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Chords of superpyth: Difference between revisions

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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.


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.
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]].  


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]].  
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 18: Line 21:
| 1–9/8–3/2
| 1–9/8–3/2
| Ambitonal
| Ambitonal
| [[6:8:9]], [[8:9:12]]
|-
|-
| 2
| 2
Line 23: Line 27:
| 1–3/2–12/7
| 1–3/2–12/7
| Utonal
| Utonal
| [[14:21:24|1/(12:8:7)]]
|-
|-
| 3
| 3
Line 28: Line 33:
| 1–8/7–12/7
| 1–8/7–12/7
| Otonal
| Otonal
| [[4:6:7]]
|-
|-
| 4
| 4
Line 33: Line 39:
| 1–9/7–3/2
| 1–9/7–3/2
| Utonal
| Utonal
| [[14:18:21|1/(9:7:6)]]
|-
|-
| 5
| 5
Line 38: 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 43: Line 51:
| 1–9/7–12/7
| 1–9/7–12/7
| Otonal
| Otonal
| [[6:7:9]]
|-
|-
| 7
| 7
Line 48: Line 57:
| 1–10/9–12/7
| 1–10/9–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
Line 53: Line 63:
| 1–10/9–9/7
| 1–10/9–9/7
| Sensamagic
| Sensamagic
|
|-
|-
| 9
| 9
Line 58: Line 69:
| 1–3/2–5/3
| 1–3/2–5/3
| Otonal
| Otonal
| [[6:9:10]]
|-
|-
| 10
| 10
Line 63: Line 75:
| 1–9/7–5/3
| 1–9/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 11
| 11
Line 68: Line 81:
| 1–10/9–5/3
| 1–10/9–5/3
| Utonal
| Utonal
| [[10:15:18|1/(9:6:5)]]
|-
|-
| 12
| 12
Line 73: Line 87:
| 1–5/4–3/2
| 1–5/4–3/2
| Otonal
| Otonal
| [[4:5:6]]
|-
|-
| 13
| 13
Line 78: Line 93:
| 1–9/8–5/4
| 1–9/8–5/4
| Otonal
| Otonal
|
|-
|-
| 14
| 14
Line 83: Line 99:
| 1–10/9–5/4
| 1–10/9–5/4
| Utonal
| Utonal
|
|-
|-
| 15
| 15
Line 88: Line 105:
| 1–5/4–5/3
| 1–5/4–5/3
| Utonal
| Utonal
| [[10:12:15|1/(6:5:4)]]
|-
|-
| 16
| 16
Line 93: Line 111:
| 1–8/7–10/7
| 1–8/7–10/7
| Otonal
| Otonal
| [[4:5:7]]
|-
|-
| 17
| 17
Line 98: Line 117:
| 1–10/7–12/7
| 1–10/7–12/7
| Otonal
| Otonal
| [[5:6:7]]
|-
|-
| 18
| 18
Line 103: Line 123:
| 1–9/7–10/7
| 1–9/7–10/7
| Otonal
| Otonal
|
|-
|-
| 19
| 19
Line 108: Line 129:
| 1–10/9–10/7
| 1–10/9–10/7
| Utonal
| Utonal
|
|-
|-
| 20
| 20
Line 113: Line 135:
| 1–10/7–5/3
| 1–10/7–5/3
| Utonal
| Utonal
| [[30:35:42|1/(7:6:5)]]
|-
|-
| 21
| 21
Line 118: Line 141:
| 1–5/4–10/7
| 1–5/4–10/7
| Utonal
| Utonal
| [[28:35:40|1/(10:8:7)]]
|-
|-
| 22
| 22
Line 123: Line 147:
| 1–11/9–12/7
| 1–11/9–12/7
| Swetismic
| Swetismic
|
|-
|-
| 23
| 23
Line 128: 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 133: Line 159:
| 1–11/9–10/7
| 1–11/9–10/7
| Swetismic
| Swetismic
|
|-
|-
| 25
| 25
Line 138: Line 165:
| 1–3/2–11/6
| 1–3/2–11/6
| Otonal
| Otonal
|
|-
|-
| 26
| 26
Line 143: Line 171:
| 1–9/7–11/6
| 1–9/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 27
| 27
Line 148: Line 177:
| 1–11/10–11/6
| 1–11/10–11/6
| Utonal
| Utonal
|
|-
|-
| 28
| 28
Line 153: Line 183:
| 1–5/3–11/6
| 1–5/3–11/6
| Otonal
| Otonal
|
|-
|-
| 29
| 29
Line 158: Line 189:
| 1–10/7–11/6
| 1–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 163: Line 195:
| 1–11/9–11/6
| 1–11/9–11/6
| Utonal
| Utonal
|
|-
|-
| 31
| 31
Line 168: Line 201:
| 1–11/8–3/2
| 1–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 32
| 32
Line 173: Line 207:
| 1–9/8–11/8
| 1–9/8–11/8
| Otonal
| Otonal
|
|-
|-
| 33
| 33
Line 178: Line 213:
| 1–11/10–11/8
| 1–11/10–11/8
| Utonal
| Utonal
|
|-
|-
| 34
| 34
Line 183: Line 219:
| 1–11/8–5/3
| 1–11/8–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 35
| 35
Line 188: Line 225:
| 1–5/4–11/8
| 1–5/4–11/8
| Otonal
| Otonal
|
|-
|-
| 36
| 36
Line 193: Line 231:
| 1–11/9–11/8
| 1–11/9–11/8
| Utonal
| Utonal
|
|-
|-
| 37
| 37
Line 198: Line 237:
| 1–11/8–11/6
| 1–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 38
| 38
Line 203: Line 243:
| 1–8/7–11/7
| 1–8/7–11/7
| Otonal
| Otonal
|
|-
|-
| 39
| 39
Line 208: Line 249:
| 1–11/7–12/7
| 1–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 40
| 40
Line 213: Line 255:
| 1–9/7–11/7
| 1–9/7–11/7
| Otonal
| Otonal
|
|-
|-
| 41
| 41
Line 218: Line 261:
| 1–11/10–11/7
| 1–11/10–11/7
| Utonal
| Utonal
|
|-
|-
| 42
| 42
Line 223: Line 267:
| 1–5/4–11/7
| 1–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 43
| 43
Line 228: Line 273:
| 1–10/7–11/7
| 1–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 44
| 44
Line 233: Line 279:
| 1–11/9–11/7
| 1–11/9–11/7
| Utonal
| Utonal
|
|-
|-
| 45
| 45
Line 238: Line 285:
| 1–11/7–11/6
| 1–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 46
| 46
Line 243: 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 820: 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 825: 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 830: 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 835: 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 840: 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 845: 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 850: 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"