/(9:6:5:4)]]
|-
|-
| 11
| 11
|  
| 0–2–3–11
| 1–8/7–12/7–10/7
| 1–8/7–10/7–12/7
|  
| Otonal
| [[4:5:6:7]]
|-
|-
| 12
| 12
|  
| 0–2–4–11
| 1–8/7–9/7–10/7
| 1–8/7–9/7–10/7
|  
| Otonal
| [[4:5:7:9]]
|-
|-
| 13
| 13
|  
| 0–3–4–11
| 1–12/7–9/7–10/7
| 1–9/7–10/7–12/7
|  
| Otonal
| [[6:7:9:10]]
|-
|-
| 14
| 14
|  
| 0–3–7–11
| 1–12/7–10/9–10/7
| 1–10/9–10/7–12/7
| Sensamagic
|  
|  
|-
|-
| 15
| 15
|  
| 0–4–7–11
| 1–9/7–10/9–10/7
| 1–10/9–9/7–10/7
| Sensamagic
|  
|  
|-
|-
| 16
| 16
|  
| 0–4–8–11
| 1–9/7–5/3–10/7
| 1–9/7–10/7–5/3
| Sensamagic
|  
|  
|-
|-
| 17
| 17
|  
| 0–7–8–11
| 1–10/9–5/3–10/7
| 1–10/9–10/7–5/3
|  
| Utonal
| [[70:90:105:126|1/(9:7:6:5)]]
|-
|-
| 18
| 18
|  
| 0–2–9–11
| 1–8/7–5/4–10/7
| 1–8/7–5/4–10/7
| Archytas/valinorsmic
|  
|  
|-
|-
| 19
| 19
|  
| 0–7–9–11
| 1–10/9–5/4–10/7
| 1–10/9–5/4–10/7
|  
| Utonal
| [[140:180:252:315|1/(9:7:5:4)]]
|-
|-
| 20
| 20
|  
| 0–8–9–11
| 1–5/3–5/4–10/7
| 1–5/4–10/7–5/3
|  
| Utonal
| [[70:84:105:120|1/(12:10:8:7)]]
|-
|-
| 21
| 21
|  
| 0–3–7–14
| 1–12/7–10/9–11/9
| 1–11/10–11/9–12/7
| Swetismic
|  
|  
|-
|-
| 22
| 22
|  
| 0–3–11–14
| 1–12/7–10/7–11/9
| 1–11/9–10/7–12/7
| Swetismic
|  
|  
|-
|-
| 23
| 23
|  
| 0–7–11–14
| 1–10/9–10/7–11/9
| 1–11/10–11/9–10/7
| Swetismic
|  
|  
|-
|-
| 24
| 24
|  
| 0–1–4–15
| 1–3/2–9/7–11/6
| 1–9/7–3/2–11/6
| Swetismic
|  
|  
|-
|-
| 25
| 25
|  
| 0–4–7–15
| 1–9/7–10/9–11/6
| 1–10/9–9/7–11/6
| Octarod
|  
|  
|-
|-
| 26
| 26
|  
| 0–1–8–15
| 1–3/2–5/3–11/6
| 1–3/2–5/3–11/6
| Otonal
|  
|  
|-
|-
| 27
| 27
|  
| 0–4–8–15
| 1–9/7–5/3–11/6
| 1–9/7–5/3–11/6
| Octarod
|  
|  
|-
|-
| 28
| 28
|  
| 0–7–8–15
| 1–10/9–5/3–11/6
| 1–10/9–5/3–11/6
| Ptolemismic
|  
|  
|-
|-
| 29
| 29
|  
| 0–4–11–15
| 1–9/7–10/7–11/6
| 1–9/7–10/7–11/6
| Swetismic
|  
|  
|-
|-
| 30
| 30
|  
| 0–7–11–15
| 1–10/9–10/7–11/6
| 1–10/9–10/7–11/6
| Octarod
|  
|  
|-
|-
| 31
| 31
|  
| 0–8–11–15
| 1–5/3–10/7–11/6
| 1–10/7–5/3–11/6
| Octarod
|  
|  
|-
|-
| 32
| 32
|  
| 0–7–14–15
| 1–10/9–11/9–11/6
| 1–11/10–11/9–11/6
| Utonal
|  
|  
|-
|-
| 33
| 33
|  
| 0–11–14–15
| 1–10/7–11/9–11/6
| 1–11/9–10/7–11/6
| Swetismic
|  
|  
|-
|-
| 34
| 34
|  
| 0–1–2–16
| 1–3/2–8/7–11/8
| 1–9/8–11/8–3/2
| Otonal
|  
|  
|-
|-
| 35
| 35
|  
| 0–1–8–16
| 1–3/2–5/3–11/8
| 1–11/8–3/2–5/3
| Ptolemismic
|  
|  
|-
|-
| 36
| 36
|  
| 0–7–8–16
| 1–10/9–5/3–11/8
| 1–10/9–5/3–11/8
| Ptolemismic
|  
|  
|-
|-
| 37
| 37
|  
| 0–1–9–16
| 1–3/2–5/4–11/8
| 1–5/4–11/8–3/2
| Otonal
|  
|  
|-
|-
| 38
| 38
|  
| 0–2–9–16
| 1–8/7–5/4–11/8
| 1–9/8–5/4–11/8
| Otonal
|  
|  
|-
|-
| 39
| 39
|  
| 0–7–9–16
| 1–10/9–5/4–11/8
| 1–10/9–5/4–11/8
| Ptolemismic/valinorsmic
|  
|  
|-
|-
| 40
| 40
|  
| 0–8–9–16
| 1–5/3–5/4–11/8
| 1–5/4–11/8–5/3
| Ptolemismic
|  
|  
|-
|-
| 41
| 41
|  
| 0–9–14–16
| 1–10/9–11/9–11/8
| 1–11/10–11/9–11/8
| Utonal
|  
|  
|-
|-
| 42
| 42
|  
| 0–1–15–16
| 1–3/2–11/6–11/8
| 1–11/8–3/2–11/6
|  
| Ambitonal
| 11-odd-limit ASS
|-
|-
| 43
| 43
|  
| 0–7–15–16
| 1–10/9–11/6–11/8
| 1–11/10–11/8–11/6
| Utonal
|  
|  
|-
|-
| 44
| 44
|  
| 0–8–15–16
| 1–5/3–11/6–11/8
| 1–11/8–5/3–11/6
| Ptolemismic
|  
|  
|-
|-
| 45
| 45
|  
| 0–14–15–16
| 1–11/9–11/6–11/8
| 1–11/9–11/8–11/6
| Utonal
|  
|  
|-
|-
| 46
| 46
|  
| 0–2–3–18
| 1–8/7–12/7–11/7
| 1–8/7–11/7–12/7
| Otonal
|  
|  
|-
|-
| 47
| 47
|  
| 0–2–4–18
| 1–8/7–9/7–11/7
| 1–8/7–9/7–11/7
| Otonal
|  
|  
|-
|-
| 48
| 48
|  
| 0–3–4–18
| 1–12/7–9/7–11/7
| 1–9/7–11/7–12/7
| Otonal
|  
|  
|-
|-
| 49
| 49
|  
| 0–3–7–18
| 1–12/7–10/9–11/7
| 1–10/9–11/7–12/7
| Octarod
|  
|  
|-
|-
| 50
| 50
|  
| 0–4–7–18
| 1–9/7–10/9–11/7
| 1–11/10–9/7–11/7
| Swetismic
|  
|  
|-
|-
| 51
| 51
|  
| 0–2–9–18
| 1–8/7–5/4–11/7
| 1–8/7–5/4–11/7
| Valinorsmic
|  
|  
|-
|-
| 52
| 52
|  
| 0–7–9–18
| 1–10/9–5/4–11/7
| 1–11/10–5/4–11/7
| Valinorsmic
|  
|  
|-
|-
| 53
| 53
|  
| 0–2–11–18
| 1–8/7–10/7–11/7
| 1–8/7–10/7–11/7
| Otonal
|  
|  
|-
|-
| 54
| 54
|  
| 0–3–11–18
| 1–12/7–10/7–11/7
| 1–10/7–11/7–12/7
| Otonal
|  
|  
|-
|-
| 55
| 55
|  
| 0–4–11–18
| 1–9/7–10/7–11/7
| 1–9/7–10/7–11/7
| Otonal
|  
|  
|-
|-
| 56
| 56
|  
| 0–7–11–18
| 1–10/9–10/7–11/7
| 1–10/9–10/7–11/7
| Ptolemismic
|  
|  
|-
|-
| 57
| 57
|  
| 0–9–11–18
| 1–5/4–10/7–11/7
| 1–5/4–10/7–11/7
| Valinorsmic
|  
|  
|-
|-
| 58
| 58
|  
| 0–3–14–18
| 1–12/7–11/9–11/7
| 1–11/9–11/7–12/7
| Swetismic
|  
|  
|-
|-
| 59
| 59
|  
| 0–7–14–18
| 1–10/9–11/9–11/7
| 1–11/10–11/9–11/7
| Utonal
|  
|  
|-
|-
| 60
| 60
|  
| 0–11–14–18
| 1–10/7–11/9–11/7
| 1–11/9–10/7–11/7
| Swetismic
|  
|  
|-
|-
| 61
| 61
|  
| 0–4–15–18
| 1–9/7–11/6–11/7
| 1–9/7–11/7–11/6
| Swetismic
|  
|  
|-
|-
| 62
| 62
|  
| 0–7–15–18
| 1–10/9–11/6–11/7
| 1–11/10–11/7–11/6
| Utonal
|  
|  
|-
|-
| 63
| 63
|  
| 0–11–15–18
| 1–10/7–11/6–11/7
| 1–10/7–11/7–11/6
| Swetismic
|  
|  
|-
|-
| 64
| 64
|  
| 0–14–15–18
| 1–11/9–11/6–11/7
| 1–11/9–11/7–11/6
| Utonal
|  
|  
|-
|-
| 65
| 65
|  
| 0–2–16–18
| 1–8/7–11/8–11/7
| 1–8/7–11/8–11/7
| Archytas
|  
|  
|-
|-
| 66
| 66
|  
| 0–7–16–18
| 1–10/9–11/8–11/7
| 1–11/10–11/8–11/7
| Utonal
|  
|  
|-
|-
| 67
| 67
|  
| 0–9–16–18
| 1–5/4–11/8–11/7
| 1–5/4–11/8–11/7
| Valinorsmic
|  
|  
|-
|-
| 68
| 68
|  
| 0–14–16–18
| 1–11/9–11/8–11/7
| 1–11/9–11/8–11/7
| Utonal
|  
|  
|-
|-
| 69
| 69
|  
| 0–15–16–18
| 1–11/6–11/8–11/7
| 1–11/8–11/7–11/6
| Utonal
|  
|  
|}
|}


== Pentads ==
== Pentads ==
{| class="wikitable"
{| class="wikitable sortable center-1"
|-
|-
! #
! #
! Generators
! class="unsortable" | Generators
! Transversal
! class="unsortable" | Transversal
! Type
! Type
! class="unsortable" | Comments
|-
|-
| 1
| 1
|  
| 0–1–2–3–4
| 1–3/2–8/7–12/7–9/7
| 1–8/7–9/7–3/2–12/7
| Archytas
|  
|  
|-
|-
| 2
| 2
|  
| 0–2–3–4–11
| 1–8/7–12/7–9/7–10/7
| 1–8/7–9/7–10/7–12/7
|  
| Otonal
| [[4:5:6:7:9]]
|-
|-
| 3
| 3
|  
| 0–3–4–7–11
| 1–12/7–9/7–10/9–10/7
| 1–10/9–9/7–10/7–12/7
| Sensamagic
|  
|  
|-
|-
| 4
| 4
|  
| 0–4–7–8–11
| 1–9/7–10/9–5/3–10/7
| 1–10/9–9/7–10/7–5/3
| Sensamagic
|  
|  
|-
|-
| 5
| 5
|  
| 0–7–8–9–11
| 1–10/9–5/3–5/4–10/7
| 1–10/9–5/4–10/7–5/3
|  
| Utonal
| [[210:252:315:360:560|1/(24:20:16:14:9)]]
|-
|-
| 6
| 6
|  
| 0–3–7–11–14
| 1–12/7–10/9–10/7–11/9
| 1–10/9–11/9–10/7–12/7
| Octarod
|  
|  
|-
|-
| 7
| 7
|  
| 0–1–4–8–15
| 1–3/2–9/7–5/3–11/6
| 1–9/7–3/2–5/3–11/6
| Octarod
|  
|  
|-
|-
| 8
| 8
|  
| 0–4–7–8–15
| 1–9/7–10/9–5/3–11/6
| 1–10/9–9/7–5/3–11/6
| Octarod
|  
|  
|-
|-
| 9
| 9
|  
| 0–4–7–11–15
| 1–9/7–10/9–10/7–11/6
| 1–9/7–10/9–10/7–11/6
| Octarod
|  
|  
|-
|-
| 10
| 10
|  
| 0–4–8–11–15
| 1–9/7–5/3–10/7–11/6
| 1–9/7–5/3–10/7–11/6
| Octarod
|  
|  
|-
|-
| 11
| 11
|  
| 0–7–8–11–15
| 1–10/9–5/3–10/7–11/6
| 1–10/9–5/3–10/7–11/6
| Octarod
|  
|  
|-
|-
| 12
| 12
|  
| 0–7–11–14–15
| 1–10/9–10/7–11/9–11/6
| 1–10/9–11/9–10/7–11/6
| Octarod
|  
|  
|-
|-
| 13
| 13
|  
| 0–1–2–9–16
| 1–3/2–8/7–5/4–11/8
| 1–9/8–5/4–11/8–3/2
|  
| Otonal
| [[4:5:6:9:11]]
|-
|-
| 14
| 14
|  
| 0–1–8–9–16
| 1–3/2–5/3–5/4–11/8
| 1–5/4–11/8–3/2–5/3
| Ptolemismic
|  
|  
|-
|-
| 15
| 15
|  
| 0–7–8–9–16
| 1–10/9–5/3–5/4–11/8
| 1–10/9–5/3–5/4–11/8
| Ptolemismic
|  
|  
|-
|-
| 16
| 16
|  
| 0–1–8–15–16
| 1–3/2–5/3–11/6–11/8
| 1–11/8–3/2–5/3–11/6
| Ptolemismic
|  
|  
|-
|-
| 17
| 17
|  
| 0–7–8–15–16
| 1–10/9–5/3–11/6–11/8
| 1–10/9–11/8–5/3–11/6
| Ptolemismic
|  
|  
|-
|-
| 18
| 18
|  
| 0–7–14–15–16
| 1–10/9–11/9–11/6–11/8
| 1–11/10–11/9–11/8–11/6
|  
| Utonal
| [[330:396:495:720:880|1/(24:20:16:11:9)]]
|-
|-
| 19
| 19
|  
| 0–2–3–4–18
| 1–8/7–12/7–9/7–11/7
| 1–8/7–9/7–11/7–12/7
|  
| Otonal
| [[4:6:7:9:11]]
|-
|-
| 20
| 20
|  
| 0–3–4–7–18
| 1–12/7–9/7–10/9–11/7
| 1–10/9–9/7–11/7–12/7
| Octarod
|  
|  
|-
|-
| 21
| 21
|  
| 0–2–3–11–18
| 1–8/7–12/7–10/7–11/7
| 1–8/7–10/7–11/7–12/7
|  
| Otonal
| [[4:5:6:7:11]]
|-
|-
| 22
| 22
|  
| 0–2–4–11–18
| 1–8/7–9/7–10/7–11/7
| 1–8/7–9/7–10/7–11/7
|  
| Otonal
| [[4:5:7:9:11]]
|-
|-
| 23
| 23
|  
| 0–3–4–11–18
| 1–12/7–9/7–10/7–11/7
| 1–9/7–10/7–11/7–12/7
|  
| Otonal
| [[5:6:7:9:11]]
|-
|-
| 24
| 24
|  
| 0–3–7–11–18
| 1–12/7–10/9–10/7–11/7
| 1–12/7–10/9–10/7–11/7
| Octarod
|  
|  
|-
|-
| 25
| 25
|  
| 0–4–7–11–18
| 1–9/7–10/9–10/7–11/7
| 1–10/9–9/7–10/7–11/7
| Octarod
|  
|  
|-
|-
| 26
| 26
|  
| 0–2–9–11–18
| 1–8/7–5/4–10/7–11/7
| 1–8/7–5/4–10/7–11/7
| Valinorsmic
|  
|  
|-
|-
| 27
| 27
|  
| 0–7–9–11–18
| 1–10/9–5/4–10/7–11/7
| 1–10/9–5/4–10/7–11/7
| Ares
|  
|  
|-
|-
| 28
| 28
|  
| 0–3–7–14–18
| 1–12/7–10/9–11/9–11/7
| 1–10/9–11/9–11/7–12/7
| Octarod
|  
|  
|-
|-
| 29
| 29
|  
| 0–3–11–14–18
| 1–12/7–10/7–11/9–11/7
| 1–11/9–10/7–11/7–12/7
| Swetismic
|  
|  
|-
|-
| 30
| 30
|  
| 0–7–11–14–18
| 1–10/9–10/7–11/9–11/7
| 1–10/9–11/9–10/7–11/7
| Octarod
|  
|  
|-
|-
| 31
| 31
|  
| 0–4–7–15–18
| 1–9/7–10/9–11/6–11/7
| 1–10/9–9/7–11/7–11/6
| Octarod
|  
|  
|-
|-
| 32
| 32
|  
| 0–4–11–15–18
| 1–9/7–10/7–11/6–11/7
| 1–9/7–10/7–11/7–11/6
| Octarod
|  
|  
|-
|-
| 33
| 33
|  
| 0–7–11–15–18
| 1–10/9–10/7–11/6–11/7
| 1–10/9–10/7–11/7–11/6
| Octarod
|  
|  
|-
|-
| 34
| 34
|  
| 0–7–14–15–18
| 1–10/9–11/9–11/6–11/7
| 1–11/10–11/9–11/7–11/6
|  
| Utonal
| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]
|-
|-
| 35
| 35
|  
| 0–11–14–15–18
| 1–10/7–11/9–11/6–11/7
| 1–11/9–10/7–11/7–11/6
| Octarod
|  
|  
|-
|-
| 36
| 36
|  
| 0–2–9–16–18
| 1–8/7–5/4–11/8–11/7
| 1–8/7–5/4–11/8–11/7
| Ares
|  
|  
|-
|-
| 37
| 37
|  
| 0–7–9–16–18
| 1–10/9–5/4–11/8–11/7
| 1–11/10–5/4–11/8–11/7
| Valinorsmic
|  
|  
|-
|-
| 38
| 38
|  
| 0–7–14–16–18
| 1–10/9–11/9–11/8–11/7
| 1–11/10–11/9–11/8–11/7
|  
| Utonal
| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]
|-
|-
| 39
| 39
|  
| 0–7–15–16–18
| 1–10/9–11/6–11/8–11/7
| 1–11/10–11/8–11/7–11/6
|  
| Utonal
| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]
|-
|-
| 40
| 40
|  
| 0–14–15–16–18
| 1–11/9–11/6–11/8–11/7
| 1–11/9–11/8–11/7–11/6
|  
| Utonal
| [[462:693:792:1008:1232|1/(24:16:14:11:9)]]
|}
|}


== Hexads ==
== Hexads ==
{| class="wikitable"
{| class="wikitable sortable center-1"
|-
|-
! #
! #
! Generators
! class="unsortable" | Generators
! Transversal
! class="unsortable" | Transversal
! Type
! Type
! class="unsortable" | Comments
|-
|-
| 1
| 1
| 0–4–7–8–11–15
| 0–4–7–8–11–15
| 1–9/7–10/9–5/3–10/7–11/6
| 1–10/9–9/7–10/7–5/3–11/6
| Octarod
|  
|  
|-
|-
Line 822: Line 986:
| 0–2–3–4–11–18
| 0–2–3–4–11–18
| 1–8/7–9/7–10/7–11/7–12/7
| 1–8/7–9/7–10/7–11/7–12/7
| otonal
| Otonal
| [[4:5:6:7:9:11]]
|-
|-
| 3
| 3
| 0–3–4–7–11–18
| 0–3–4–7–11–18
| 1–12/7–9/7–10/9–10/7–11/7
| 1–10/9–9/7–10/7–11/7–12/7
| Octarod
|  
|  
|-
|-
| 4
| 4
| 0–3–7–11–14–18
| 0–3–7–11–14–18
| 1–12/7–10/9–10/7–11/9–11/7
| 1–10/9–11/9–10/7–11/7–12/7
| Octarod
|  
|  
|-
|-
| 5
| 5
| 0–4–7–11–15–18
| 0–4–7–11–15–18
| 1–9/7–10/9–10/7–11/6–11/7
| 1–10/9–9/7–10/7–11/7–11/6
| Octarod
|  
|  
|-
|-
Line 842: Line 1,010:
| 0–7–11–14–15–18
| 0–7–11–14–15–18
| 1–10/9–10/7–11/9–11/6–11/7
| 1–10/9–10/7–11/9–11/6–11/7
| Octarod
|  
|  
|-
|-
Line 847: Line 1,016:
| 0–7–14–15–16–18
| 0–7–14–15–16–18
| 1–11/10–11/9–11/8–11/7–11/6
| 1–11/10–11/9–11/8–11/7–11/6
| utonal
| Utonal
| [[2310:2772:3465:3960:5040:6160|1/(24:20:16:14:11:9)]]
|}
|}


[[Category:Todo:expand]]
[[Category:Superpyth]]
[[Category:Lists of chords]]
[[Category:Dyadic chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
Retrieved from "https://en.xen.wiki/w/Chords_of_superpyth"