24edo: Difference between revisions
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| Line 19: | Line 19: | ||
| style="text-align:center;" | Degree | | style="text-align:center;" | Degree | ||
| style="text-align:center;" | Cents | | style="text-align:center;" | Cents | ||
|pions | |||
|7mus | |||
| style="text-align:center;" | Approximate Ratios* | | style="text-align:center;" | Approximate Ratios* | ||
| colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|ups and downs notation]] | | colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|ups and downs notation]] | ||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| style="text-align:center;" | 0 | | colspan="3" style="text-align:center;" | 0 | ||
| style="text-align:center;" | 1/1 | | style="text-align:center;" | 1/1 | ||
| style="text-align:center;" | P1 | | style="text-align:center;" | P1 | ||
| Line 31: | Line 33: | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:center;" | 50 | | style="text-align:center;" | 50 | ||
|53 | |||
|64 (40<sub>16</sub>) | |||
| style="text-align:center;" | 33/32, 34/33 | | style="text-align:center;" | 33/32, 34/33 | ||
| style="text-align:center;" | ^P1, vm2 | | style="text-align:center;" | ^P1, vm2 | ||
| Line 38: | Line 42: | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:center;" | 100 | | style="text-align:center;" | 100 | ||
|106 | |||
|128 (80<sub>16</sub>) | |||
| style="text-align:center;" | 17/16, 18/17 | | style="text-align:center;" | 17/16, 18/17 | ||
| style="text-align:center;" | A1, m2 | | style="text-align:center;" | A1, m2 | ||
| Line 45: | Line 51: | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:center;" | 150 | | style="text-align:center;" | 150 | ||
|159 | |||
|192 (C0<sub>16</sub>) | |||
| style="text-align:center;" | 12/11 | | style="text-align:center;" | 12/11 | ||
| style="text-align:center;" | ~2 | | style="text-align:center;" | ~2 | ||
| Line 52: | Line 60: | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:center;" | 200 | | style="text-align:center;" | 200 | ||
|212 | |||
|256 (100<sub>16</sub>) | |||
| style="text-align:center;" | 9/8 | | style="text-align:center;" | 9/8 | ||
| style="text-align:center;" | M2 | | style="text-align:center;" | M2 | ||
| Line 59: | Line 69: | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:center;" | 250 | | style="text-align:center;" | 250 | ||
|265 | |||
|320 (140<sub>16</sub>) | |||
| style="text-align:center;" | 22/19 | | style="text-align:center;" | 22/19 | ||
| style="text-align:center;" | ^M2, vm3 | | style="text-align:center;" | ^M2, vm3 | ||
| Line 66: | Line 78: | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:center;" | 300 | | style="text-align:center;" | 300 | ||
|318 | |||
|384 (180<sub>16</sub>) | |||
| style="text-align:center;" | 19/16 | | style="text-align:center;" | 19/16 | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
| Line 73: | Line 87: | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:center;" | 350 | | style="text-align:center;" | 350 | ||
|383 | |||
|448 (1C0<sub>16</sub>) | |||
| style="text-align:center;" | 11/9 | | style="text-align:center;" | 11/9 | ||
| style="text-align:center;" | ~3 | | style="text-align:center;" | ~3 | ||
| Line 80: | Line 96: | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:center;" | 400 | | style="text-align:center;" | 400 | ||
|424 | |||
|512 (200<sub>16</sub>) | |||
| style="text-align:center;" | 24/19 | | style="text-align:center;" | 24/19 | ||
| style="text-align:center;" | M3 | | style="text-align:center;" | M3 | ||
| Line 87: | Line 105: | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:center;" | 450 | | style="text-align:center;" | 450 | ||
|477 | |||
|576 (240<sub>16</sub>) | |||
| style="text-align:center;" | 22/17 | | style="text-align:center;" | 22/17 | ||
| style="text-align:center;" | ^M3, vP4 | | style="text-align:center;" | ^M3, vP4 | ||
| Line 94: | Line 114: | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:center;" | 500 | | style="text-align:center;" | 500 | ||
|530 | |||
|640 (280<sub>16</sub>) | |||
| style="text-align:center;" | 4/3 | | style="text-align:center;" | 4/3 | ||
| style="text-align:center;" | P4 | | style="text-align:center;" | P4 | ||
| Line 101: | Line 123: | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:center;" | 550 | | style="text-align:center;" | 550 | ||
|583 | |||
|704 (2C0<sub>16</sub>) | |||
| style="text-align:center;" | 11/8 | | style="text-align:center;" | 11/8 | ||
| style="text-align:center;" | ^P4 | | style="text-align:center;" | ^P4 | ||
| Line 108: | Line 132: | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:center;" | 600 | | style="text-align:center;" | 600 | ||
|636 | |||
|768 (300<sub>16</sub>) | |||
| style="text-align:center;" | 17/12 | | style="text-align:center;" | 17/12 | ||
| style="text-align:center;" | A4, d5 | | style="text-align:center;" | A4, d5 | ||
| Line 115: | Line 141: | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:center;" | 650 | | style="text-align:center;" | 650 | ||
|689 | |||
|832 (340<sub>16</sub>) | |||
| style="text-align:center;" | 16/11 | | style="text-align:center;" | 16/11 | ||
| style="text-align:center;" | vP5 | | style="text-align:center;" | vP5 | ||
| Line 122: | Line 150: | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:center;" | 700 | | style="text-align:center;" | 700 | ||
|742 | |||
|896 (380<sub>16</sub>) | |||
| style="text-align:center;" | 3/2 | | style="text-align:center;" | 3/2 | ||
| style="text-align:center;" | P5 | | style="text-align:center;" | P5 | ||
| Line 129: | Line 159: | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:center;" | 750 | | style="text-align:center;" | 750 | ||
|795 | |||
|960 (3C0<sub>16</sub>) | |||
| style="text-align:center;" | 17/11 | | style="text-align:center;" | 17/11 | ||
| style="text-align:center;" | ^P5, vm6 | | style="text-align:center;" | ^P5, vm6 | ||
| Line 136: | Line 168: | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:center;" | 800 | | style="text-align:center;" | 800 | ||
|848 | |||
|1024 (400<sub>16</sub>) | |||
| style="text-align:center;" | 19/12 | | style="text-align:center;" | 19/12 | ||
| style="text-align:center;" | m6 | | style="text-align:center;" | m6 | ||
| Line 143: | Line 177: | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| style="text-align:center;" | 850 | | style="text-align:center;" | 850 | ||
|901 | |||
|1088 (340<sub>16</sub>) | |||
| style="text-align:center;" | 18/11 | | style="text-align:center;" | 18/11 | ||
| style="text-align:center;" | ~6 | | style="text-align:center;" | ~6 | ||
| Line 150: | Line 186: | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| style="text-align:center;" | 900 | | style="text-align:center;" | 900 | ||
|954 | |||
|1152 (480<sub>16</sub>) | |||
| style="text-align:center;" | 32/19 | | style="text-align:center;" | 32/19 | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
| Line 157: | Line 195: | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:center;" | 950 | | style="text-align:center;" | 950 | ||
|1007 | |||
|1216 (4C0<sub>16</sub>) | |||
| style="text-align:center;" | 19/11 | | style="text-align:center;" | 19/11 | ||
| style="text-align:center;" | ^M6, vm7 | | style="text-align:center;" | ^M6, vm7 | ||
| Line 164: | Line 204: | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| style="text-align:center;" | 1000 | | style="text-align:center;" | 1000 | ||
|1060 | |||
|1280 (500<sub>16</sub>) | |||
| style="text-align:center;" | 16/9 | | style="text-align:center;" | 16/9 | ||
| style="text-align:center;" | m7 | | style="text-align:center;" | m7 | ||
| Line 171: | Line 213: | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| style="text-align:center;" | 1050 | | style="text-align:center;" | 1050 | ||
|1113 | |||
|1344 (540<sub>16</sub>) | |||
| style="text-align:center;" | 11/6 | | style="text-align:center;" | 11/6 | ||
| style="text-align:center;" | ~7 | | style="text-align:center;" | ~7 | ||
| Line 178: | Line 222: | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| style="text-align:center;" | 1100 | | style="text-align:center;" | 1100 | ||
|1166 | |||
|1408 (580<sub>16</sub>) | |||
| style="text-align:center;" | 17/9, 32/17 | | style="text-align:center;" | 17/9, 32/17 | ||
| style="text-align:center;" | M7 | | style="text-align:center;" | M7 | ||
| Line 185: | Line 231: | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| style="text-align:center;" | 1150 | | style="text-align:center;" | 1150 | ||
|1219 | |||
|1472 (%C0<sub>16</sub>) | |||
| style="text-align:center;" | 33/17, 64/33 | | style="text-align:center;" | 33/17, 64/33 | ||
| style="text-align:center;" | ^M7, vP8 | | style="text-align:center;" | ^M7, vP8 | ||
| Line 192: | Line 240: | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| style="text-align:center;" | 1200 | | style="text-align:center;" | 1200 | ||
|1272 | |||
|1536 (600<sub>16</sub>) | |||
| style="text-align:center;" | 2/1 | | style="text-align:center;" | 2/1 | ||
| style="text-align:center;" | P8 | | style="text-align:center;" | P8 | ||
| Line 422: | Line 472: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! colspan=" | ! colspan="4" | The twelve new intervals in 24edo | ||
! colspan="3" | some nearby JI intervals | ! colspan="3" | some nearby JI intervals | ||
|- | |- | ||
! | cents | ! | cents | ||
!pions | |||
!7mus | |||
! | common names | ! | common names | ||
! | frequency ratio | ! | frequency ratio | ||
| Line 432: | Line 484: | ||
|- | |- | ||
| style="text-align:center;" | 50 | | style="text-align:center;" | 50 | ||
|53 | |||
|64 (40<sub>16</sub>) | |||
| style="text-align:center;" | quartertone | | style="text-align:center;" | quartertone | ||
| Line 442: | Line 496: | ||
[[33/32|33/32]] | [[33/32|33/32]] | ||
| style="text-align:center;" | 48. | | style="text-align:center;" | 48.77 | ||
50.184 | 50.184 | ||
| Line 458: | Line 512: | ||
|- | |- | ||
| style="text-align:center;" | 150 | | style="text-align:center;" | 150 | ||
|159 | |||
|192 (C0<sub>16</sub>) | |||
| style="text-align:center;" | neutral second | | style="text-align:center;" | neutral second | ||
| style="text-align:center;" | [[12/11|12/11]] | | style="text-align:center;" | [[12/11|12/11]] | ||
| Line 464: | Line 520: | ||
|- | |- | ||
| style="text-align:center;" | 250 | | style="text-align:center;" | 250 | ||
|265 | |||
|320 (140<sub>16</sub>) | |||
| style="text-align:center;" | ultra second | | style="text-align:center;" | ultra second | ||
| Line 484: | Line 542: | ||
|- | |- | ||
| style="text-align:center;" | 350 | | style="text-align:center;" | 350 | ||
|383 | |||
|448 (1C0<sub>16</sub>) | |||
| style="text-align:center;" | neutral third | | style="text-align:center;" | neutral third | ||
| style="text-align:center;" | [[11/9|11/9]] | | style="text-align:center;" | [[11/9|11/9]] | ||
| Line 502: | Line 562: | ||
|- | |- | ||
| style="text-align:center;" | 450 | | style="text-align:center;" | 450 | ||
|477 | |||
|576 (240<sub>16</sub>) | |||
| style="text-align:center;" | minor fourth, ultra third, narrow fourth | | style="text-align:center;" | minor fourth, ultra third, narrow fourth | ||
| style="text-align:center;" | [[22/17|22/17]] | | style="text-align:center;" | [[22/17|22/17]] | ||
| Line 520: | Line 582: | ||
|- | |- | ||
| style="text-align:center;" | 550 | | style="text-align:center;" | 550 | ||
|583 | |||
|704 (2C0<sub>16</sub>) | |||
| style="text-align:center;" | wide fourth | | style="text-align:center;" | wide fourth | ||
| style="text-align:center;" | [[11/8|11/8]] | | style="text-align:center;" | [[11/8|11/8]] | ||
| Line 526: | Line 590: | ||
|- | |- | ||
| style="text-align:center;" | 650 | | style="text-align:center;" | 650 | ||
|689 | |||
|832 (340<sub>16</sub>) | |||
| style="text-align:center;" | narrow fifth | | style="text-align:center;" | narrow fifth | ||
| style="text-align:center;" | [[16/11|16/11]] | | style="text-align:center;" | [[16/11|16/11]] | ||
| Line 532: | Line 598: | ||
|- | |- | ||
| style="text-align:center;" | 750 | | style="text-align:center;" | 750 | ||
|795 | |||
|960 (3C0<sub>16</sub>) | |||
| style="text-align:center;" | wide fifth, infra sixth | | style="text-align:center;" | wide fifth, infra sixth | ||
| style="text-align:center;" | [[20/13|20/13]] | | style="text-align:center;" | [[20/13|20/13]] | ||
| Line 550: | Line 618: | ||
|- | |- | ||
| style="text-align:center;" | 850 | | style="text-align:center;" | 850 | ||
|901 | |||
|1088 (340<sub>16</sub>) | |||
| style="text-align:center;" | neutral sixth | | style="text-align:center;" | neutral sixth | ||
| style="text-align:center;" | [[13/8|13/8]] | | style="text-align:center;" | [[13/8|13/8]] | ||
| Line 568: | Line 638: | ||
|- | |- | ||
| style="text-align:center;" | 950 | | style="text-align:center;" | 950 | ||
|1007 | |||
|1216 (4C0<sub>16</sub>) | |||
| style="text-align:center;" | ultra sixth , infra seventh | | style="text-align:center;" | ultra sixth , infra seventh | ||
| style="text-align:center;" | [[45/26|45/26]] | | style="text-align:center;" | [[45/26|45/26]] | ||
| Line 586: | Line 658: | ||
|- | |- | ||
| style="text-align:center;" | 1050 | | style="text-align:center;" | 1050 | ||
|1113 | |||
|1344 (540<sub>16</sub>) | |||
| style="text-align:center;" | neutral seventh | | style="text-align:center;" | neutral seventh | ||
| style="text-align:center;" | [[11/6|11/6]] | | style="text-align:center;" | [[11/6|11/6]] | ||
| Line 592: | Line 666: | ||
|- | |- | ||
| style="text-align:center;" | 1150 | | style="text-align:center;" | 1150 | ||
|1219 | |||
|1472 (%C0<sub>16</sub>) | |||
| style="text-align:center;" | ultra seventh, narrow octave | | style="text-align:center;" | ultra seventh, narrow octave | ||
| style="text-align:center;" | [[31/16|31/16]] | | style="text-align:center;" | [[31/16|31/16]] | ||