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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]], 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 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
Line 257: Line 307:
| 1–8/7–3/2–12/7
| 1–8/7–3/2–12/7
| Archytas
| Archytas
|
|-
|-
| 2
| 2
Line 262: Line 313:
| 1–9/8–9/7–3/2
| 1–9/8–9/7–3/2
| Utonal
| Utonal
| [[28:36:42:63|1/(9:7:6:4)]]
|-
|-
| 3
| 3
Line 267: Line 319:
| 1–9/7–3/2–12/7
| 1–9/7–3/2–12/7
| Ambitonal
| Ambitonal
| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]]
|-
|-
| 4
| 4
Line 272: Line 325:
| 1–8/7–9/7–12/7
| 1–8/7–9/7–12/7
| Otonal
| Otonal
| [[4:6:7:9]]
|-
|-
| 5
| 5
Line 277: Line 331:
| 1–10/9–9/7–12/7
| 1–10/9–9/7–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 6
| 6
Line 282: Line 337:
| 1–9/7–3/2–5/3
| 1–9/7–3/2–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 7
| 7
Line 287: Line 343:
| 1–9/7–10/9–5/3
| 1–9/7–10/9–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
Line 292: Line 349:
| 1–9/8–5/4–3/2
| 1–9/8–5/4–3/2
| Otonal
| Otonal
| [[4:5:6:9]]
|-
|-
| 9
| 9
Line 297: Line 355:
| 1–5/4–3/2–5/3
| 1–5/4–3/2–5/3
| Ambitonal
| Ambitonal
| [[10:12:15:18]], [[12:15:18:20]]<br>9-odd-limit ASS
|-
|-
| 10
| 10
Line 302: Line 361:
| 1–10/9–5/4–5/3
| 1–10/9–5/4–5/3
| Utonal
| Utonal
| [[20:30:36:45|1/(9:6:5:4)]]
|-
|-
| 11
| 11
Line 307: Line 367:
| 1–8/7–10/7–12/7
| 1–8/7–10/7–12/7
| Otonal
| Otonal
| [[4:5:6:7]]
|-
|-
| 12
| 12
Line 312: Line 373:
| 1–8/7–9/7–10/7
| 1–8/7–9/7–10/7
| Otonal
| Otonal
| [[4:5:7:9]]
|-
|-
| 13
| 13
Line 317: Line 379:
| 1–9/7–10/7–12/7
| 1–9/7–10/7–12/7
| Otonal
| Otonal
| [[6:7:9:10]]
|-
|-
| 14
| 14
Line 322: Line 385:
| 1–10/9–10/7–12/7
| 1–10/9–10/7–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 15
| 15
Line 327: Line 391:
| 1–10/9–9/7–10/7
| 1–10/9–9/7–10/7
| Sensamagic
| Sensamagic
|
|-
|-
| 16
| 16
Line 332: Line 397:
| 1–9/7–10/7–5/3
| 1–9/7–10/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 17
| 17
Line 337: Line 403:
| 1–10/9–10/7–5/3
| 1–10/9–10/7–5/3
| Utonal
| Utonal
| [[70:90:105:126|1/(9:7:6:5)]]
|-
|-
| 18
| 18
Line 342: Line 409:
| 1–8/7–5/4–10/7
| 1–8/7–5/4–10/7
| Archytas/valinorsmic
| Archytas/valinorsmic
|
|-
|-
| 19
| 19
Line 347: Line 415:
| 1–10/9–5/4–10/7
| 1–10/9–5/4–10/7
| Utonal
| Utonal
| [[140:180:252:315|1/(9:7:5:4)]]
|-
|-
| 20
| 20
Line 352: Line 421:
| 1–5/4–10/7–5/3
| 1–5/4–10/7–5/3
| Utonal
| Utonal
| [[70:84:105:120|1/(12:10:8:7)]]
|-
|-
| 21
| 21
| 0–3–7–14
| 0–3–7–14
| 1–10/9–11/9–12/7
| 1–11/10–11/9–12/7
| Swetismic
| Swetismic
|
|-
|-
| 22
| 22
Line 362: Line 433:
| 1–11/9–10/7–12/7
| 1–11/9–10/7–12/7
| Swetismic
| Swetismic
|
|-
|-
| 23
| 23
| 0–7–11–14
| 0–7–11–14
| 1–10/9–11/9–10/7
| 1–11/10–11/9–10/7
| Swetismic
| Swetismic
|
|-
|-
| 24
| 24
Line 372: Line 445:
| 1–9/7–3/2–11/6
| 1–9/7–3/2–11/6
| Swetismic
| Swetismic
|
|-
|-
| 25
| 25
Line 377: Line 451:
| 1–10/9–9/7–11/6
| 1–10/9–9/7–11/6
| Octarod
| Octarod
|
|-
|-
| 26
| 26
Line 382: Line 457:
| 1–3/2–5/3–11/6
| 1–3/2–5/3–11/6
| Otonal
| Otonal
|
|-
|-
| 27
| 27
Line 387: Line 463:
| 1–9/7–5/3–11/6
| 1–9/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 28
| 28
Line 392: Line 469:
| 1–10/9–5/3–11/6
| 1–10/9–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 29
| 29
Line 397: Line 475:
| 1–9/7–10/7–11/6
| 1–9/7–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 402: Line 481:
| 1–10/9–10/7–11/6
| 1–10/9–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 31
| 31
Line 407: Line 487:
| 1–10/7–5/3–11/6
| 1–10/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 32
| 32
Line 412: Line 493:
| 1–11/10–11/9–11/6
| 1–11/10–11/9–11/6
| Utonal
| Utonal
|
|-
|-
| 33
| 33
Line 417: Line 499:
| 1–11/9–10/7–11/6
| 1–11/9–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 34
| 34
Line 422: Line 505:
| 1–9/8–11/8–3/2
| 1–9/8–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 35
| 35
Line 427: Line 511:
| 1–11/8–3/2–5/3
| 1–11/8–3/2–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 36
| 36
Line 432: Line 517:
| 1–10/9–5/3–11/8
| 1–10/9–5/3–11/8
| Ptolemismic
| Ptolemismic
|
|-
|-
| 37
| 37
Line 437: Line 523:
| 1–5/4–11/8–3/2
| 1–5/4–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 38
| 38
Line 442: Line 529:
| 1–9/8–5/4–11/8
| 1–9/8–5/4–11/8
| Otonal
| Otonal
|
|-
|-
| 39
| 39
| 0–7–9–16
| 0–7–9–16
| 1–10/9–5/4–11/8
| 1–10/9–5/4–11/8
| Ptolemismic
| Ptolemismic/valinorsmic
|
|-
|-
| 40
| 40
Line 452: Line 541:
| 1–5/4–11/8–5/3
| 1–5/4–11/8–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 41
| 41
Line 457: Line 547:
| 1–11/10–11/9–11/8
| 1–11/10–11/9–11/8
| Utonal
| Utonal
|
|-
|-
| 42
| 42
Line 462: Line 553:
| 1–11/8–3/2–11/6
| 1–11/8–3/2–11/6
| Ambitonal
| Ambitonal
| 11-odd-limit ASS
|-
|-
| 43
| 43
Line 467: Line 559:
| 1–11/10–11/8–11/6
| 1–11/10–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 44
| 44
Line 472: Line 565:
| 1–11/8–5/3–11/6
| 1–11/8–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 45
| 45
Line 477: Line 571:
| 1–11/9–11/8–11/6
| 1–11/9–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 46
| 46
Line 482: Line 577:
| 1–8/7–11/7–12/7
| 1–8/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 47
| 47
Line 487: Line 583:
| 1–8/7–9/7–11/7
| 1–8/7–9/7–11/7
| Otonal
| Otonal
|
|-
|-
| 48
| 48
Line 492: Line 589:
| 1–9/7–11/7–12/7
| 1–9/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 49
| 49
Line 497: Line 595:
| 1–10/9–11/7–12/7
| 1–10/9–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 50
| 50
| 0–4–7–18
| 0–4–7–18
| 1–10/9–9/7–11/7
| 1–11/10–9/7–11/7
| Swetismic
| Swetismic
|
|-
|-
| 51
| 51
Line 507: Line 607:
| 1–8/7–5/4–11/7
| 1–8/7–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 52
| 52
| 0–7–9–18
| 0–7–9–18
| 1–10/9–5/4–11/7
| 1–11/10–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 53
| 53
Line 517: Line 619:
| 1–8/7–10/7–11/7
| 1–8/7–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 54
| 54
Line 522: Line 625:
| 1–10/7–11/7–12/7
| 1–10/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 55
| 55
Line 527: Line 631:
| 1–9/7–10/7–11/7
| 1–9/7–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 56
| 56
Line 532: Line 637:
| 1–10/9–10/7–11/7
| 1–10/9–10/7–11/7
| Ptolemismic
| Ptolemismic
|
|-
|-
| 57
| 57
Line 537: Line 643:
| 1–5/4–10/7–11/7
| 1–5/4–10/7–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 58
| 58
Line 542: Line 649:
| 1–11/9–11/7–12/7
| 1–11/9–11/7–12/7
| Swetismic
| Swetismic
|
|-
|-
| 59
| 59
Line 547: Line 655:
| 1–11/10–11/9–11/7
| 1–11/10–11/9–11/7
| Utonal
| Utonal
|
|-
|-
| 60
| 60
Line 552: Line 661:
| 1–11/9–10/7–11/7
| 1–11/9–10/7–11/7
| Swetismic
| Swetismic
|
|-
|-
| 61
| 61
Line 557: Line 667:
| 1–9/7–11/7–11/6
| 1–9/7–11/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 62
| 62
Line 562: Line 673:
| 1–11/10–11/7–11/6
| 1–11/10–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 63
| 63
Line 567: Line 679:
| 1–10/7–11/7–11/6
| 1–10/7–11/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 64
| 64
Line 572: Line 685:
| 1–11/9–11/7–11/6
| 1–11/9–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 65
| 65
Line 577: Line 691:
| 1–8/7–11/8–11/7
| 1–8/7–11/8–11/7
| Archytas
| Archytas
|
|-
|-
| 66
| 66
Line 582: Line 697:
| 1–11/10–11/8–11/7
| 1–11/10–11/8–11/7
| Utonal
| Utonal
|
|-
|-
| 67
| 67
Line 587: Line 703:
| 1–5/4–11/8–11/7
| 1–5/4–11/8–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 68
| 68
Line 592: Line 709:
| 1–11/9–11/8–11/7
| 1–11/9–11/8–11/7
| Utonal
| Utonal
|
|-
|-
| 69
| 69
Line 597: Line 715:
| 1–11/8–11/7–11/6
| 1–11/8–11/7–11/6
| Utonal
| 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
Line 611: Line 731:
| 1–8/7–9/7–3/2–12/7
| 1–8/7–9/7–3/2–12/7
| Archytas
| Archytas
|
|-
|-
| 2
| 2
Line 616: Line 737:
| 1–8/7–9/7–10/7–12/7
| 1–8/7–9/7–10/7–12/7
| Otonal
| Otonal
| [[4:5:6:7:9]]
|-
|-
| 3
| 3
Line 621: Line 743:
| 1–10/9–9/7–10/7–12/7
| 1–10/9–9/7–10/7–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 4
| 4
Line 626: Line 749:
| 1–10/9–9/7–10/7–5/3
| 1–10/9–9/7–10/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 5
| 5
Line 631: Line 755:
| 1–10/9–5/4–10/7–5/3
| 1–10/9–5/4–10/7–5/3
| Utonal
| Utonal
| [[210:252:315:360:560|1/(24:20:16:14:9)]]
|-
|-
| 6
| 6
Line 636: Line 761:
| 1–10/9–11/9–10/7–12/7
| 1–10/9–11/9–10/7–12/7
| Octarod
| Octarod
|
|-
|-
| 7
| 7
Line 641: Line 767:
| 1–9/7–3/2–5/3–11/6
| 1–9/7–3/2–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 8
| 8
Line 646: Line 773:
| 1–10/9–9/7–5/3–11/6
| 1–10/9–9/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 9
| 9
Line 651: Line 779:
| 1–9/7–10/9–10/7–11/6
| 1–9/7–10/9–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 10
| 10
Line 656: Line 785:
| 1–9/7–5/3–10/7–11/6
| 1–9/7–5/3–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 11
| 11
Line 661: Line 791:
| 1–10/9–5/3–10/7–11/6
| 1–10/9–5/3–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 12
| 12
Line 666: Line 797:
| 1–10/9–11/9–10/7–11/6
| 1–10/9–11/9–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 13
| 13
Line 671: Line 803:
| 1–9/8–5/4–11/8–3/2
| 1–9/8–5/4–11/8–3/2
| Otonal
| Otonal
| [[4:5:6:9:11]]
|-
|-
| 14
| 14
Line 676: Line 809:
| 1–5/4–11/8–3/2–5/3
| 1–5/4–11/8–3/2–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 15
| 15
Line 681: Line 815:
| 1–10/9–5/3–5/4–11/8
| 1–10/9–5/3–5/4–11/8
| Ptolemismic
| Ptolemismic
|
|-
|-
| 16
| 16
Line 686: Line 821:
| 1–11/8–3/2–5/3–11/6
| 1–11/8–3/2–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 17
| 17
Line 691: Line 827:
| 1–10/9–11/8–5/3–11/6
| 1–10/9–11/8–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 18
| 18
Line 696: Line 833:
| 1–11/10–11/9–11/8–11/6
| 1–11/10–11/9–11/8–11/6
| Utonal
| Utonal
| [[330:396:495:720:880|1/(24:20:16:11:9)]]
|-
|-
| 19
| 19
Line 701: Line 839:
| 1–8/7–9/7–11/7–12/7
| 1–8/7–9/7–11/7–12/7
| Otonal
| Otonal
| [[4:6:7:9:11]]
|-
|-
| 20
| 20
Line 706: Line 845:
| 1–10/9–9/7–11/7–12/7
| 1–10/9–9/7–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 21
| 21
Line 711: Line 851:
| 1–8/7–10/7–11/7–12/7
| 1–8/7–10/7–11/7–12/7
| Otonal
| Otonal
| [[4:5:6:7:11]]
|-
|-
| 22
| 22
Line 716: Line 857:
| 1–8/7–9/7–10/7–11/7
| 1–8/7–9/7–10/7–11/7
| Otonal
| Otonal
| [[4:5:7:9:11]]
|-
|-
| 23
| 23
Line 721: Line 863:
| 1–9/7–10/7–11/7–12/7
| 1–9/7–10/7–11/7–12/7
| Otonal
| Otonal
| [[5:6:7:9:11]]
|-
|-
| 24
| 24
Line 726: Line 869:
| 1–12/7–10/9–10/7–11/7
| 1–12/7–10/9–10/7–11/7
| Octarod
| Octarod
|
|-
|-
| 25
| 25
Line 731: Line 875:
| 1–10/9–9/7–10/7–11/7
| 1–10/9–9/7–10/7–11/7
| Octarod
| Octarod
|
|-
|-
| 26
| 26
Line 736: Line 881:
| 1–8/7–5/4–10/7–11/7
| 1–8/7–5/4–10/7–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 27
| 27
Line 741: Line 887:
| 1–10/9–5/4–10/7–11/7
| 1–10/9–5/4–10/7–11/7
| Ares
| Ares
|
|-
|-
| 28
| 28
Line 746: Line 893:
| 1–10/9–11/9–11/7–12/7
| 1–10/9–11/9–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 29
| 29
Line 751: Line 899:
| 1–11/9–10/7–11/7–12/7
| 1–11/9–10/7–11/7–12/7
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 756: Line 905:
| 1–10/9–11/9–10/7–11/7
| 1–10/9–11/9–10/7–11/7
| Octarod
| Octarod
|
|-
|-
| 31
| 31
Line 761: Line 911:
| 1–10/9–9/7–11/7–11/6
| 1–10/9–9/7–11/7–11/6
| Octarod
| Octarod
|
|-
|-
| 32
| 32
Line 766: Line 917:
| 1–9/7–10/7–11/7–11/6
| 1–9/7–10/7–11/7–11/6
| Octarod
| Octarod
|
|-
|-
| 33
| 33
Line 771: Line 923:
| 1–10/9–10/7–11/7–11/6
| 1–10/9–10/7–11/7–11/6
| Octarod
| Octarod
|
|-
|-
| 34
| 34
Line 776: Line 929:
| 1–11/10–11/9–11/7–11/6
| 1–11/10–11/9–11/7–11/6
| Utonal
| Utonal
| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]
|-
|-
| 35
| 35
Line 781: Line 935:
| 1–11/9–10/7–11/7–11/6
| 1–11/9–10/7–11/7–11/6
| Octarod
| Octarod
|
|-
|-
| 36
| 36
Line 786: Line 941:
| 1–8/7–5/4–11/8–11/7
| 1–8/7–5/4–11/8–11/7
| Ares
| Ares
|
|-
|-
| 37
| 37
Line 791: Line 947:
| 1–11/10–5/4–11/8–11/7
| 1–11/10–5/4–11/8–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 38
| 38
Line 796: Line 953:
| 1–11/10–11/9–11/8–11/7
| 1–11/10–11/9–11/8–11/7
| Utonal
| Utonal
| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]
|-
|-
| 39
| 39
Line 801: Line 959:
| 1–11/10–11/8–11/7–11/6
| 1–11/10–11/8–11/7–11/6
| Utonal
| Utonal
| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]
|-
|-
| 40
| 40
Line 806: Line 965:
| 1–11/9–11/8–11/7–11/6
| 1–11/9–11/8–11/7–11/6
| Utonal
| 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"