Chords of superpyth: Difference between revisions

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Line 13: Line 13:
! class="unsortable" | Transversal
! class="unsortable" | Transversal
! Type
! Type
! Comments
|-
|-
| 1
| 1
Line 18: Line 19:
| 1–9/8–3/2
| 1–9/8–3/2
| Ambitonal
| Ambitonal
| [[6:8:9]], [[8:9:12]]
|-
|-
| 2
| 2
Line 23: Line 25:
| 1–3/2–12/7
| 1–3/2–12/7
| Utonal
| Utonal
| [[14:21:24|1/(12:8:7)]]
|-
|-
| 3
| 3
Line 28: Line 31:
| 1–8/7–12/7
| 1–8/7–12/7
| Otonal
| Otonal
| [[4:6:7]]
|-
|-
| 4
| 4
Line 33: Line 37:
| 1–9/7–3/2
| 1–9/7–3/2
| Utonal
| Utonal
| [[14:18:21|1/(9:7:6)]]
|-
|-
| 5
| 5
Line 38: Line 43:
| 1–8/7–9/7
| 1–8/7–9/7
| Otonal/utonal
| Otonal/utonal
|
|-
|-
| 6
| 6
Line 43: Line 49:
| 1–9/7–12/7
| 1–9/7–12/7
| Otonal
| Otonal
| [[6:7:9]]
|-
|-
| 7
| 7
Line 48: Line 55:
| 1–10/9–12/7
| 1–10/9–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
Line 53: Line 61:
| 1–10/9–9/7
| 1–10/9–9/7
| Sensamagic
| Sensamagic
|
|-
|-
| 9
| 9
Line 58: Line 67:
| 1–3/2–5/3
| 1–3/2–5/3
| Otonal
| Otonal
| [[6:9:10]]
|-
|-
| 10
| 10
Line 63: Line 73:
| 1–9/7–5/3
| 1–9/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 11
| 11
Line 68: Line 79:
| 1–10/9–5/3
| 1–10/9–5/3
| Utonal
| Utonal
| [[10:15:18|1/(9:6:5)]]
|-
|-
| 12
| 12
Line 73: Line 85:
| 1–5/4–3/2
| 1–5/4–3/2
| Otonal
| Otonal
| [[4:5:6]]
|-
|-
| 13
| 13
Line 78: Line 91:
| 1–9/8–5/4
| 1–9/8–5/4
| Otonal
| Otonal
|
|-
|-
| 14
| 14
Line 83: Line 97:
| 1–10/9–5/4
| 1–10/9–5/4
| Utonal
| Utonal
|
|-
|-
| 15
| 15
Line 88: Line 103:
| 1–5/4–5/3
| 1–5/4–5/3
| Utonal
| Utonal
| [[10:12:15|1/(6:5:4)]]
|-
|-
| 16
| 16
Line 93: Line 109:
| 1–8/7–10/7
| 1–8/7–10/7
| Otonal
| Otonal
| [[4:5:7]]
|-
|-
| 17
| 17
Line 98: Line 115:
| 1–10/7–12/7
| 1–10/7–12/7
| Otonal
| Otonal
| [[5:6:7]]
|-
|-
| 18
| 18
Line 103: Line 121:
| 1–9/7–10/7
| 1–9/7–10/7
| Otonal
| Otonal
|
|-
|-
| 19
| 19
Line 108: Line 127:
| 1–10/9–10/7
| 1–10/9–10/7
| Utonal
| Utonal
|
|-
|-
| 20
| 20
Line 113: Line 133:
| 1–10/7–5/3
| 1–10/7–5/3
| Utonal
| Utonal
| [[30:35:42|1/(7:6:5)]]
|-
|-
| 21
| 21
Line 118: Line 139:
| 1–5/4–10/7
| 1–5/4–10/7
| Utonal
| Utonal
| [[20:28:35|1/(7:5:4)]]
|-
|-
| 22
| 22
Line 123: Line 145:
| 1–11/9–12/7
| 1–11/9–12/7
| Swetismic
| Swetismic
|
|-
|-
| 23
| 23
Line 128: Line 151:
| 1–10/9–11/9
| 1–10/9–11/9
| Otonal/utonal
| Otonal/utonal
|
|-
|-
| 24
| 24
Line 133: Line 157:
| 1–11/9–10/7
| 1–11/9–10/7
| Swetismic
| Swetismic
|
|-
|-
| 25
| 25
Line 138: Line 163:
| 1–3/2–11/6
| 1–3/2–11/6
| Otonal
| Otonal
|
|-
|-
| 26
| 26
Line 143: Line 169:
| 1–9/7–11/6
| 1–9/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 27
| 27
Line 148: Line 175:
| 1–11/10–11/6
| 1–11/10–11/6
| Utonal
| Utonal
|
|-
|-
| 28
| 28
Line 153: Line 181:
| 1–5/3–11/6
| 1–5/3–11/6
| Otonal
| Otonal
|
|-
|-
| 29
| 29
Line 158: Line 187:
| 1–10/7–11/6
| 1–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 163: Line 193:
| 1–11/9–11/6
| 1–11/9–11/6
| Utonal
| Utonal
|
|-
|-
| 31
| 31
Line 168: Line 199:
| 1–11/8–3/2
| 1–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 32
| 32
Line 173: Line 205:
| 1–9/8–11/8
| 1–9/8–11/8
| Otonal
| Otonal
|
|-
|-
| 33
| 33
Line 178: Line 211:
| 1–11/10–11/8
| 1–11/10–11/8
| Utonal
| Utonal
|
|-
|-
| 34
| 34
Line 183: Line 217:
| 1–11/8–5/3
| 1–11/8–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 35
| 35
Line 188: Line 223:
| 1–5/4–11/8
| 1–5/4–11/8
| Otonal
| Otonal
|
|-
|-
| 36
| 36
Line 193: Line 229:
| 1–11/9–11/8
| 1–11/9–11/8
| Utonal
| Utonal
|
|-
|-
| 37
| 37
Line 198: Line 235:
| 1–11/8–11/6
| 1–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 38
| 38
Line 203: Line 241:
| 1–8/7–11/7
| 1–8/7–11/7
| Otonal
| Otonal
|
|-
|-
| 39
| 39
Line 208: Line 247:
| 1–11/7–12/7
| 1–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 40
| 40
Line 213: Line 253:
| 1–9/7–11/7
| 1–9/7–11/7
| Otonal
| Otonal
|
|-
|-
| 41
| 41
Line 218: Line 259:
| 1–11/10–11/7
| 1–11/10–11/7
| Utonal
| Utonal
|
|-
|-
| 42
| 42
Line 223: Line 265:
| 1–5/4–11/7
| 1–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 43
| 43
Line 228: Line 271:
| 1–10/7–11/7
| 1–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 44
| 44
Line 233: Line 277:
| 1–11/9–11/7
| 1–11/9–11/7
| Utonal
| Utonal
|
|-
|-
| 45
| 45
Line 238: Line 283:
| 1–11/7–11/6
| 1–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 46
| 46
Line 243: Line 289:
| 1–11/8–11/7
| 1–11/8–11/7
| Utonal
| Utonal
|
|}
|}


Line 252: Line 299:
! class="unsortable" | Transversal
! class="unsortable" | Transversal
! Type
! Type
! Comments
|-
|-
| 1
| 1
Line 257: Line 305:
| 1–8/7–3/2–12/7
| 1–8/7–3/2–12/7
| Archytas
| Archytas
|
|-
|-
| 2
| 2
Line 262: Line 311:
| 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 317:
| 1–9/7–3/2–12/7
| 1–9/7–3/2–12/7
| Ambitonal
| Ambitonal
| [[12:14:18:21]], [[14:18:21:24]]
|-
|-
| 4
| 4
Line 272: Line 323:
| 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 329:
| 1–10/9–9/7–12/7
| 1–10/9–9/7–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 6
| 6
Line 282: Line 335:
| 1–9/7–3/2–5/3
| 1–9/7–3/2–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 7
| 7
Line 287: Line 341:
| 1–9/7–10/9–5/3
| 1–9/7–10/9–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 8
| 8
Line 292: Line 347:
| 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 353:
| 1–5/4–3/2–5/3
| 1–5/4–3/2–5/3
| Ambitonal
| Ambitonal
| [[10:12:15:18]], [[12:15:18:20]]
|-
|-
| 10
| 10
Line 302: Line 359:
| 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 365:
| 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 371:
| 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 377:
| 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 383:
| 1–10/9–10/7–12/7
| 1–10/9–10/7–12/7
| Sensamagic
| Sensamagic
|
|-
|-
| 15
| 15
Line 327: Line 389:
| 1–10/9–9/7–10/7
| 1–10/9–9/7–10/7
| Sensamagic
| Sensamagic
|
|-
|-
| 16
| 16
Line 332: Line 395:
| 1–9/7–10/7–5/3
| 1–9/7–10/7–5/3
| Sensamagic
| Sensamagic
|
|-
|-
| 17
| 17
Line 337: Line 401:
| 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 407:
| 1–8/7–5/4–10/7
| 1–8/7–5/4–10/7
| Archytas/valinorsmic
| Archytas/valinorsmic
|
|-
|-
| 19
| 19
Line 347: Line 413:
| 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 419:
| 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
Line 357: Line 425:
| 1–11/10–11/9–12/7
| 1–11/10–11/9–12/7
| Swetismic
| Swetismic
|
|-
|-
| 22
| 22
Line 362: Line 431:
| 1–11/9–10/7–12/7
| 1–11/9–10/7–12/7
| Swetismic
| Swetismic
|
|-
|-
| 23
| 23
Line 367: Line 437:
| 1–11/10–11/9–10/7
| 1–11/10–11/9–10/7
| Swetismic
| Swetismic
|
|-
|-
| 24
| 24
Line 372: Line 443:
| 1–9/7–3/2–11/6
| 1–9/7–3/2–11/6
| Swetismic
| Swetismic
|
|-
|-
| 25
| 25
Line 377: Line 449:
| 1–10/9–9/7–11/6
| 1–10/9–9/7–11/6
| Octarod
| Octarod
|
|-
|-
| 26
| 26
Line 382: Line 455:
| 1–3/2–5/3–11/6
| 1–3/2–5/3–11/6
| Otonal
| Otonal
|
|-
|-
| 27
| 27
Line 387: Line 461:
| 1–9/7–5/3–11/6
| 1–9/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 28
| 28
Line 392: Line 467:
| 1–10/9–5/3–11/6
| 1–10/9–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 29
| 29
Line 397: Line 473:
| 1–9/7–10/7–11/6
| 1–9/7–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 30
| 30
Line 402: Line 479:
| 1–10/9–10/7–11/6
| 1–10/9–10/7–11/6
| Octarod
| Octarod
|
|-
|-
| 31
| 31
Line 407: Line 485:
| 1–10/7–5/3–11/6
| 1–10/7–5/3–11/6
| Octarod
| Octarod
|
|-
|-
| 32
| 32
Line 412: Line 491:
| 1–11/10–11/9–11/6
| 1–11/10–11/9–11/6
| Utonal
| Utonal
|
|-
|-
| 33
| 33
Line 417: Line 497:
| 1–11/9–10/7–11/6
| 1–11/9–10/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 34
| 34
Line 422: Line 503:
| 1–9/8–11/8–3/2
| 1–9/8–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 35
| 35
Line 427: Line 509:
| 1–11/8–3/2–5/3
| 1–11/8–3/2–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 36
| 36
Line 432: Line 515:
| 1–10/9–5/3–11/8
| 1–10/9–5/3–11/8
| Ptolemismic
| Ptolemismic
|
|-
|-
| 37
| 37
Line 437: Line 521:
| 1–5/4–11/8–3/2
| 1–5/4–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 38
| 38
Line 442: Line 527:
| 1–9/8–5/4–11/8
| 1–9/8–5/4–11/8
| Otonal
| Otonal
|
|-
|-
| 39
| 39
Line 447: Line 533:
| 1–10/9–5/4–11/8
| 1–10/9–5/4–11/8
| Ptolemismic
| Ptolemismic
|
|-
|-
| 40
| 40
Line 452: Line 539:
| 1–5/4–11/8–5/3
| 1–5/4–11/8–5/3
| Ptolemismic
| Ptolemismic
|
|-
|-
| 41
| 41
Line 457: Line 545:
| 1–11/10–11/9–11/8
| 1–11/10–11/9–11/8
| Utonal
| Utonal
|
|-
|-
| 42
| 42
Line 462: Line 551:
| 1–11/8–3/2–11/6
| 1–11/8–3/2–11/6
| Ambitonal
| Ambitonal
|
|-
|-
| 43
| 43
Line 467: Line 557:
| 1–11/10–11/8–11/6
| 1–11/10–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 44
| 44
Line 472: Line 563:
| 1–11/8–5/3–11/6
| 1–11/8–5/3–11/6
| Ptolemismic
| Ptolemismic
|
|-
|-
| 45
| 45
Line 477: Line 569:
| 1–11/9–11/8–11/6
| 1–11/9–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 46
| 46
Line 482: Line 575:
| 1–8/7–11/7–12/7
| 1–8/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 47
| 47
Line 487: Line 581:
| 1–8/7–9/7–11/7
| 1–8/7–9/7–11/7
| Otonal
| Otonal
|
|-
|-
| 48
| 48
Line 492: Line 587:
| 1–9/7–11/7–12/7
| 1–9/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 49
| 49
Line 497: Line 593:
| 1–10/9–11/7–12/7
| 1–10/9–11/7–12/7
| Octarod
| Octarod
|
|-
|-
| 50
| 50
Line 502: Line 599:
| 1–11/10–9/7–11/7
| 1–11/10–9/7–11/7
| Swetismic
| Swetismic
|
|-
|-
| 51
| 51
Line 507: Line 605:
| 1–8/7–5/4–11/7
| 1–8/7–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 52
| 52
Line 512: Line 611:
| 1–11/10–5/4–11/7
| 1–11/10–5/4–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 53
| 53
Line 517: Line 617:
| 1–8/7–10/7–11/7
| 1–8/7–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 54
| 54
Line 522: Line 623:
| 1–10/7–11/7–12/7
| 1–10/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 55
| 55
Line 527: Line 629:
| 1–9/7–10/7–11/7
| 1–9/7–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 56
| 56
Line 532: Line 635:
| 1–10/9–10/7–11/7
| 1–10/9–10/7–11/7
| Ptolemismic
| Ptolemismic
|
|-
|-
| 57
| 57
Line 537: Line 641:
| 1–5/4–10/7–11/7
| 1–5/4–10/7–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 58
| 58
Line 542: Line 647:
| 1–11/9–11/7–12/7
| 1–11/9–11/7–12/7
| Swetismic
| Swetismic
|
|-
|-
| 59
| 59
Line 547: Line 653:
| 1–11/10–11/9–11/7
| 1–11/10–11/9–11/7
| Utonal
| Utonal
|
|-
|-
| 60
| 60
Line 552: Line 659:
| 1–11/9–10/7–11/7
| 1–11/9–10/7–11/7
| Swetismic
| Swetismic
|
|-
|-
| 61
| 61
Line 557: Line 665:
| 1–9/7–11/7–11/6
| 1–9/7–11/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 62
| 62
Line 562: Line 671:
| 1–11/10–11/7–11/6
| 1–11/10–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 63
| 63
Line 567: Line 677:
| 1–10/7–11/7–11/6
| 1–10/7–11/7–11/6
| Swetismic
| Swetismic
|
|-
|-
| 64
| 64
Line 572: Line 683:
| 1–11/9–11/7–11/6
| 1–11/9–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 65
| 65
Line 577: Line 689:
| 1–8/7–11/8–11/7
| 1–8/7–11/8–11/7
| Archytas
| Archytas
|
|-
|-
| 66
| 66
Line 582: Line 695:
| 1–11/10–11/8–11/7
| 1–11/10–11/8–11/7
| Utonal
| Utonal
|
|-
|-
| 67
| 67
Line 587: Line 701:
| 1–5/4–11/8–11/7
| 1–5/4–11/8–11/7
| Valinorsmic
| Valinorsmic
|
|-
|-
| 68
| 68
Line 592: Line 707:
| 1–11/9–11/8–11/7
| 1–11/9–11/8–11/7
| Utonal
| Utonal
|
|-
|-
| 69
| 69
Line 597: Line 713:
| 1–11/8–11/7–11/6
| 1–11/8–11/7–11/6
| Utonal
| Utonal
|
|}
|}


Line 606: Line 723:
! class="unsortable" | Transversal
! class="unsortable" | Transversal
! Type
! Type
! Comments
|-
|-
| 1
| 1
Line 611: Line 729:
| 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 735:
| 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 741:
| 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 747:
| 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 753:
| 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 759:
| 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 765:
| 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 771:
| 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 777:
| 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 783:
| 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 789:
| 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 795:
| 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 801:
| 1–9/8–5/4–11/8–3/2
| 1–9/8–5/4–11/8–3/2
| Otonal
| Otonal
|
|-
|-
| 14
| 14
Line 676: Line 807:
| 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 813:
| 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 819:
| 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 825:
| 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 831:
| 1–11/10–11/9–11/8–11/6
| 1–11/10–11/9–11/8–11/6
| Utonal
| Utonal
|
|-
|-
| 19
| 19
Line 701: Line 837:
| 1–8/7–9/7–11/7–12/7
| 1–8/7–9/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 20
| 20
Line 706: Line 843:
| 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 849:
| 1–8/7–10/7–11/7–12/7
| 1–8/7–10/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 22
| 22
Line 716: Line 855:
| 1–8/7–9/7–10/7–11/7
| 1–8/7–9/7–10/7–11/7
| Otonal
| Otonal
|
|-
|-
| 23
| 23
Line 721: Line 861:
| 1–9/7–10/7–11/7–12/7
| 1–9/7–10/7–11/7–12/7
| Otonal
| Otonal
|
|-
|-
| 24
| 24
Line 726: Line 867:
| 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 873:
| 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 879:
| 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 885:
| 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 891:
| 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 897:
| 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 903:
| 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 909:
| 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 915:
| 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 921:
| 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 927:
| 1–11/10–11/9–11/7–11/6
| 1–11/10–11/9–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 35
| 35
Line 781: Line 933:
| 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 939:
| 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 945:
| 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 951:
| 1–11/10–11/9–11/8–11/7
| 1–11/10–11/9–11/8–11/7
| Utonal
| Utonal
|
|-
|-
| 39
| 39
Line 801: Line 957:
| 1–11/10–11/8–11/7–11/6
| 1–11/10–11/8–11/7–11/6
| Utonal
| Utonal
|
|-
|-
| 40
| 40
Line 806: Line 963:
| 1–11/9–11/8–11/7–11/6
| 1–11/9–11/8–11/7–11/6
| Utonal
| Utonal
|
|}
|}


Line 815: Line 973:
! class="unsortable" | Transversal
! class="unsortable" | Transversal
! Type
! Type
! Comments
|-
|-
| 1
| 1
Line 820: Line 979:
| 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 985:
| 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 991:
| 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 997:
| 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 1,003:
| 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 1,009:
| 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 1,015:
| 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:Todo:expand]]

Revision as of 16:23, 17 December 2025

This user page is editable by any wiki editor.

As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.

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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 Comments
1 0–1–2 1–9/8–3/2 Ambitonal 6:8:9, 8:9:12
2 0–1–3 1–3/2–12/7 Utonal 1/(12:8:7)
3 0–2–3 1–8/7–12/7 Otonal 4:6:7
4 0–1–4 1–9/7–3/2 Utonal 1/(9:7:6)
5 0–2–4 1–8/7–9/7 Otonal/utonal
6 0–3–4 1–9/7–12/7 Otonal 6:7:9
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 6:9:10
10 0–4–8 1–9/7–5/3 Sensamagic
11 0–7–8 1–10/9–5/3 Utonal 1/(9:6:5)
12 0–1–9 1–5/4–3/2 Otonal 4:5:6
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 1/(6:5:4)
16 0–2–11 1–8/7–10/7 Otonal 4:5:7
17 0–3–11 1–10/7–12/7 Otonal 5:6:7
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 1/(7:6:5)
21 0–9–11 1–5/4–10/7 Utonal 1/(7:5:4)
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 Comments
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 1/(9:7:6:4)
3 0–1–3–4 1–9/7–3/2–12/7 Ambitonal 12:14:18:21, 14:18:21:24
4 0–2–3–4 1–8/7–9/7–12/7 Otonal 4:6:7:9
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 4:5:6:9
9 0–1–8–9 1–5/4–3/2–5/3 Ambitonal 10:12:15:18, 12:15:18:20
10 0–7–8–9 1–10/9–5/4–5/3 Utonal 1/(9:6:5:4)
11 0–2–3–11 1–8/7–10/7–12/7 Otonal 4:5:6:7
12 0–2–4–11 1–8/7–9/7–10/7 Otonal 4:5:7:9
13 0–3–4–11 1–9/7–10/7–12/7 Otonal 6:7:9:10
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 1/(9:7:6:5)
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 1/(9:7:5:4)
20 0–8–9–11 1–5/4–10/7–5/3 Utonal 1/(12:10:8:7)
21 0–3–7–14 1–11/10–11/9–12/7 Swetismic
22 0–3–11–14 1–11/9–10/7–12/7 Swetismic
23 0–7–11–14 1–11/10–11/9–10/7 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 1–11/10–9/7–11/7 Swetismic
51 0–2–9–18 1–8/7–5/4–11/7 Valinorsmic
52 0–7–9–18 1–11/10–5/4–11/7 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 Comments
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 4:5:6:7:9
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 1/(24:20:16:14:9)
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 Comments
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 4:5:6:7:9:11
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 1/(24:20:16:14:11:9)
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