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
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 80/81
* −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 63/64
* −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.