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72edo: Difference between revisions

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! Degrees
! Degrees
! Cents
! Cents
! Approximate Ratios<ref group="note">{{sg|limit=17-limit}} For lower limits see [[Table of 72edo intervals]].</ref>
! Approximate ratios<ref group="note">{{sg|limit=17-limit}} For lower limits see [[Table of 72edo intervals]].</ref>
! colspan="3" | [[Ups and downs notation|Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
! colspan="3" |[[SKULO interval names|SKULO interval names and notation]]
! colspan="3" | [[SKULO interval names|SKULO interval names and notation]]
!(K, S, U)  
! (K, S, U)  
|-
|-
| 0
| 0
| 0.000
| 0.0
| 1/1
| 1/1
| P1
| P1
Line 51: Line 51:
|-
|-
| 1
| 1
| 16.667
| 16.7
| 81/80
| 81/80
| ^1
| ^1
Line 62: Line 62:
|-
|-
| 2
| 2
| 33.333
| 33.3
| 45/44, 64/63
| 45/44, 64/63
| ^^
| ^^
Line 73: Line 73:
|-
|-
| 3
| 3
| 50.000
| 50.0
| 33/32
| 33/32
| ^<sup>3</sup>1, v<sup>3</sup>m2
| ^<sup>3</sup>1, v<sup>3</sup>m2
Line 84: Line 84:
|-
|-
| 4
| 4
| 66.667
| 66.7
| 25/24
| 25/24
| vvm2
| vvm2
Line 95: Line 95:
|-
|-
| 5
| 5
| 83.333
| 83.3
| 21/20
| 21/20
| vm2
| vm2
Line 106: Line 106:
|-
|-
| 6
| 6
| 100.000
| 100.0
| 35/33, 17/16, 18/17
| 35/33, 17/16, 18/17
| m2
| m2
Line 117: Line 117:
|-
|-
| 7
| 7
| 116.667
| 116.7
| 15/14, 16/15
| 15/14, 16/15
| ^m2
| ^m2
Line 128: Line 128:
|-
|-
| 8
| 8
| 133.333
| 133.3
| 27/25, 13/12, 14/13
| 27/25, 13/12, 14/13
| ^^m2, v~2
| ^^m2, v~2
Line 139: Line 139:
|-
|-
| 9
| 9
| 150.000
| 150.0
| 12/11
| 12/11
| ~2
| ~2
Line 150: Line 150:
|-
|-
| 10
| 10
| 166.667
| 166.7
| 11/10
| 11/10
| ^~2, vvM2
| ^~2, vvM2
Line 161: Line 161:
|-
|-
| 11
| 11
| 183.333
| 183.3
| 10/9
| 10/9
| vM2
| vM2
Line 172: Line 172:
|-
|-
| 12
| 12
| 200.000
| 200.0
| 9/8
| 9/8
| M2
| M2
Line 183: Line 183:
|-
|-
| 13
| 13
| 216.667
| 216.7
| 25/22, 17/15
| 25/22, 17/15
| ^M2
| ^M2
Line 194: Line 194:
|-
|-
| 14
| 14
| 233.333
| 233.3
| 8/7
| 8/7
| ^^M2
| ^^M2
Line 205: Line 205:
|-
|-
| 15
| 15
| 250.000
| 250.0
| 81/70,  15/13
| 81/70,  15/13
| ^<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
| ^<sup>3</sup>E, <br />v<sup>3</sup>F
| ^<sup>3</sup>E, <br>v<sup>3</sup>F
| HM2, hm3
| HM2, hm3
| hypermajor 2nd, hypominor 3rd
| hypermajor 2nd, hypominor 3rd
Line 216: Line 216:
|-
|-
| 16
| 16
| 266.667
| 266.7
| 7/6
| 7/6
| vvm3
| vvm3
Line 227: Line 227:
|-
|-
| 17
| 17
| 283.333
| 283.3
| 33/28, 13/11, 20/17
| 33/28, 13/11, 20/17
| vm3
| vm3
Line 238: Line 238:
|-
|-
| 18
| 18
| 300.000
| 300.0
| 25/21
| 25/21
| m3
| m3
Line 249: Line 249:
|-
|-
| 19
| 19
| 316.667
| 316.7
| 6/5
| 6/5
| ^m3
| ^m3
Line 260: Line 260:
|-
|-
| 20
| 20
| 333.333
| 333.3
| 40/33, 17/14
| 40/33, 17/14
| ^^m3, v~3
| ^^m3, v~3
Line 271: Line 271:
|-
|-
| 21
| 21
| 350.000
| 350.0
| 11/9
| 11/9
| ~3
| ~3
Line 282: Line 282:
|-
|-
| 22
| 22
| 366.667
| 366.7
| 99/80, 16/13, 21/17
| 99/80, 16/13, 21/17
| ^~3, vvM3
| ^~3, vvM3
Line 293: Line 293:
|-
|-
| 23
| 23
| 383.333
| 383.3
| 5/4
| 5/4
| vM3
| vM3
Line 304: Line 304:
|-
|-
| 24
| 24
| 400.000
| 400.0
| 44/35
| 44/35
| M3
| M3
Line 315: Line 315:
|-
|-
| 25
| 25
| 416.667
| 416.7
| 14/11
| 14/11
| ^M3
| ^M3
Line 326: Line 326:
|-
|-
| 26
| 26
| 433.333
| 433.3
| 9/7
| 9/7
| ^^M3
| ^^M3
Line 337: Line 337:
|-
|-
| 27
| 27
| 450.000
| 450.0
| 35/27, 13/10
| 35/27, 13/10
| ^<sup>3</sup>M3, v<sup>3</sup>4
| ^<sup>3</sup>M3, v<sup>3</sup>4
Line 348: Line 348:
|-
|-
| 28
| 28
| 466.667
| 466.7
| 21/16, 17/13
| 21/16, 17/13
| vv4
| vv4
Line 359: Line 359:
|-
|-
| 29
| 29
| 483.333
| 483.3
| 33/25
| 33/25
| v4
| v4
Line 370: Line 370:
|-
|-
| 30
| 30
| 500.000
| 500.0
| 4/3
| 4/3
| P4
| P4
Line 381: Line 381:
|-
|-
| 31
| 31
| 516.667
| 516.7
| 27/20
| 27/20
| ^4
| ^4
Line 392: Line 392:
|-
|-
| 32
| 32
| 533.333
| 533.3
| 15/11
| 15/11
| ^^4, v~4
| ^^4, v~4
Line 403: Line 403:
|-
|-
| 33
| 33
| 550.000
| 550.0
| 11/8
| 11/8
| ~4
| ~4
Line 414: Line 414:
|-
|-
| 34
| 34
| 566.667
| 566.7
| 25/18, 18/13
| 25/18, 18/13
| ^~4, vvA4
| ^~4, vvA4
Line 425: Line 425:
|-
|-
| 35
| 35
| 583.333
| 583.3
| 7/5
| 7/5
| vA4, vd5
| vA4, vd5
| downaug 4th,  
| downaug 4th, <br>downdim 5th
downdim 5th
| vG#, vAb
| vG#, vAb
| kA4, ld5
| kA4, ld5
Line 437: Line 436:
|-
|-
| 36
| 36
| 600.000
| 600.0
| 99/70, 17/12
| 99/70, 17/12
| A4, d5
| A4, d5
Line 448: Line 447:
|-
|-
| 37
| 37
| 616.667
| 616.7
| 10/7
| 10/7
| ^A4, ^d5
| ^A4, ^d5
Line 459: Line 458:
|-
|-
| 38
| 38
| 633.333
| 633.3
| 36/25, 13/9
| 36/25, 13/9
| v~5, ^^d5
| v~5, ^^d5
| downmid 5th,  
| downmid 5th, <br>dupdim 5th
dupdim 5th
| ^^Ab
| ^^Ab
| SA4, KKd5
| SA4, KKd5
Line 471: Line 469:
|-
|-
| 39
| 39
| 650.000
| 650.0
| 16/11
| 16/11
| ~5
| ~5
Line 482: Line 480:
|-
|-
| 40
| 40
| 666.667
| 666.7
| 22/15
| 22/15
| vv5, ^~5
| vv5, ^~5
Line 493: Line 491:
|-
|-
| 41
| 41
| 683.333
| 683.3
| 40/27
| 40/27
| v5
| v5
Line 504: Line 502:
|-
|-
| 42
| 42
| 700.000
| 700.0
| 3/2
| 3/2
| P5
| P5
Line 515: Line 513:
|-
|-
| 43
| 43
| 716.667
| 716.7
| 50/33
| 50/33
| ^5
| ^5
Line 526: Line 524:
|-
|-
| 44
| 44
| 733.333
| 733.3
| 32/21
| 32/21
| ^^5
| ^^5
Line 537: Line 535:
|-
|-
| 45
| 45
| 750.000
| 750.0
| 54/35, 17/11
| 54/35, 17/11
| ^<sup>3</sup>5, v<sup>3</sup>m6
| ^<sup>3</sup>5, v<sup>3</sup>m6
Line 548: Line 546:
|-
|-
| 46
| 46
| 766.667
| 766.7
| 14/9
| 14/9
| vvm6
| vvm6
Line 559: Line 557:
|-
|-
| 47
| 47
| 783.333
| 783.3
| 11/7
| 11/7
| vm6
| vm6
Line 570: Line 568:
|-
|-
| 48
| 48
| 800.000
| 800.0
| 35/22
| 35/22
| m6
| m6
Line 581: Line 579:
|-
|-
| 49
| 49
| 816.667
| 816.7
| 8/5
| 8/5
| ^m6
| ^m6
Line 592: Line 590:
|-
|-
| 50
| 50
| 833.333
| 833.3
| 81/50, 13/8
| 81/50, 13/8
| ^^m6, v~6
| ^^m6, v~6
Line 603: Line 601:
|-
|-
| 51
| 51
| 850.000
| 850.0
| 18/11
| 18/11
| ~6
| ~6
Line 614: Line 612:
|-
|-
| 52
| 52
| 866.667
| 866.7
| 33/20, 28/17
| 33/20, 28/17
| ^~6, vvM6
| ^~6, vvM6
Line 625: Line 623:
|-
|-
| 53
| 53
| 883.333
| 883.3
| 5/3
| 5/3
| vM6
| vM6
Line 636: Line 634:
|-
|-
| 54
| 54
| 900.000
| 900.0
| 27/16
| 27/16
| M6
| M6
Line 647: Line 645:
|-
|-
| 55
| 55
| 916.667
| 916.7
| 56/33, 17/10
| 56/33, 17/10
| ^M6
| ^M6
Line 658: Line 656:
|-
|-
| 56
| 56
| 933.333
| 933.3
| 12/7
| 12/7
| ^^M6
| ^^M6
Line 669: Line 667:
|-
|-
| 57
| 57
| 950.000
| 950.0
| 121/70
| 121/70
| ^<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
| ^<sup>3</sup>B, <br />v<sup>3</sup>C
| ^<sup>3</sup>B, <br>v<sup>3</sup>C
| HM6, hm7
| HM6, hm7
| hypermajor 6th, hypominor 7th
| hypermajor 6th, hypominor 7th
Line 680: Line 678:
|-
|-
| 58
| 58
| 966.667
| 966.7
| 7/4
| 7/4
| vvm7
| vvm7
Line 691: Line 689:
|-
|-
| 59
| 59
| 983.333
| 983.3
| 44/25
| 44/25
| vm7
| vm7
Line 702: Line 700:
|-
|-
| 60
| 60
| 1000.000
| 1000.0
| 16/9
| 16/9
| m7
| m7
Line 713: Line 711:
|-
|-
| 61
| 61
| 1016.667
| 1016.7
| 9/5
| 9/5
| ^m7
| ^m7
Line 724: Line 722:
|-
|-
| 62
| 62
| 1033.333
| 1033.3
| 20/11
| 20/11
| ^^m7, v~7
| ^^m7, v~7
Line 735: Line 733:
|-
|-
| 63
| 63
| 1050.000
| 1050.0
| 11/6
| 11/6
| ~7
| ~7
Line 746: Line 744:
|-
|-
| 64
| 64
| 1066.667
| 1066.7
| 50/27
| 50/27
| ^~7, vvM7
| ^~7, vvM7
Line 757: Line 755:
|-
|-
| 65
| 65
| 1083.333
| 1083.3
| 15/8
| 15/8
| vM7
| vM7
Line 768: Line 766:
|-
|-
| 66
| 66
| 1100.000
| 1100.0
| 66/35, 17/9
| 66/35, 17/9
| M7
| M7
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|-
|-
| 67
| 67
| 1116.667
| 1116.7
| 21/11
| 21/11
| ^M7
| ^M7
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|-
|-
| 68
| 68
| 1133.333
| 1133.3
| 27/14, 48/25
| 27/14, 48/25
| ^^M7
| ^^M7
Line 801: Line 799:
|-
|-
| 69
| 69
| 1150.000
| 1150.0
| 35/18
| 35/18
| ^<sup>3</sup>M7, v<sup>3</sup>8
| ^<sup>3</sup>M7, v<sup>3</sup>8
Line 812: Line 810:
|-
|-
| 70
| 70
| 1166.667
| 1166.7
| 49/25
| 49/25
| vv8
| vv8
Line 823: Line 821:
|-
|-
| 71
| 71
| 1183.333
| 1183.3
| 99/50
| 99/50
| v8
| v8
Line 834: Line 832:
|-
|-
| 72
| 72
| 1200.000
| 1200.0
| 2/1
| 2/1
| P8
| P8
Line 852: Line 850:
! Quality
! Quality
! [[Color notation|Color]]
! [[Color notation|Color]]
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
Line 862: Line 860:
| minor
| minor
| fourthward wa
| fourthward wa
| (a b), b &lt; -1
| (a b), b < -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
Line 870: Line 868:
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| rowspan="2" |dupminor,
| rowspan="2" | dupminor, <br>downmid
downmid
| luyo
| luyo
| (a b 1 0 -1)
| (a b 1 0 -1)
Line 889: Line 886:
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| rowspan="2" |upmid,
| rowspan="2" | upmid, <br>dudmajor
dudmajor
| logu
| logu
| (a b -1 0 1)
| (a b -1 0 1)
Line 906: Line 902:
| major
| major
| fifthward wa
| fifthward wa
| (a b), b &gt; 1
| (a b), b > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
Line 914: Line 910:
| 9/7, 12/7
| 9/7, 12/7
|-
|-
| rowspan="2" |trupmajor,
| rowspan="2" | trupmajor, <br>trudminor
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 928: Line 923:
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! [[Kite's color notation|Color of the 3rd]]
! [[Color notation|Color of the 3rd]]
! JI Chord
! JI chord
! Notes as Edosteps
! Notes as edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo
| zo
Line 973: Line 968:


=== Relationship between primes and rings ===
=== Relationship between primes and rings ===
In 72tet, there are 6 [[Ring number|rings]]. 12edo is the plain ring; thus every 6 degrees is the 3-limit.
In 72tet, there are 6 [[ring number|rings]]. 12edo is the plain ring; thus every 6 degrees is the 3-limit.


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:
* &minus;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 80/81
* &minus;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 63/64
* +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
Retrieved from "https://en.xen.wiki/w/72edo"