Chords of orwell: Difference between revisions
Use comment to link to chord articles instead of listing all the rotations |
Remark on tetrads |
||
| Line 328: | Line 328: | ||
! Transversal | ! Transversal | ||
! Type | ! Type | ||
! | ! Comment | ||
! Example in 22edo | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 334: | Line 335: | ||
| 1–7/6–11/8–8/5 | | 1–7/6–11/8–8/5 | ||
| Orwellian | | Orwellian | ||
| | |||
| [[File:OrwellTetrad22edo.mp3]] | | [[File:OrwellTetrad22edo.mp3]] | ||
|- | |- | ||
| Line 340: | Line 342: | ||
| 1–11/8–8/5–11/10 | | 1–11/8–8/5–11/10 | ||
| Keenanismic | | Keenanismic | ||
| | |||
| [[File:Orwell_0_2_3_5_22edo.mp3]] | | [[File:Orwell_0_2_3_5_22edo.mp3]] | ||
|- | |- | ||
| Line 346: | Line 349: | ||
| 1–7/6–8/5–9/7 | | 1–7/6–8/5–9/7 | ||
| Unimarvel | | Unimarvel | ||
| | |||
| [[File:Orwell_0_1_3_6_22edo.mp3]] | | [[File:Orwell_0_1_3_6_22edo.mp3]] | ||
|- | |- | ||
| Line 352: | Line 356: | ||
| 1–8/5–11/10–9/7 | | 1–8/5–11/10–9/7 | ||
| Unimarvel | | Unimarvel | ||
| | |||
| [[File:Orwell_0_3_5_6_22edo.mp3]] | | [[File:Orwell_0_3_5_6_22edo.mp3]] | ||
|- | |- | ||
| Line 358: | Line 363: | ||
| 1–7/6–11/8–3/2 | | 1–7/6–11/8–3/2 | ||
| Big brother | | Big brother | ||
| | |||
| [[File:Orwell_0_1_2_7_22edo.mp3]] | | [[File:Orwell_0_1_2_7_22edo.mp3]] | ||
|- | |- | ||
| Line 364: | Line 370: | ||
| 1–11/8–11/10–3/2 | | 1–11/8–11/10–3/2 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| [[File:Orwell_0_2_5_7_22edo.mp3]] | | [[File:Orwell_0_2_5_7_22edo.mp3]] | ||
|- | |- | ||
| Line 370: | Line 377: | ||
| 1–7/6–9/7–3/2 | | 1–7/6–9/7–3/2 | ||
| Swetismic | | Swetismic | ||
| | |||
| [[File:Orwell_0_1_6_7_22edo.mp3]] | | [[File:Orwell_0_1_6_7_22edo.mp3]] | ||
|- | |- | ||
| Line 376: | Line 384: | ||
| 1–11/10–9/7–3/2 | | 1–11/10–9/7–3/2 | ||
| Big brother | | Big brother | ||
| | |||
| [[File:Orwell_0_5_6_7_22edo.mp3]] | | [[File:Orwell_0_5_6_7_22edo.mp3]] | ||
|- | |- | ||
| Line 382: | Line 391: | ||
| 1–7/6–11/8–7/4 | | 1–7/6–11/8–7/4 | ||
| Mothwellsmic | | Mothwellsmic | ||
| | |||
| [[File:Orwell_0_1_2_8_22edo.mp3]] | | [[File:Orwell_0_1_2_8_22edo.mp3]] | ||
|- | |- | ||
| Line 388: | Line 398: | ||
| 1–7/6–8/5–7/4 | | 1–7/6–8/5–7/4 | ||
| Zeus | | Zeus | ||
| | |||
| [[File:Orwell_0_1_3_8_22edo.mp3]] | | [[File:Orwell_0_1_3_8_22edo.mp3]] | ||
|- | |- | ||
| Line 394: | Line 405: | ||
| 1–11/8–8/5–7/4 | | 1–11/8–8/5–7/4 | ||
| Orwell | | Orwell | ||
| | |||
| [[File:Orwell_0_2_3_8_22edo.mp3]] | | [[File:Orwell_0_2_3_8_22edo.mp3]] | ||
|- | |- | ||
| Line 400: | Line 412: | ||
| 1–11/8–11/10–7/4 | | 1–11/8–11/10–7/4 | ||
| Minerva | | Minerva | ||
| | |||
| [[File:Orwell_0_2_5_8_22edo.mp3]] | | [[File:Orwell_0_2_5_8_22edo.mp3]] | ||
|- | |- | ||
| Line 406: | Line 419: | ||
| 1–8/5–11/10–7/4 | | 1–8/5–11/10–7/4 | ||
| Valinorsmic | | Valinorsmic | ||
| | |||
| [[File:Orwell_0_3_5_8_22edo.mp3]] | | [[File:Orwell_0_3_5_8_22edo.mp3]] | ||
|- | |- | ||
| Line 412: | Line 426: | ||
| 1–7/6–14/11–7/4 | | 1–7/6–14/11–7/4 | ||
| Utonal | | Utonal | ||
| | |||
| [[File:Orwell_0_1_6_8_22edo.mp3]] | | [[File:Orwell_0_1_6_8_22edo.mp3]] | ||
|- | |- | ||
| Line 418: | Line 433: | ||
| 1–8/5–9/7–7/4 | | 1–8/5–9/7–7/4 | ||
| Minerva | | Minerva | ||
| | |||
| | | | ||
|- | |- | ||
| Line 424: | Line 440: | ||
| 1–11/10–9/7–7/4 | | 1–11/10–9/7–7/4 | ||
| Orwell | | Orwell | ||
| | |||
| | | | ||
|- | |- | ||
| Line 430: | Line 447: | ||
| 1–7/6–3/2–7/4 | | 1–7/6–3/2–7/4 | ||
| Ambitonal | | Ambitonal | ||
| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]] | |||
| | | | ||
|- | |- | ||
| Line 436: | Line 454: | ||
| 1–11/8–3/2–7/4 | | 1–11/8–3/2–7/4 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 442: | Line 461: | ||
| 1–11/10–3/2–7/4 | | 1–11/10–3/2–7/4 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 448: | Line 468: | ||
| 1–9/7–3/2–7/4 | | 1–9/7–3/2–7/4 | ||
| Mothwellsmic | | Mothwellsmic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 454: | Line 475: | ||
| 1–11/8–8/5–6/5 | | 1–11/8–8/5–6/5 | ||
| Keenanismic | | Keenanismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 460: | Line 482: | ||
| 1–11/8–11/10–6/5 | | 1–11/8–11/10–6/5 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 466: | Line 489: | ||
| 1–8/5–11/10–6/5 | | 1–8/5–11/10–6/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 472: | Line 496: | ||
| 1–11/8–3/2–6/5 | | 1–11/8–3/2–6/5 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 478: | Line 503: | ||
| 1–12/11–3/2–6/5 | | 1–12/11–3/2–6/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 484: | Line 510: | ||
| 1–11/8–7/4–6/5 | | 1–11/8–7/4–6/5 | ||
| Orwellian | | Orwellian | ||
| | |||
| | | | ||
|- | |- | ||
| Line 490: | Line 517: | ||
| 1–8/5–7/4–6/5 | | 1–8/5–7/4–6/5 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 496: | Line 524: | ||
| 1–11/10–7/4–6/5 | | 1–11/10–7/4–6/5 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 502: | Line 531: | ||
| 1–3/2–7/4–6/5 | | 1–3/2–7/4–6/5 | ||
| Keenanismic | | Keenanismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 508: | Line 538: | ||
| 1–7/6–8/5–7/5 | | 1–7/6–8/5–7/5 | ||
| Keenanismic | | Keenanismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 514: | Line 545: | ||
| 1–8/5–11/10–7/5 | | 1–8/5–11/10–7/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 520: | Line 552: | ||
| 1–7/6–14/11–7/5 | | 1–7/6–14/11–7/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 526: | Line 559: | ||
| 1–8/5–9/7–7/5 | | 1–8/5–9/7–7/5 | ||
| Minerva | | Minerva | ||
| | |||
| | | | ||
|- | |- | ||
| Line 532: | Line 566: | ||
| 1–11/10–9/7–7/5 | | 1–11/10–9/7–7/5 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 538: | Line 573: | ||
| 1–7/6–7/4–7/5 | | 1–7/6–7/4–7/5 | ||
| Utonal | | Utonal | ||
| [[70:84:105:120|1/(12:10:8:7)]] | |||
| | | | ||
|- | |- | ||
| Line 544: | Line 580: | ||
| 1–8/5–7/4–7/5 | | 1–8/5–7/4–7/5 | ||
| Valinorsmic | | Valinorsmic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 550: | Line 587: | ||
| 1–11/10–7/4–7/5 | | 1–11/10–7/4–7/5 | ||
| Minerva | | Minerva | ||
| | |||
| | | | ||
|- | |- | ||
| Line 556: | Line 594: | ||
| 1–14/11–7/4–7/5 | | 1–14/11–7/4–7/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 562: | Line 601: | ||
| 1–8/5–6/5–7/5 | | 1–8/5–6/5–7/5 | ||
| Otonal | | Otonal | ||
| [[4:5:6:7]] | |||
| | | | ||
|- | |- | ||
| Line 568: | Line 608: | ||
| 1–11/10–6/5–7/5 | | 1–11/10–6/5–7/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 574: | Line 615: | ||
| 1–7/4–6/5–7/5 | | 1–7/4–6/5–7/5 | ||
| Keenanismic | | Keenanismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 580: | Line 622: | ||
| 1–7/6–11/8–18/11 | | 1–7/6–11/8–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 586: | Line 629: | ||
| 1–11/8–11/10–18/11 | | 1–11/8–11/10–18/11 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 592: | Line 636: | ||
| 1–7/6–9/7–18/11 | | 1–7/6–9/7–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 598: | Line 643: | ||
| 1–12/11–14/11–18/11 | | 1–12/11–14/11–18/11 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 604: | Line 650: | ||
| 1–7/6–3/2–18/11 | | 1–7/6–3/2–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 610: | Line 657: | ||
| 1–11/8–3/2–18/11 | | 1–11/8–3/2–18/11 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 616: | Line 664: | ||
| 1–12/11–3/2–18/11 | | 1–12/11–3/2–18/11 | ||
| Ambitonal | | Ambitonal | ||
| 11-odd-limit ASS | |||
| | | | ||
|- | |- | ||
| Line 622: | Line 671: | ||
| 1–9/7–3/2–18/11 | | 1–9/7–3/2–18/11 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 628: | Line 678: | ||
| 1–11/8–6/5–18/11 | | 1–11/8–6/5–18/11 | ||
| Zeus | | Zeus | ||
| | |||
| | | | ||
|- | |- | ||
| Line 634: | Line 685: | ||
| 1–11/10–6/5–18/11 | | 1–11/10–6/5–18/11 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 640: | Line 692: | ||
| 1–3/2–6/5–18/11 | | 1–3/2–6/5–18/11 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 646: | Line 699: | ||
| 1–7/6–7/5–18/11 | | 1–7/6–7/5–18/11 | ||
| Swetismic | | Swetismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 652: | Line 706: | ||
| 1–11/10–7/5–18/11 | | 1–11/10–7/5–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 658: | Line 713: | ||
| 1–9/7–7/5–18/11 | | 1–9/7–7/5–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 664: | Line 720: | ||
| 1–6/5–7/5–18/11 | | 1–6/5–7/5–18/11 | ||
| Big brother | | Big brother | ||
| | |||
| | | | ||
|- | |- | ||
| Line 670: | Line 727: | ||
| 1–11/8–8/5–9/8 | | 1–11/8–8/5–9/8 | ||
| Unimarvel | | Unimarvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 676: | Line 734: | ||
| 1–8/5–9/7–9/8 | | 1–8/5–9/7–9/8 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 682: | Line 741: | ||
| 1–11/8–3/2–9/8 | | 1–11/8–3/2–9/8 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 688: | Line 748: | ||
| 1–9/7–3/2–9/8 | | 1–9/7–3/2–9/8 | ||
| Utonal | | Utonal | ||
| [[28:36:42:63|1/(9:7:6:4)]] | |||
| | | | ||
|- | |- | ||
| Line 694: | Line 755: | ||
| 1–11/8–7/4–9/8 | | 1–11/8–7/4–9/8 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 700: | Line 762: | ||
| 1–8/5–7/4–9/8 | | 1–8/5–7/4–9/8 | ||
| Minerva | | Minerva | ||
| | |||
| | | | ||
|- | |- | ||
| Line 706: | Line 769: | ||
| 1–9/7–7/4–9/8 | | 1–9/7–7/4–9/8 | ||
| Mothwellsmic | | Mothwellsmic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 712: | Line 776: | ||
| 1–3/2–7/4–9/8 | | 1–3/2–7/4–9/8 | ||
| Otonal | | Otonal | ||
| [[4:6:7:9]] | |||
| | | | ||
|- | |- | ||
| Line 718: | Line 783: | ||
| 1–8/5–7/5–9/8 | | 1–8/5–7/5–9/8 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 724: | Line 790: | ||
| 1–9/7–7/5–9/8 | | 1–9/7–7/5–9/8 | ||
| Minerva | | Minerva | ||
| | |||
| | | | ||
|- | |- | ||
| Line 730: | Line 797: | ||
| 1–7/4–7/5–9/8 | | 1–7/4–7/5–9/8 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 736: | Line 804: | ||
| 1–11/8–18/11–9/8 | | 1–11/8–18/11–9/8 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 742: | Line 811: | ||
| 1–9/7–18/11–9/8 | | 1–9/7–18/11–9/8 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 748: | Line 818: | ||
| 1–3/2–18/11–9/8 | | 1–3/2–18/11–9/8 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 754: | Line 825: | ||
| 1–7/5–18/11–9/8 | | 1–7/5–18/11–9/8 | ||
| Unimarvel | | Unimarvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 760: | Line 832: | ||
| 1–8/5–11/10–9/5 | | 1–8/5–11/10–9/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 766: | Line 839: | ||
| 1–8/5–9/7–9/5 | | 1–8/5–9/7–9/5 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 772: | Line 846: | ||
| 1–11/10–9/7–9/5 | | 1–11/10–9/7–9/5 | ||
| Swetismic | | Swetismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 778: | Line 853: | ||
| 1–11/10–3/2–9/5 | | 1–11/10–3/2–9/5 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 784: | Line 860: | ||
| 1–9/7–3/2–9/5 | | 1–9/7–3/2–9/5 | ||
| Utonal | | Utonal | ||
| [[70:90:105:126|1/(9:7:6:5)]] | |||
| | | | ||
|- | |- | ||
| Line 790: | Line 867: | ||
| 1–8/5–6/5–9/5 | | 1–8/5–6/5–9/5 | ||
| Otonal | | Otonal | ||
| [[4:5:6:9]] | |||
| | | | ||
|- | |- | ||
| Line 796: | Line 874: | ||
| 1–11/10–6/5–9/5 | | 1–11/10–6/5–9/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 802: | Line 881: | ||
| 1–3/2–6/5–9/5 | | 1–3/2–6/5–9/5 | ||
| Ambitonal | | Ambitonal | ||
| [[10:12:15:18]], [[12:15:18:20]]<br>9-odd-limit ASS | |||
| | | | ||
|- | |- | ||
| Line 808: | Line 888: | ||
| 1–8/5–7/5–9/5 | | 1–8/5–7/5–9/5 | ||
| Otonal | | Otonal | ||
| [[4:5:7:9]] | |||
| | | | ||
|- | |- | ||
| Line 814: | Line 895: | ||
| 1–11/10–7/5–9/5 | | 1–11/10–7/5–9/5 | ||
| Otonal | | Otonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 820: | Line 902: | ||
| 1–9/7–7/5–9/5 | | 1–9/7–7/5–9/5 | ||
| Mothwellsmic | | Mothwellsmic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 826: | Line 909: | ||
| 1–6/5–7/5–9/5 | | 1–6/5–7/5–9/5 | ||
| Otonal | | Otonal | ||
| [[5:6:7:9]] | |||
| | | | ||
|- | |- | ||
| Line 832: | Line 916: | ||
| 1–11/10–18/11–9/5 | | 1–11/10–18/11–9/5 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 838: | Line 923: | ||
| 1–9/7–18/11–9/5 | | 1–9/7–18/11–9/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 844: | Line 930: | ||
| 1–3/2–18/11–9/5 | | 1–3/2–18/11–9/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|- | |- | ||
| Line 850: | Line 937: | ||
| 1–6/5–18/11–9/5 | | 1–6/5–18/11–9/5 | ||
| Biyatismic | | Biyatismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 856: | Line 944: | ||
| 1–7/5–18/11–9/5 | | 1–7/5–18/11–9/5 | ||
| Swetismic | | Swetismic | ||
| | |||
| | | | ||
|- | |- | ||
| Line 862: | Line 951: | ||
| 1–8/5–9/8–9/5 | | 1–8/5–9/8–9/5 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 868: | Line 958: | ||
| 1–9/7–9/8–9/5 | | 1–9/7–9/8–9/5 | ||
| Utonal | | Utonal | ||
| [[140:180:252:315|1/(9:7:5:4)]] | |||
| | | | ||
|- | |- | ||
| Line 874: | Line 965: | ||
| 1–3/2–9/8–9/5 | | 1–3/2–9/8–9/5 | ||
| Utonal | | Utonal | ||
| [[20:30:36:45|1/(9:6:5:4)]] | |||
| | | | ||
|- | |- | ||
| Line 880: | Line 972: | ||
| 1–7/5–9/8–9/5 | | 1–7/5–9/8–9/5 | ||
| Marvel | | Marvel | ||
| | |||
| | | | ||
|- | |- | ||
| Line 886: | Line 979: | ||
| 1–18/11–9/8–9/5 | | 1–18/11–9/8–9/5 | ||
| Utonal | | Utonal | ||
| | |||
| | | | ||
|} | |} | ||
Revision as of 09:56, 24 January 2026
Below are listed the 11-odd-limit dyadic chords of 11-limit orwell temperament. Typing the chords requires consideration of the fact that orwell equates certain 11-odd-limit consonances—it conflates 14/11 and 9/7, 11/7 and 14/9, 12/11 and 11/10, and 11/6 and 20/11. 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 which employs 9/7 and 11/10 and their inversions. Those requiring tempering only by 225/224 are labeled marvel, by 99/98 mothwellsmic, by 121/120 biyatismic, by 176/175 valinorsmic, by 385/384 keenanismic, and by 540/539 swetismic. If it requires any two of 99/98, 176/175 and 225/224, it is labeled minerva, any two of 99/98, 121/120 or 540/539, big brother, any two of 121/120, 176/175 or 385/384, zeus, any two of 225/224, 385/384 or 540/539, unimarvel. If it requires both 99/98 and 385/384 it is labeled orwellian, and if it requires three independent commas among those discussed above, it is labeled orwell. Orwell has mos of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic has three triads and a tetrad, the nine-note mos is of course much better supplied and with thirteen notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable major triad.
For diagrams showing how some of these chords might map to a keyboard such as the Axis-49, see Orwell on an isomorphic keyboard.
Triads
| # | Generators | Transversal | Type | Comment |
|---|---|---|---|---|
| 1 | 0–1–2 | 1–7/6–11/8 | Mothwellsmic | |
| 2 | 0–1–3 | 1–7/6–8/5 | Keenanismic | |
| 3 | 0–2–3 | 1–11/8–8/5 | Keenanismic | |
| 4 | 0–2–5 | 1–11/10–11/8 | Utonal | |
| 5 | 0–3–5 | 1–11/10–8/5 | Otonal | |
| 6 | 0–1–6 | 1–7/6–14/11 | Utonal | |
| 7 | 0–3–6 | 1–9/7–8/5 | Marvel | |
| 8 | 0–5–6 | 1–12/11–14/11 | Otonal | |
| 9 | 0–1–7 | 1–7/6–3/2 | Otonal | 6:7:9 |
| 10 | 0–2–7 | 1–11/8–3/2 | Otonal | |
| 11 | 0–5–7 | 1–12/11–3/2 | Utonal | |
| 12 | 0–6–7 | 1–9/7–3/2 | Utonal | 1/(9:7:6) |
| 13 | 0–1–8 | 1–7/6–7/4 | Utonal | 1/(12:8:7) |
| 14 | 0–2–8 | 1–11/8–7/4 | Otonal | |
| 15 | 0–3–8 | 1–8/5–7/4 | Valinorsmic | |
| 16 | 0–5–8 | 1–11/10–7/4 | Valinorsmic | |
| 17 | 0–6–8 | 1–14/11–7/4 | Utonal | |
| 18 | 0–7–8 | 1–3/2–7/4 | Otonal | 4:6:7 |
| 19 | 0–2–10 | 1–6/5–11/8 | Keenanismic | |
| 20 | 0–3–10 | 1–6/5–8/5 | Otonal | 4:5:6 |
| 21 | 0–5–10 | 1–11/10–6/5 | Otonal | |
| 22 | 0–7–10 | 1–6/5–3/2 | Utonal | 1/(6:5:4) |
| 23 | 0–8–10 | 1–6/5–7/4 | Keenanismic | |
| 24 | 0–1–11 | 1–7/6–7/5 | Utonal | 1/(7:6:5) |
| 25 | 0–3–11 | 1–7/5–8/5 | Otonal | 4:5:7 |
| 26 | 0–5–11 | 1–11/10–7/5 | Otonal | |
| 27 | 0–6–11 | 1–14/11–7/5 | Utonal | |
| 28 | 0–8–11 | 1–7/5–7/4 | Utonal | 1/(10:8:7) |
| 29 | 0–10–11 | 1–6/5–7/5 | Otonal | 5:6:7 |
| 30 | 0–1–12 | 1–7/6–18/11 | Swetismic | |
| 31 | 0–2–12 | 1–11/8–18/11 | Biyatismic | |
| 32 | 0–5–12 | 1–12/11–18/11 | Otonal | |
| 33 | 0–6–12 | 1–9/7–18/11 | Utonal | |
| 34 | 0–7–12 | 1–3/2–18/11 | Utonal | |
| 35 | 0–10–12 | 1–6/5–18/11 | Biyatismic | |
| 36 | 0–11–12 | 1–7/5–18/11 | Swetismic | |
| 37 | 0–2–14 | 1–9/8–11/8 | Otonal | |
| 38 | 0–3–14 | 1–9/8–8/5 | Marvel | |
| 39 | 0–6–14 | 1–9/8–9/7 | Utonal | |
| 40 | 0–7–14 | 1–9/8–3/2 | Ambitonal | 6:8:9, 8:9:12 |
| 41 | 0–8–14 | 1–9/8–7/4 | Otonal | |
| 42 | 0–11–14 | 1–9/8–7/5 | Marvel | |
| 43 | 0–12–14 | 1–9/8–18/11 | Utonal | |
| 44 | 0–3–17 | 1–8/5–9/5 | Otonal | |
| 45 | 0–5–17 | 1–11/10–9/5 | Otonal | |
| 46 | 0–6–17 | 1–9/7–9/5 | Utonal | |
| 47 | 0–7–17 | 1–3/2–9/5 | Utonal | 1/(9:6:5) |
| 48 | 0–10–17 | 1–6/5–9/5 | Otonal | 6:9:10 |
| 49 | 0–11–17 | 1–7/5–9/5 | Otonal | |
| 50 | 0–12–17 | 1–18/11–9/5 | Utonal | |
| 51 | 0–14–17 | 1–9/8–9/5 | Utonal |
Tetrads
| # | Chord | Transversal | Type | Comment | Example in 22edo |
|---|---|---|---|---|---|
| 1 | 0–1–2–3 | 1–7/6–11/8–8/5 | Orwellian | ||
| 2 | 0–2–3–5 | 1–11/8–8/5–11/10 | Keenanismic | ||
| 3 | 0–1–3–6 | 1–7/6–8/5–9/7 | Unimarvel | ||
| 4 | 0–3–5–6 | 1–8/5–11/10–9/7 | Unimarvel | ||
| 5 | 0–1–2–7 | 1–7/6–11/8–3/2 | Big brother | ||
| 6 | 0–2–5–7 | 1–11/8–11/10–3/2 | Biyatismic | ||
| 7 | 0–1–6–7 | 1–7/6–9/7–3/2 | Swetismic | ||
| 8 | 0–5–6–7 | 1–11/10–9/7–3/2 | Big brother | ||
| 9 | 0–1–2–8 | 1–7/6–11/8–7/4 | Mothwellsmic | ||
| 10 | 0–1–3–8 | 1–7/6–8/5–7/4 | Zeus | ||
| 11 | 0–2–3–8 | 1–11/8–8/5–7/4 | Orwell | ||
| 12 | 0–2–5–8 | 1–11/8–11/10–7/4 | Minerva | ||
| 13 | 0–3–5–8 | 1–8/5–11/10–7/4 | Valinorsmic | ||
| 14 | 0–1–6–8 | 1–7/6–14/11–7/4 | Utonal | ||
| 15 | 0–3–6–8 | 1–8/5–9/7–7/4 | Minerva | ||
| 16 | 0–5–6–8 | 1–11/10–9/7–7/4 | Orwell | ||
| 17 | 0–1–7–8 | 1–7/6–3/2–7/4 | Ambitonal | 12:14:18:21, 14:18:21:24 9-odd-limit ASS |
|
| 18 | 0–2–7–8 | 1–11/8–3/2–7/4 | Otonal | ||
| 19 | 0–5–7–8 | 1–11/10–3/2–7/4 | Zeus | ||
| 20 | 0–6–7–8 | 1–9/7–3/2–7/4 | Mothwellsmic | ||
| 21 | 0–2–3–10 | 1–11/8–8/5–6/5 | Keenanismic | ||
| 22 | 0–2–5–10 | 1–11/8–11/10–6/5 | Zeus | ||
| 23 | 0–3–5–10 | 1–8/5–11/10–6/5 | Otonal | ||
| 24 | 0–2–7–10 | 1–11/8–3/2–6/5 | Zeus | ||
| 25 | 0–5–7–10 | 1–12/11–3/2–6/5 | Utonal | ||
| 26 | 0–2–8–10 | 1–11/8–7/4–6/5 | Orwellian | ||
| 27 | 0–3–8–10 | 1–8/5–7/4–6/5 | Zeus | ||
| 28 | 0–5–8–10 | 1–11/10–7/4–6/5 | Zeus | ||
| 29 | 0–7–8–10 | 1–3/2–7/4–6/5 | Keenanismic | ||
| 30 | 0–1–3–11 | 1–7/6–8/5–7/5 | Keenanismic | ||
| 31 | 0–3–5–11 | 1–8/5–11/10–7/5 | Otonal | ||
| 32 | 0–1–6–11 | 1–7/6–14/11–7/5 | Utonal | ||
| 33 | 0–3–6–11 | 1–8/5–9/7–7/5 | Minerva | ||
| 34 | 0–5–6–11 | 1–11/10–9/7–7/5 | Big brother | ||
| 35 | 0–1–8–11 | 1–7/6–7/4–7/5 | Utonal | 1/(12:10:8:7) | |
| 36 | 0–3–8–11 | 1–8/5–7/4–7/5 | Valinorsmic | ||
| 37 | 0–5–8–11 | 1–11/10–7/4–7/5 | Minerva | ||
| 38 | 0–6–8–11 | 1–14/11–7/4–7/5 | Utonal | ||
| 39 | 0–3–10–11 | 1–8/5–6/5–7/5 | Otonal | 4:5:6:7 | |
| 40 | 0–5–10–11 | 1–11/10–6/5–7/5 | Otonal | ||
| 41 | 0–8–10–11 | 1–7/4–6/5–7/5 | Keenanismic | ||
| 42 | 0–1–2–12 | 1–7/6–11/8–18/11 | Big brother | ||
| 43 | 0–2–5–12 | 1–11/8–11/10–18/11 | Biyatismic | ||
| 44 | 0–1–6–12 | 1–7/6–9/7–18/11 | Big brother | ||
| 45 | 0–5–6–12 | 1–12/11–14/11–18/11 | Otonal | ||
| 46 | 0–1–7–12 | 1–7/6–3/2–18/11 | Big brother | ||
| 47 | 0–2–7–12 | 1–11/8–3/2–18/11 | Biyatismic | ||
| 48 | 0–5–7–12 | 1–12/11–3/2–18/11 | Ambitonal | 11-odd-limit ASS | |
| 49 | 0–6–7–12 | 1–9/7–3/2–18/11 | Utonal | ||
| 50 | 0–2–10–12 | 1–11/8–6/5–18/11 | Zeus | ||
| 51 | 0–5–10–12 | 1–11/10–6/5–18/11 | Biyatismic | ||
| 52 | 0–7–10–12 | 1–3/2–6/5–18/11 | Biyatismic | ||
| 53 | 0–1–11–12 | 1–7/6–7/5–18/11 | Swetismic | ||
| 54 | 0–5–11–12 | 1–11/10–7/5–18/11 | Big brother | ||
| 55 | 0–6–11–12 | 1–9/7–7/5–18/11 | Big brother | ||
| 56 | 0–10–11–12 | 1–6/5–7/5–18/11 | Big brother | ||
| 57 | 0–2–3–14 | 1–11/8–8/5–9/8 | Unimarvel | ||
| 58 | 0–3–6–14 | 1–8/5–9/7–9/8 | Marvel | ||
| 59 | 0–2–7–14 | 1–11/8–3/2–9/8 | Otonal | ||
| 60 | 0–6–7–14 | 1–9/7–3/2–9/8 | Utonal | 1/(9:7:6:4) | |
| 61 | 0–2–8–14 | 1–11/8–7/4–9/8 | Otonal | ||
| 62 | 0–3–8–14 | 1–8/5–7/4–9/8 | Minerva | ||
| 63 | 0–6–8–14 | 1–9/7–7/4–9/8 | Mothwellsmic | ||
| 64 | 0–7–8–14 | 1–3/2–7/4–9/8 | Otonal | 4:6:7:9 | |
| 65 | 0–3–11–14 | 1–8/5–7/5–9/8 | Marvel | ||
| 66 | 0–6–11–14 | 1–9/7–7/5–9/8 | Minerva | ||
| 67 | 0–8–11–14 | 1–7/4–7/5–9/8 | Marvel | ||
| 68 | 0–2–12–14 | 1–11/8–18/11–9/8 | Biyatismic | ||
| 69 | 0–6–12–14 | 1–9/7–18/11–9/8 | Utonal | ||
| 70 | 0–7–12–14 | 1–3/2–18/11–9/8 | Utonal | ||
| 71 | 0–11–12–14 | 1–7/5–18/11–9/8 | Unimarvel | ||
| 72 | 0–3–5–17 | 1–8/5–11/10–9/5 | Otonal | ||
| 73 | 0–3–6–17 | 1–8/5–9/7–9/5 | Marvel | ||
| 74 | 0–5–6–17 | 1–11/10–9/7–9/5 | Swetismic | ||
| 75 | 0–5–7–17 | 1–11/10–3/2–9/5 | Biyatismic | ||
| 76 | 0–6–7–17 | 1–9/7–3/2–9/5 | Utonal | 1/(9:7:6:5) | |
| 77 | 0–3–10–17 | 1–8/5–6/5–9/5 | Otonal | 4:5:6:9 | |
| 78 | 0–5–10–17 | 1–11/10–6/5–9/5 | Otonal | ||
| 79 | 0–7–10–17 | 1–3/2–6/5–9/5 | Ambitonal | 10:12:15:18, 12:15:18:20 9-odd-limit ASS |
|
| 80 | 0–3–11–17 | 1–8/5–7/5–9/5 | Otonal | 4:5:7:9 | |
| 81 | 0–5–11–17 | 1–11/10–7/5–9/5 | Otonal | ||
| 82 | 0–6–11–17 | 1–9/7–7/5–9/5 | Mothwellsmic | ||
| 83 | 0–10–11–17 | 1–6/5–7/5–9/5 | Otonal | 5:6:7:9 | |
| 84 | 0–5–12–17 | 1–11/10–18/11–9/5 | Biyatismic | ||
| 85 | 0–6–12–17 | 1–9/7–18/11–9/5 | Utonal | ||
| 86 | 0–7–12–17 | 1–3/2–18/11–9/5 | Utonal | ||
| 87 | 0–10–12–17 | 1–6/5–18/11–9/5 | Biyatismic | ||
| 88 | 0–11–12–17 | 1–7/5–18/11–9/5 | Swetismic | ||
| 89 | 0–3–14–17 | 1–8/5–9/8–9/5 | Marvel | ||
| 90 | 0–6–14–17 | 1–9/7–9/8–9/5 | Utonal | 1/(9:7:5:4) | |
| 91 | 0–7–14–17 | 1–3/2–9/8–9/5 | Utonal | 1/(9:6:5:4) | |
| 92 | 0–11–14–17 | 1–7/5–9/8–9/5 | Marvel | ||
| 93 | 0–12–14–17 | 1–18/11–9/8–9/5 | Utonal |
Pentads
| # | Chord | Transversal | Type |
|---|---|---|---|
| 1 | 0–1–2–3–8 | 1–7/6–11/8–8/5–7/4 | Orwell |
| 2 | 0–2–3–5–8 | 1–11/8–8/5–11/10–7/4 | Orwell |
| 3 | 0–1–3–6–8 | 1–7/6–8/5–9/7–7/4 | Orwell |
| 4 | 0–3–5–6–8 | 1–8/5–11/10–9/7–7/4 | Orwell |
| 5 | 0–1–2–7–8 | 1–7/6–11/8–3/2–7/4 | Big brother |
| 6 | 0–2–5–7–8 | 1–11/8–11/10–3/2–7/4 | Orwell |
| 7 | 0–1–6–7–8 | 1–7/6–9/7–3/2–7/4 | Big brother |
| 8 | 0–5–6–7–8 | 1–11/10–9/7–3/2–7/4 | Orwell |
| 9 | 0–2–3–5–10 | 1–11/8–8/5–11/10–6/5 | Zeus |
| 10 | 0–2–5–7–10 | 1–11/8–11/10–3/2–6/5 | Zeus |
| 11 | 0–2–3–8–10 | 1–11/8–8/5–7/4–6/5 | Orwell |
| 12 | 0–2–5–8–10 | 1–11/8–11/10–7/4–6/5 | Orwell |
| 13 | 0–3–5–8–10 | 1–8/5–11/10–7/4–6/5 | Zeus |
| 14 | 0–2–7–8–10 | 1–11/8–3/2–7/4–6/5 | Orwell |
| 15 | 0–5–7–8–10 | 1–11/10–3/2–7/4–6/5 | Zeus |
| 16 | 0–1–3–6–11 | 1–7/6–8/5–9/7–7/5 | Orwell |
| 17 | 0–3–5–6–11 | 1–8/5–11/10–9/7–7/5 | Orwell |
| 18 | 0–1–3–8–11 | 1–7/6–8/5–7/4–7/5 | Zeus |
| 19 | 0–3–5–8–11 | 1–8/5–11/10–7/4–7/5 | Minerva |
| 20 | 0–1–6–8–11 | 1–7/6–14/11–7/4–7/5 | Utonal |
| 21 | 0–3–6–8–11 | 1–8/5–9/7–7/4–7/5 | Minerva |
| 22 | 0–5–6–8–11 | 1–11/10–9/7–7/4–7/5 | Orwell |
| 23 | 0–3–5–10–11 | 1–8/5–11/10–6/5–7/5 | Otonal |
| 24 | 0–3–8–10–11 | 1–8/5–7/4–6/5–7/5 | Zeus |
| 25 | 0–5–8–10–11 | 1–11/10–7/4–6/5–7/5 | Orwell |
| 26 | 0–1–2–7–12 | 1–7/6–11/8–3/2–18/11 | Big brother |
| 27 | 0–2–5–7–12 | 1–11/8–11/10–3/2–18/11 | Biyatismic |
| 28 | 0–1–6–7–12 | 1–7/6–9/7–3/2–18/11 | Big brother |
| 29 | 0–5–6–7–12 | 1–11/10–9/7–3/2–18/11 | Big brother |
| 30 | 0–2–5–10–12 | 1–11/8–11/10–6/5–18/11 | Zeus |
| 31 | 0–2–7–10–12 | 1–11/8–3/2–6/5–18/11 | Zeus |
| 32 | 0–5–7–10–12 | 1–11/10–3/2–6/5–18/11 | Biyatismic |
| 33 | 0–1–6–11–12 | 1–7/6–9/7–7/5–18/11 | Big brother |
| 34 | 0–5–6–11–12 | 1–11/10–9/7–7/5–18/11 | Big brother |
| 35 | 0–5–10–11–12 | 1–11/10–6/5–7/5–18/11 | Big brother |
| 36 | 0–2–3–8–14 | 1–11/8–8/5–7/4–9/8 | Orwell |
| 37 | 0–3–6–8–14 | 1–8/5–9/7–7/4–9/8 | Minerva |
| 38 | 0–2–7–8–14 | 1–11/8–3/2–7/4–9/8 | Otonal |
| 39 | 0–6–7–8–14 | 1–9/7–3/2–7/4–9/8 | Mothwellsmic |
| 40 | 0–3–6–11–14 | 1–8/5–9/7–7/5–9/8 | Minerva |
| 41 | 0–3–8–11–14 | 1–8/5–7/4–7/5–9/8 | Minerva |
| 42 | 0–6–8–11–14 | 1–9/7–7/4–7/5–9/8 | Minerva |
| 43 | 0–2–7–12–14 | 1–11/8–3/2–18/11–9/8 | Biyatismic |
| 44 | 0–6–7–12–14 | 1–9/7–3/2–18/11–9/8 | Utonal |
| 45 | 0–6–11–12–14 | 1–9/7–7/5–18/11–9/8 | Orwell |
| 46 | 0–3–5–6–17 | 1–8/5–11/10–9/7–9/5 | Unimarvel |
| 47 | 0–5–6–7–17 | 1–11/10–9/7–3/2–9/5 | Big brother |
| 48 | 0–3–5–10–17 | 1–8/5–11/10–6/5–9/5 | Otonal |
| 49 | 0–5–7–10–17 | 1–11/10–3/2–6/5–9/5 | Biyatismic |
| 50 | 0–3–5–11–17 | 1–8/5–11/10–7/5–9/5 | Otonal |
| 51 | 0–3–6–11–17 | 1–8/5–9/7–7/5–9/5 | Minerva |
| 52 | 0–5–6–11–17 | 1–11/10–9/7–7/5–9/5 | Big brother |
| 53 | 0–3–10–11–17 | 1–8/5–6/5–7/5–9/5 | Otonal |
| 54 | 0–5–10–11–17 | 1–11/10–6/5–7/5–9/5 | Otonal |
| 55 | 0–5–6–12–17 | 1–11/10–9/7–18/11–9/5 | Big brother |
| 56 | 0–5–7–12–17 | 1–11/10–3/2–18/11–9/5 | Biyatismic |
| 57 | 0–6–7–12–17 | 1–9/7–3/2–18/11–9/5 | Utonal |
| 58 | 0–5–10–12–17 | 1–11/10–6/5–18/11–9/5 | Biyatismic |
| 59 | 0–7–10–12–17 | 1–3/2–6/5–18/11–9/5 | Biyatismic |
| 60 | 0–5–11–12–17 | 1–11/10–7/5–18/11–9/5 | Big brother |
| 61 | 0–6–11–12–17 | 1–9/7–7/5–18/11–9/5 | Big brother |
| 62 | 0–10–11–12–17 | 1–6/5–7/5–18/11–9/5 | Big brother |
| 63 | 0–3–6–14–17 | 1–8/5–9/7–9/8–9/5 | Marvel |
| 64 | 0–6–7–14–17 | 1–9/7–3/2–9/8–9/5 | Utonal |
| 65 | 0–3–11–14–17 | 1–8/5–7/5–9/8–9/5 | Marvel |
| 66 | 0–6–11–14–17 | 1–9/7–7/5–9/8–9/5 | Minerva |
| 67 | 0–6–12–14–17 | 1–9/7–18/11–9/8–9/5 | Utonal |
| 68 | 0–7–12–14–17 | 1–3/2–18/11–9/8–9/5 | Utonal |
| 69 | 0–11–12–14–17 | 1–7/5–18/11–9/8–9/5 | Unimarvel |
Hexads
| # | Chord | Transversal | Type |
|---|---|---|---|
| 1 | 0–2–3–5–8–10 | 1–11/8–8/5–11/10–7/4–6/5 | Orwell |
| 2 | 0–2–5–7–8–10 | 1–11/8–11/10–3/2–7/4–6/5 | Orwell |
| 3 | 0–1–3–6–8–11 | 1–7/6–8/5–9/7–7/4–7/5 | Orwell |
| 4 | 0–3–5–6–8–11 | 1–8/5–11/10–9/7–7/4–7/5 | Orwell |
| 5 | 0–3–5–8–10–11 | 1–8/5–11/10–7/4–6/5–7/5 | Orwell |
| 6 | 0–2–5–7–10–12 | 1–11/8–11/10–3/2–6/5–18/11 | Zeus |
| 7 | 0–3–6–8–11–14 | 1–8/5–9/7–7/4–7/5–9/8 | Minerva |
| 8 | 0–3–5–6–11–17 | 1–8/5–11/10–9/7–7/5–9/5 | Orwell |
| 9 | 0–3–5–10–11–17 | 1–8/5–11/10–6/5–7/5–9/5 | Otonal |
| 10 | 0–5–6–7–12–17 | 1–11/10–9/7–3/2–18/11–9/5 | Big brother |
| 11 | 0–5–7–10–12–17 | 1–11/10–3/2–6/5–18/11–9/5 | Biyatismic |
| 12 | 0–5–6–11–12–17 | 1–11/10–9/7–7/5–18/11–9/5 | Big brother |
| 13 | 0–5–10–11–12–17 | 1–11/10–6/5–7/5–18/11–9/5 | Big brother |
| 14 | 0–3–6–11–14–17 | 1–8/5–9/7–7/5–9/8–9/5 | Minerva |
| 15 | 0–6–7–12–14–17 | 1–9/7–3/2–18/11–9/8–9/5 | Utonal |
| 16 | 0–6–11–12–14–17 | 1–9/7–7/5–18/11–9/8–9/5 | Orwell |