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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
Line 16: Line 21:
| 1–9/8–3/2
| 1–9/8–3/2
| Ambitonal
| Ambitonal
| [[6:8:9]], [[8:9:12]]
|-
|-
| 2
| 2
Line 21: Line 27:
| 1–3/2–12/7
| 1–3/2–12/7
| Utonal
| Utonal
| [[14:21:24|1/(12:8:7)]]
|-
|-
| 3
| 3
Line 26: Line 33:
| 1–8/7–12/7
| 1–8/7–12/7
| Otonal
| Otonal
| [[4:6:7]]
|-
|-
| 4
| 4
Line 31: Line 39:
| 1–9/7–3/2
| 1–9/7–3/2
| Utonal
| Utonal
| [[14:18:21|1/(9:7:6)]]
|-
|-
| 5
| 5
Line 36: Line 45:
| 1–8/7–9/7
| 1–8/7–9/7
| Otonal/utonal
| Otonal/utonal
| 7:8:9~1/(9:8:7)
|-
|-
| 6
| 6
Line 41: Line 51:
| 1–9/7–12/7
| 1–9/7–12/7
| Otonal
| Otonal
| [[6:7:9]]
|-
|-
| 7
| 7
Line 46: Line 57:
| 1–10/9–12/7
| 1–10/9–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
Line 51: Line 63:
| 1–10/9–9/7
| 1–10/9–9/7
| Sensamagic
| Sensamagic
|
|-
|-
| 9
| 9
Line 56: Line 69:
| 1–3/2–5/3
| 1–3/2–5/3
| Otonal
| Otonal
| [[6:9:10]]
|-
|-
| 10
| 10
Line 61: Line 75:
| 1–9/7–5/3
| 1–9/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 11
| 11
Line 66: Line 81:
| 1–10/9–5/3
| 1–10/9–5/3
| Utonal
| Utonal
| [[10:15:18|1/(9:6:5)]]
|-
|-
| 12
| 12
Line 71: Line 87:
| 1–5/4–3/2
| 1–5/4–3/2
| Otonal
| Otonal
| [[4:5:6]]
|-
|-
| 13
| 13
Line 76: Line 93:
| 1–9/8–5/4
| 1–9/8–5/4
| Otonal
| Otonal
|
|-
|-
| 14
| 14
Line 81: Line 99:
| 1–10/9–5/4
| 1–10/9–5/4
| Utonal
| Utonal
|
|-
|-
| 15
| 15
Line 86: Line 105:
| 1–5/4–5/3
| 1–5/4–5/3
| Utonal
| Utonal
| [[10:12:15|1/(6:5:4)]]
|-
|-
| 16
| 16
Line 91: Line 111:
| 1–8/7–10/7
| 1–8/7–10/7
| Otonal
| Otonal
| [[4:5:7]]
|-
|-
| 17
| 17
Line 96: Line 117:
| 1–10/7–12/7
| 1–10/7–12/7
| Otonal
| Otonal
| [[5:6:7]]
|-
|-
| 18
| 18
Line 101: Line 123:
| 1–9/7–10/7
| 1–9/7–10/7
| Otonal
| Otonal
|
|-
|-
| 19
| 19
Line 106: Line 129:
| 1–10/9–10/7
| 1–10/9–10/7
| Utonal
| Utonal
|
|-
|-
| 20
| 20
Line 111: Line 135:
| 1–10/7–5/3
| 1–10/7–5/3
| Utonal
| Utonal
| [[30:35:42|1/(7:6:5)]]
|-
|-
| 21
| 21
Line 116: Line 141:
| 1–5/4–10/7
| 1–5/4–10/7
| Utonal
| Utonal
| [[28:35:40|1/(10:8:7)]]
|-
|-
| 22
| 22
Line 121: Line 147:
| 1–11/9–12/7
| 1–11/9–12/7
| Swetismic
| Swetismic
|
|-
|-
| 23
| 23
Line 126: Line 153:
| 1–10/9–11/9
| 1–10/9–11/9
| Otonal/utonal
| Otonal/utonal
| 9:10:11~1/(11:10:9)
|-
|-
| 24
| 24
Line 131: Line 159:
| 1–11/9–10/7
| 1–11/9–10/7
| Swetismic
| Swetismic
|
|-
|-
| 25
| 25
Line 136: Line 165:
| 1–3/2–11/6
| 1–3/2–11/6
| Otonal
| Otonal
|
|-
|-
| 26
| 26
Line 141: Line 171:
| 1–9/7–11/6
| 1–9/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 27
| 27
Line 146: Line 177:
| 1–11/10–11/6
| 1–11/10–11/6
| Utonal
| Utonal
|
|-
|-
| 28
| 28
Line 151: Line 183:
| 1–5/3–11/6
| 1–5/3–11/6
| Otonal
| Otonal
|
|-
|-
| 29
| 29
Line 156: Line 189:
| 1–10/7–11/6
| 1–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 161: Line 195:
| 1–11/9–11/6
| 1–11/9–11/6
| Utonal
| Utonal
|
|-
|-
| 31
| 31
Line 166: Line 201:
| 1–11/8–3/2
| 1–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 32
| 32
Line 171: Line 207:
| 1–9/8–11/8
| 1–9/8–11/8
| Otonal
| Otonal
|
|-
|-
| 33
| 33
Line 176: Line 213:
| 1–11/10–11/8
| 1–11/10–11/8
| Utonal
| Utonal
|
|-
|-
| 34
| 34
Line 181: Line 219:
| 1–11/8–5/3
| 1–11/8–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 35
| 35
Line 186: Line 225:
| 1–5/4–11/8
| 1–5/4–11/8
| Otonal
| Otonal
|
|-
|-
| 36
| 36
Line 191: Line 231:
| 1–11/9–11/8
| 1–11/9–11/8
| Utonal
| Utonal
|
|-
|-
| 37
| 37
Line 196: Line 237:
| 1–11/8–11/6
| 1–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 38
| 38
Line 201: Line 243:
| 1–8/7–11/7
| 1–8/7–11/7
| Otonal
| Otonal
|
|-
|-
| 39
| 39
Line 206: Line 249:
| 1–11/7–12/7
| 1–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 40
| 40
Line 211: Line 255:
| 1–9/7–11/7
| 1–9/7–11/7
| Otonal
| Otonal
|
|-
|-
| 41
| 41
Line 216: Line 261:
| 1–11/10–11/7
| 1–11/10–11/7
| Utonal
| Utonal
|
|-
|-
| 42
| 42
Line 221: Line 267:
| 1–5/4–11/7
| 1–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 43
| 43
Line 226: Line 273:
| 1–10/7–11/7
| 1–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 44
| 44
Line 231: Line 279:
| 1–11/9–11/7
| 1–11/9–11/7
| Utonal
| Utonal
|
|-
|-
| 45
| 45
Line 236: Line 285:
| 1–11/7–11/6
| 1–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 46
| 46
Line 241: Line 291:
| 1–11/8–11/7
| 1–11/8–11/7
| Utonal
| 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
Line 818: Line 981:
| 1–10/9–9/7–10/7–5/3–11/6
| 1–10/9–9/7–10/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 2
| 2
Line 823: Line 987:
| 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
Line 828: Line 993:
| 1–10/9–9/7–10/7–11/7–12/7
| 1–10/9–9/7–10/7–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 4
| 4
Line 833: Line 999:
| 1–10/9–11/9–10/7–11/7–12/7
| 1–10/9–11/9–10/7–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 5
| 5
Line 838: Line 1,005:
| 1–10/9–9/7–10/7–11/7–11/6
| 1–10/9–9/7–10/7–11/7–11/6
| Octarod
| Octarod
|
|-
|-
| 6
| 6
Line 843: Line 1,011:
| 1–10/9–10/7–11/9–11/6–11/7
| 1–10/9–10/7–11/9–11/6–11/7
| Octarod
| Octarod
|
|-
|-
| 7
| 7
Line 848: Line 1,017:
| 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"