72edo: Difference between revisions
m →Notation: I think I got the solution to this display problem |
→Intervals: sed -E "s#[0-9]+/[0-9]+#\\[\\[&\\]\\]#g" 72EDOintervals.txt > 72EDOintervals.new.txt |
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| Line 43: | Line 43: | ||
| 0 | | 0 | ||
| 0.0 | | 0.0 | ||
| 1/1 | | [[1/1]] | ||
| P1 | | P1 | ||
| perfect unison | | perfect unison | ||
| Line 54: | Line 54: | ||
| 1 | | 1 | ||
| 16.7 | | 16.7 | ||
| 81/80, 91/90, 99/98, 100/99, 105/104 | | [[81/80]], [[91/90]], [[99/98]], [[100/99]], [[105/104]] | ||
| ^1 | | ^1 | ||
| up unison | | up unison | ||
| Line 65: | Line 65: | ||
| 2 | | 2 | ||
| 33.3 | | 33.3 | ||
| 45/44, 49/48, 50/49, 55/54, 64/63 | | [[45/44]], [[49/48]], [[50/49]], [[55/54]], [[64/63]] | ||
| ^^ | | ^^ | ||
| dup unison | | dup unison | ||
| Line 76: | Line 76: | ||
| 3 | | 3 | ||
| 50.0 | | 50.0 | ||
| 33/32, 36/35, 40/39 | | [[33/32]], [[36/35]], [[40/39]] | ||
| ^<sup>3</sup>1, v<sup>3</sup>m2 | | ^<sup>3</sup>1, v<sup>3</sup>m2 | ||
| trup unison, trudminor 2nd | | trup unison, trudminor 2nd | ||
| Line 87: | Line 87: | ||
| 4 | | 4 | ||
| 66.7 | | 66.7 | ||
| 25/24, 26/25, 27/26, 28/27 | | [[25/24]], [[26/25]], [[27/26]], [[28/27]] | ||
| vvm2 | | vvm2 | ||
| dudminor 2nd | | dudminor 2nd | ||
| Line 98: | Line 98: | ||
| 5 | | 5 | ||
| 83.3 | | 83.3 | ||
| 20/19, 21/20, 22/21 | | [[20/19]], [[21/20]], [[22/21]] | ||
| vm2 | | vm2 | ||
| downminor 2nd | | downminor 2nd | ||
| Line 109: | Line 109: | ||
| 6 | | 6 | ||
| 100.0 | | 100.0 | ||
| 17/16, 18/17, 19/18 | | [[17/16]], [[18/17]], [[19/18]] | ||
| m2 | | m2 | ||
| minor 2nd | | minor 2nd | ||
| Line 120: | Line 120: | ||
| 7 | | 7 | ||
| 116.7 | | 116.7 | ||
| 15/14, 16/15 | | [[15/14]], [[16/15]] | ||
| ^m2 | | ^m2 | ||
| upminor 2nd | | upminor 2nd | ||
| Line 131: | Line 131: | ||
| 8 | | 8 | ||
| 133.3 | | 133.3 | ||
| 13/12, 14/13, 27/25 | | [[13/12]], [[14/13]], [[27/25]] | ||
| ^^m2, v~2 | | ^^m2, v~2 | ||
| dupminor 2nd, downmid 2nd | | dupminor 2nd, downmid 2nd | ||
| Line 142: | Line 142: | ||
| 9 | | 9 | ||
| 150.0 | | 150.0 | ||
| 12/11 | | [[12/11]] | ||
| ~2 | | ~2 | ||
| mid 2nd | | mid 2nd | ||
| Line 153: | Line 153: | ||
| 10 | | 10 | ||
| 166.7 | | 166.7 | ||
| 11/10 | | [[11/10]] | ||
| ^~2, vvM2 | | ^~2, vvM2 | ||
| upmid 2nd, dudmajor 2nd | | upmid 2nd, dudmajor 2nd | ||
| Line 164: | Line 164: | ||
| 11 | | 11 | ||
| 183.3 | | 183.3 | ||
| 10/9 | | [[10/9]] | ||
| vM2 | | vM2 | ||
| downmajor 2nd | | downmajor 2nd | ||
| Line 175: | Line 175: | ||
| 12 | | 12 | ||
| 200.0 | | 200.0 | ||
| 9/8, 19/17 | | [[9/8]], [[19/17]] | ||
| M2 | | M2 | ||
| major 2nd | | major 2nd | ||
| Line 186: | Line 186: | ||
| 13 | | 13 | ||
| 216.7 | | 216.7 | ||
| 17/15, 25/22 | | [[17/15]], [[25/22]] | ||
| ^M2 | | ^M2 | ||
| upmajor 2nd | | upmajor 2nd | ||
| Line 197: | Line 197: | ||
| 14 | | 14 | ||
| 233.3 | | 233.3 | ||
| 8/7 | | [[8/7]] | ||
| ^^M2 | | ^^M2 | ||
| dupmajor 2nd | | dupmajor 2nd | ||
| Line 208: | Line 208: | ||
| 15 | | 15 | ||
| 250.0 | | 250.0 | ||
| 15/13, 22/19 | | [[15/13]], [[22/19]] | ||
| ^<sup>3</sup>M2, <br>v<sup>3</sup>m3 | | ^<sup>3</sup>M2, <br>v<sup>3</sup>m3 | ||
| trupmajor 2nd,<br>trudminor 3rd | | trupmajor 2nd,<br>trudminor 3rd | ||
| Line 219: | Line 219: | ||
| 16 | | 16 | ||
| 266.7 | | 266.7 | ||
| 7/6 | | [[7/6]] | ||
| vvm3 | | vvm3 | ||
| dudminor 3rd | | dudminor 3rd | ||
| Line 230: | Line 230: | ||
| 17 | | 17 | ||
| 283.3 | | 283.3 | ||
| 13/11, 20/17 | | [[13/11]], [[20/17]] | ||
| vm3 | | vm3 | ||
| downminor 3rd | | downminor 3rd | ||
| Line 241: | Line 241: | ||
| 18 | | 18 | ||
| 300.0 | | 300.0 | ||
| 19/16, 25/21, 32/27 | | [[19/16]], [[25/21]], [[32/27]] | ||
| m3 | | m3 | ||
| minor 3rd | | minor 3rd | ||
| Line 252: | Line 252: | ||
| 19 | | 19 | ||
| 316.7 | | 316.7 | ||
| 6/5 | | [[6/5]] | ||
| ^m3 | | ^m3 | ||
| upminor 3rd | | upminor 3rd | ||
| Line 263: | Line 263: | ||
| 20 | | 20 | ||
| 333.3 | | 333.3 | ||
| 17/14, 39/32, 40/33 | | [[17/14]], [[39/32]], [[40/33]] | ||
| ^^m3, v~3 | | ^^m3, v~3 | ||
| dupminor 3rd, downmid 3rd | | dupminor 3rd, downmid 3rd | ||
| Line 274: | Line 274: | ||
| 21 | | 21 | ||
| 350.0 | | 350.0 | ||
| 11/9, 27/22 | | [[11/9]], [[27/22]] | ||
| ~3 | | ~3 | ||
| mid 3rd | | mid 3rd | ||
| Line 285: | Line 285: | ||
| 22 | | 22 | ||
| 366.7 | | 366.7 | ||
| 16/13, 21/17, 26/21 | | [[16/13]], [[21/17]], [[26/21]] | ||
| ^~3, vvM3 | | ^~3, vvM3 | ||
| upmid 3rd, dudmajor 3rd | | upmid 3rd, dudmajor 3rd | ||
| Line 296: | Line 296: | ||
| 23 | | 23 | ||
| 383.3 | | 383.3 | ||
| 5/4 | | [[5/4]] | ||
| vM3 | | vM3 | ||
| downmajor 3rd | | downmajor 3rd | ||
| Line 307: | Line 307: | ||
| 24 | | 24 | ||
| 400.0 | | 400.0 | ||
| 24/19 | | [[24/19]] | ||
| M3 | | M3 | ||
| major 3rd | | major 3rd | ||
| Line 318: | Line 318: | ||
| 25 | | 25 | ||
| 416.7 | | 416.7 | ||
| 14/11, 19/15 | | [[14/11]], [[19/15]] | ||
| ^M3 | | ^M3 | ||
| upmajor 3rd | | upmajor 3rd | ||
| Line 329: | Line 329: | ||
| 26 | | 26 | ||
| 433.3 | | 433.3 | ||
| 9/7 | | [[9/7]] | ||
| ^^M3 | | ^^M3 | ||
| dupmajor 3rd | | dupmajor 3rd | ||
| Line 340: | Line 340: | ||
| 27 | | 27 | ||
| 450.0 | | 450.0 | ||
| 13/10, 22/17 | | [[13/10]], [[22/17]] | ||
| ^<sup>3</sup>M3, v<sup>3</sup>4 | | ^<sup>3</sup>M3, v<sup>3</sup>4 | ||
| trupmajor 3rd, trud 4th | | trupmajor 3rd, trud 4th | ||
| Line 351: | Line 351: | ||
| 28 | | 28 | ||
| 466.7 | | 466.7 | ||
| 17/13, 21/16 | | [[17/13]], [[21/16]] | ||
| vv4 | | vv4 | ||
| dud 4th | | dud 4th | ||
| Line 362: | Line 362: | ||
| 29 | | 29 | ||
| 483.3 | | 483.3 | ||
| 33/25 | | [[33/25]] | ||
| v4 | | v4 | ||
| down 4th | | down 4th | ||
| Line 373: | Line 373: | ||
| 30 | | 30 | ||
| 500.0 | | 500.0 | ||
| 4/3 | | [[4/3]] | ||
| P4 | | P4 | ||
| perfect 4th | | perfect 4th | ||
| Line 384: | Line 384: | ||
| 31 | | 31 | ||
| 516.7 | | 516.7 | ||
| 27/20 | | [[27/20]] | ||
| ^4 | | ^4 | ||
| up 4th | | up 4th | ||
| Line 395: | Line 395: | ||
| 32 | | 32 | ||
| 533.3 | | 533.3 | ||
| 15/11, 19/14, ''26/19'' | | [[15/11]], [[19/14]], ''[[26/19]]'' | ||
| ^^4, v~4 | | ^^4, v~4 | ||
| dup 4th, downmid 4th | | dup 4th, downmid 4th | ||
| Line 406: | Line 406: | ||
| 33 | | 33 | ||
| 550.0 | | 550.0 | ||
| 11/8 | | [[11/8]] | ||
| ~4 | | ~4 | ||
| mid 4th | | mid 4th | ||
| Line 417: | Line 417: | ||
| 34 | | 34 | ||
| 566.7 | | 566.7 | ||
| 18/13, 25/18 | | [[18/13]], [[25/18]] | ||
| ^~4, vvA4 | | ^~4, vvA4 | ||
| upmid 4th, dudaug 4th | | upmid 4th, dudaug 4th | ||
| Line 428: | Line 428: | ||
| 35 | | 35 | ||
| 583.3 | | 583.3 | ||
| 7/5 | | [[7/5]] | ||
| vA4, vd5 | | vA4, vd5 | ||
| downaug 4th, <br>downdim 5th | | downaug 4th, <br>downdim 5th | ||
| Line 439: | Line 439: | ||
| 36 | | 36 | ||
| 600.0 | | 600.0 | ||
| 17/12, 24/17 | | [[17/12]], [[24/17]] | ||
| A4, d5 | | A4, d5 | ||
| aug 4th, dim 5th | | aug 4th, dim 5th | ||
| Line 450: | Line 450: | ||
| 37 | | 37 | ||
| 616.7 | | 616.7 | ||
| 10/7 | | [[10/7]] | ||
| ^A4, ^d5 | | ^A4, ^d5 | ||
| upaug 4th, updim 5th | | upaug 4th, updim 5th | ||
| Line 461: | Line 461: | ||
| 38 | | 38 | ||
| 633.3 | | 633.3 | ||
| 13/9, 36/25 | | [[13/9]], [[36/25]] | ||
| v~5, ^^d5 | | v~5, ^^d5 | ||
| downmid 5th, <br>dupdim 5th | | downmid 5th, <br>dupdim 5th | ||
| Line 472: | Line 472: | ||
| 39 | | 39 | ||
| 650.0 | | 650.0 | ||
| 16/11 | | [[16/11]] | ||
| ~5 | | ~5 | ||
| mid 5th | | mid 5th | ||
| Line 483: | Line 483: | ||
| 40 | | 40 | ||
| 666.7 | | 666.7 | ||
| ''19/13'', 22/15, 28/19 | | ''[[19/13]]'', [[22/15]], [[28/19]] | ||
| vv5, ^~5 | | vv5, ^~5 | ||
| dud 5th, upmid 5th | | dud 5th, upmid 5th | ||
| Line 494: | Line 494: | ||
| 41 | | 41 | ||
| 683.3 | | 683.3 | ||
| 40/27 | | [[40/27]] | ||
| v5 | | v5 | ||
| down 5th | | down 5th | ||
| Line 505: | Line 505: | ||
| 42 | | 42 | ||
| 700.0 | | 700.0 | ||
| 3/2 | | [[3/2]] | ||
| P5 | | P5 | ||
| perfect 5th | | perfect 5th | ||
| Line 516: | Line 516: | ||
| 43 | | 43 | ||
| 716.7 | | 716.7 | ||
| 50/33 | | [[50/33]] | ||
| ^5 | | ^5 | ||
| up 5th | | up 5th | ||
| Line 527: | Line 527: | ||
| 44 | | 44 | ||
| 733.3 | | 733.3 | ||
| 26/17, 32/21 | | [[26/17]], [[32/21]] | ||
| ^^5 | | ^^5 | ||
| dup 5th | | dup 5th | ||
| Line 538: | Line 538: | ||
| 45 | | 45 | ||
| 750.0 | | 750.0 | ||
| 17/11, 20/13 | | [[17/11]], [[20/13]] | ||
| ^<sup>3</sup>5, v<sup>3</sup>m6 | | ^<sup>3</sup>5, v<sup>3</sup>m6 | ||
| trup 5th, trudminor 6th | | trup 5th, trudminor 6th | ||
| Line 549: | Line 549: | ||
| 46 | | 46 | ||
| 766.7 | | 766.7 | ||
| 14/9 | | [[14/9]] | ||
| vvm6 | | vvm6 | ||
| dudminor 6th | | dudminor 6th | ||
| Line 560: | Line 560: | ||
| 47 | | 47 | ||
| 783.3 | | 783.3 | ||
| 11/7, 30/19 | | [[11/7]], [[30/19]] | ||
| vm6 | | vm6 | ||
| downminor 6th | | downminor 6th | ||
| Line 571: | Line 571: | ||
| 48 | | 48 | ||
| 800.0 | | 800.0 | ||
| 19/12 | | [[19/12]] | ||
| m6 | | m6 | ||
| minor 6th | | minor 6th | ||
| Line 582: | Line 582: | ||
| 49 | | 49 | ||
| 816.7 | | 816.7 | ||
| 8/5 | | [[8/5]] | ||
| ^m6 | | ^m6 | ||
| upminor 6th | | upminor 6th | ||
| Line 593: | Line 593: | ||
| 50 | | 50 | ||
| 833.3 | | 833.3 | ||
| 13/8, 21/13, 34/21 | | [[13/8]], [[21/13]], [[34/21]] | ||
| ^^m6, v~6 | | ^^m6, v~6 | ||
| dupminor 6th, downmid 6th | | dupminor 6th, downmid 6th | ||
| Line 604: | Line 604: | ||
| 51 | | 51 | ||
| 850.0 | | 850.0 | ||
| 18/11, 44/27 | | [[18/11]], [[44/27]] | ||
| ~6 | | ~6 | ||
| mid 6th | | mid 6th | ||
| Line 615: | Line 615: | ||
| 52 | | 52 | ||
| 866.7 | | 866.7 | ||
| 28/17, 33/20, 64/39 | | [[28/17]], [[33/20]], [[64/39]] | ||
| ^~6, vvM6 | | ^~6, vvM6 | ||
| upmid 6th, dudmajor 6th | | upmid 6th, dudmajor 6th | ||
| Line 626: | Line 626: | ||
| 53 | | 53 | ||
| 883.3 | | 883.3 | ||
| 5/3 | | [[5/3]] | ||
| vM6 | | vM6 | ||
| downmajor 6th | | downmajor 6th | ||
| Line 637: | Line 637: | ||
| 54 | | 54 | ||
| 900.0 | | 900.0 | ||
| 27/16, 32/19, 42/25 | | [[27/16]], [[32/19]], [[42/25]] | ||
| M6 | | M6 | ||
| major 6th | | major 6th | ||
| Line 648: | Line 648: | ||
| 55 | | 55 | ||
| 916.7 | | 916.7 | ||
| 17/10, 22/13 | | [[17/10]], [[22/13]] | ||
| ^M6 | | ^M6 | ||
| upmajor 6th | | upmajor 6th | ||
| Line 659: | Line 659: | ||
| 56 | | 56 | ||
| 933.3 | | 933.3 | ||
| 12/7 | | [[12/7]] | ||
| ^^M6 | | ^^M6 | ||
| dupmajor 6th | | dupmajor 6th | ||
| Line 670: | Line 670: | ||
| 57 | | 57 | ||
| 950.0 | | 950.0 | ||
| 19/11, 26/15 | | [[19/11]], [[26/15]] | ||
| ^<sup>3</sup>M6, <br>v<sup>3</sup>m7 | | ^<sup>3</sup>M6, <br>v<sup>3</sup>m7 | ||
| trupmajor 6th,<br>trudminor 7th | | trupmajor 6th,<br>trudminor 7th | ||
| Line 681: | Line 681: | ||
| 58 | | 58 | ||
| 966.7 | | 966.7 | ||
| 7/4 | | [[7/4]] | ||
| vvm7 | | vvm7 | ||
| dudminor 7th | | dudminor 7th | ||
| Line 692: | Line 692: | ||
| 59 | | 59 | ||
| 983.3 | | 983.3 | ||
| 30/17, 44/25 | | [[30/17]], [[44/25]] | ||
| vm7 | | vm7 | ||
| downminor 7th | | downminor 7th | ||
| Line 703: | Line 703: | ||
| 60 | | 60 | ||
| 1000.0 | | 1000.0 | ||
| 16/9, 34/19 | | [[16/9]], [[34/19]] | ||
| m7 | | m7 | ||
| minor 7th | | minor 7th | ||
| Line 714: | Line 714: | ||
| 61 | | 61 | ||
| 1016.7 | | 1016.7 | ||
| 9/5 | | [[9/5]] | ||
| ^m7 | | ^m7 | ||
| upminor 7th | | upminor 7th | ||
| Line 725: | Line 725: | ||
| 62 | | 62 | ||
| 1033.3 | | 1033.3 | ||
| 20/11 | | [[20/11]] | ||
| ^^m7, v~7 | | ^^m7, v~7 | ||
| dupminor 7th, downmid 7th | | dupminor 7th, downmid 7th | ||
| Line 736: | Line 736: | ||
| 63 | | 63 | ||
| 1050.0 | | 1050.0 | ||
| 11/6 | | [[11/6]] | ||
| ~7 | | ~7 | ||
| mid 7th | | mid 7th | ||
| Line 747: | Line 747: | ||
| 64 | | 64 | ||
| 1066.7 | | 1066.7 | ||
| 13/7, 24/13, 50/27 | | [[13/7]], [[24/13]], [[50/27]] | ||
| ^~7, vvM7 | | ^~7, vvM7 | ||
| upmid 7th, dudmajor 7th | | upmid 7th, dudmajor 7th | ||
| Line 758: | Line 758: | ||
| 65 | | 65 | ||
| 1083.3 | | 1083.3 | ||
| 15/8, 28/15 | | [[15/8]], [[28/15]] | ||
| vM7 | | vM7 | ||
| downmajor 7th | | downmajor 7th | ||
| Line 769: | Line 769: | ||
| 66 | | 66 | ||
| 1100.0 | | 1100.0 | ||
| 17/9, 32/17, 36/19 | | [[17/9]], [[32/17]], [[36/19]] | ||
| M7 | | M7 | ||
| major 7th | | major 7th | ||
| Line 780: | Line 780: | ||
| 67 | | 67 | ||
| 1116.7 | | 1116.7 | ||
| 19/10, 21/11, 40/21 | | [[19/10]], [[21/11]], [[40/21]] | ||
| ^M7 | | ^M7 | ||
| upmajor 7th | | upmajor 7th | ||
| Line 791: | Line 791: | ||
| 68 | | 68 | ||
| 1133.3 | | 1133.3 | ||
| 25/13, 27/14, 48/25, 52/27 | | [[25/13]], [[27/14]], [[48/25]], [[52/27]] | ||
| ^^M7 | | ^^M7 | ||
| dupmajor 7th | | dupmajor 7th | ||
| Line 802: | Line 802: | ||
| 69 | | 69 | ||
| 1150.0 | | 1150.0 | ||
| 35/18, 39/20, 64/33 | | [[35/18]], [[39/20]], [[64/33]] | ||
| ^<sup>3</sup>M7, v<sup>3</sup>8 | | ^<sup>3</sup>M7, v<sup>3</sup>8 | ||
| trupmajor 7th, trud octave | | trupmajor 7th, trud octave | ||
| Line 813: | Line 813: | ||
| 70 | | 70 | ||
| 1166.7 | | 1166.7 | ||
| 49/25, 55/28, 63/32, 88/45, 96/49 | | [[49/25]], [[55/28]], [[63/32]], [[88/45]], [[96/49]] | ||
| vv8 | | vv8 | ||
| dud octave | | dud octave | ||
| Line 824: | Line 824: | ||
| 71 | | 71 | ||
| 1183.3 | | 1183.3 | ||
| 99/50, 160/81, 180/91, 196/99, 208/105 | | [[99/50]], [[160/81]], [[180/91]], [[196/99]], [[208/105]] | ||
| v8 | | v8 | ||
| down octave | | down octave | ||
| Line 835: | Line 835: | ||
| 72 | | 72 | ||
| 1200.0 | | 1200.0 | ||
| 2/1 | | [[2/1]] | ||
| P8 | | P8 | ||
| perfect octave | | perfect octave | ||
| Line 859: | Line 859: | ||
| zo | | zo | ||
| (a b 0 1) | | (a b 0 1) | ||
| 7/6, 7/4 | | [[7/6]], [[7/4]] | ||
|- | |- | ||
| minor | | minor | ||
| fourthward wa | | fourthward wa | ||
| (a b), b < -1 | | (a b), b < -1 | ||
| 32/27, 16/9 | | [[32/27]], [[16/9]] | ||
|- | |- | ||
| upminor | | upminor | ||
| gu | | gu | ||
| (a b -1) | | (a b -1) | ||
| 6/5, 9/5 | | [[6/5]], [[9/5]] | ||
|- | |- | ||
| rowspan="2" | dupminor, <br>downmid | | rowspan="2" | dupminor, <br>downmid | ||
| luyo | | luyo | ||
| (a b 1 0 -1) | | (a b 1 0 -1) | ||
| 15/11 | | [[15/11]] | ||
|- | |- | ||
| tho | | tho | ||
| (a b 0 0 0 1) | | (a b 0 0 0 1) | ||
| 13/8, 13/9 | | [[13/8]], [[13/9]] | ||
|- | |- | ||
| rowspan="2" | mid | | rowspan="2" | mid | ||
| ilo | | ilo | ||
| (a b 0 0 1) | | (a b 0 0 1) | ||
| 11/9, 11/6 | | [[11/9]], [[11/6]] | ||
|- | |- | ||
| lu | | lu | ||
| (a b 0 0 -1) | | (a b 0 0 -1) | ||
| 12/11, 18/11 | | [[12/11]], [[18/11]] | ||
|- | |- | ||
| rowspan="2" | upmid, <br>dudmajor | | rowspan="2" | upmid, <br>dudmajor | ||
| logu | | logu | ||
| (a b -1 0 1) | | (a b -1 0 1) | ||
| 11/10 | | [[11/10]] | ||
|- | |- | ||
| thu | | thu | ||
| (a b 0 0 0 -1) | | (a b 0 0 0 -1) | ||
| 16/13, 18/13 | | [[16/13]], [[18/13]] | ||
|- | |- | ||
| downmajor | | downmajor | ||
| yo | | yo | ||
| (a b 1) | | (a b 1) | ||
| 5/4, 5/3 | | [[5/4]], [[5/3]] | ||
|- | |- | ||
| major | | major | ||
| fifthward wa | | fifthward wa | ||
| (a b), b > 1 | | (a b), b > 1 | ||
| 9/8, 27/16 | | [[9/8]], [[27/16]] | ||
|- | |- | ||
| dupmajor | | dupmajor | ||
| ru | | ru | ||
| (a b 0 -1) | | (a b 0 -1) | ||
| 9/7, 12/7 | | [[9/7]], [[12/7]] | ||
|- | |- | ||
| rowspan="2" | trupmajor, <br>trudminor | | rowspan="2" | trupmajor, <br>trudminor | ||
| thogu | | thogu | ||
| (a b -1 0 0 1) | | (a b -1 0 0 1) | ||
| 13/10 | | [[13/10]] | ||
|- | |- | ||
| thuyo | | thuyo | ||
| (a b 1 0 0 -1) | | (a b 1 0 0 -1) | ||
| 15/13 | | [[15/13]] | ||
|} | |} | ||
All 72edo chords can be named using ups and downs. An up, down or mid after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads: | All 72edo chords can be named using ups and downs. An up, down or mid after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads: | ||
| Line 974: | Line 974: | ||
Then, after each subsequent degree in reverse, a new prime limit is unveiled from it: | Then, after each subsequent degree in reverse, a new prime limit is unveiled from it: | ||
* −1 degree (the down ring) corrects 81/64 to 5/4 via 80 | * −1 degree (the down ring) corrects [[81/64]] to [[5/4]] via descending [[81/80]] | ||
* −2 degrees (the dud ring) corrects 16/9 to 7/4 via 63 | * −2 degrees (the dud ring) corrects [[16/9]] to [[7/4]] via descending [[64/63]] | ||
* +3 degrees (the trup ring) corrects 4/3 to 11/8 via 33/32 | * +3 degrees (the trup ring) corrects [[4/3]] to [[11/8]] via [[33/32]] | ||
* +2 degrees (the dup ring) corrects 128/81 to 13/8 via 1053/1024 | * +2 degrees (the dup ring) corrects [[128/81]] to [[13/8]] via [[1053/1024]] | ||
* 0 degrees (the plain ring) corrects 256/243 to 17/16 via 4131/4096 | * 0 degrees (the plain ring) corrects [[256/243]] to [[17/16]] via [[4131/4096]] | ||
* 0 degrees (the plain ring) corrects 32/27 to 19/16 via 513/512 | * 0 degrees (the plain ring) corrects [[32/27]] to [[19/16]] via [[513/512]] | ||
Thus the product of a ratio's monzo with {{map| 0 0 -1 -2 3 2 0 0 }}, modulo 6, specifies which ring the ratio lies on. | Thus the product of a ratio's monzo with {{map| 0 0 -1 -2 3 2 0 0 }}, modulo 6, specifies which ring the ratio lies on. | ||