87edo: Difference between revisions
+restles temperament |
space between table metachar and content |
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! colspan="2" rowspan="2" |[[Ups and Downs Notation]] | ! colspan="2" rowspan="2" |[[Ups and Downs Notation]] | ||
|- | |- | ||
!13-Limit | ! 13-Limit | ||
!31-Limit No-7s Extension | ! 31-Limit No-7s Extension | ||
|- | |- | ||
|0 | | 0 | ||
|0.000 | | 0.000 | ||
|[[1/1]] | | [[1/1]] | ||
| | | | ||
|P1 | | P1 | ||
|D | | D | ||
|- | |- | ||
|1 | | 1 | ||
|13.793 | | 13.793 | ||
|[[126/125]], [[100/99]], [[91/90]] | | [[126/125]], [[100/99]], [[91/90]] | ||
| | | | ||
|^1 | | ^1 | ||
|^D | | ^D | ||
|- | |- | ||
|2 | | 2 | ||
|27.586 | | 27.586 | ||
|[[81/80]], [[64/63]], [[49/48]], [[55/54]], [[65/64]] | | [[81/80]], [[64/63]], [[49/48]], [[55/54]], [[65/64]] | ||
| | | | ||
|^^1 | | ^^1 | ||
|^^D | | ^^D | ||
|- | |- | ||
|3 | | 3 | ||
|41.379 | | 41.379 | ||
|[[50/49]], [[45/44]], [[40/39]] | | [[50/49]], [[45/44]], [[40/39]] | ||
|[[39/38]] | | [[39/38]] | ||
|^<sup>3</sup>1 | | ^<sup>3</sup>1 | ||
|^<sup>3</sup>D/v<sup>3</sup>Eb | | ^<sup>3</sup>D/v<sup>3</sup>Eb | ||
|- | |- | ||
|4 | | 4 | ||
|55.172 | | 55.172 | ||
|[[28/27]], [[36/35]], [[33/32]] | | [[28/27]], [[36/35]], [[33/32]] | ||
|[[34/33]], [[30/29]], [[32/31]], [[31/30]] | | [[34/33]], [[30/29]], [[32/31]], [[31/30]] | ||
|vvm2 | | vvm2 | ||
|vvEb | | vvEb | ||
|- | |- | ||
|5 | | 5 | ||
|68.966 | | 68.966 | ||
|[[25/24]], [[27/26]], [[26/25]] | | [[25/24]], [[27/26]], [[26/25]] | ||
|[[24/23]] | | [[24/23]] | ||
|vm2 | | vm2 | ||
|vEb | | vEb | ||
|- | |- | ||
|6 | | 6 | ||
|82.759 | | 82.759 | ||
|[[21/20]], [[22/21]] | | [[21/20]], [[22/21]] | ||
|[[20/19]], [[23/22]] | | [[20/19]], [[23/22]] | ||
|m2 | | m2 | ||
|Eb | | Eb | ||
|- | |- | ||
|7 | | 7 | ||
|96.552 | | 96.552 | ||
|[[35/33]] | | [[35/33]] | ||
|[[18/17]], [[19/18]] | | [[18/17]], [[19/18]] | ||
|^m2 | | ^m2 | ||
|^Eb | | ^Eb | ||
|- | |- | ||
|8 | | 8 | ||
|110.345 | | 110.345 | ||
|[[16/15]] | | [[16/15]] | ||
|[[17/16]], [[33/31]], [[31/29]] | | [[17/16]], [[33/31]], [[31/29]] | ||
|^^m2 | | ^^m2 | ||
|^^Eb | | ^^Eb | ||
|- | |- | ||
|9 | | 9 | ||
|124.138 | | 124.138 | ||
|[[15/14]], [[14/13]] | | [[15/14]], [[14/13]] | ||
|[[29/27]] | | [[29/27]] | ||
|vv~2 | | vv~2 | ||
|^<sup>3</sup>Eb | | ^<sup>3</sup>Eb | ||
|- | |- | ||
|10 | | 10 | ||
|137.931 | | 137.931 | ||
|[[13/12]], [[27/25]] | | [[13/12]], [[27/25]] | ||
|[[25/23]] | | [[25/23]] | ||
|v~2 | | v~2 | ||
|^<sup>4</sup>Eb | | ^<sup>4</sup>Eb | ||
|- | |- | ||
|11 | | 11 | ||
|151.724 | | 151.724 | ||
|[[12/11]], [[35/32]] | | [[12/11]], [[35/32]] | ||
| | | | ||
|^~2 | | ^~2 | ||
|v<sup>4</sup>E | | v<sup>4</sup>E | ||
|- | |- | ||
|12 | | 12 | ||
|165.517 | | 165.517 | ||
|[[11/10]] | | [[11/10]] | ||
|[[32/29]], [[34/31]] | | [[32/29]], [[34/31]] | ||
|^^~2 | | ^^~2 | ||
|v<sup>3</sup>E | | v<sup>3</sup>E | ||
|- | |- | ||
|13 | | 13 | ||
|179.310 | | 179.310 | ||
|[[10/9]] | | [[10/9]] | ||
| | | | ||
|vvM2 | | vvM2 | ||
|vvE | | vvE | ||
|- | |- | ||
|14 | | 14 | ||
|193.103 | | 193.103 | ||
|[[28/25]] | | [[28/25]] | ||
|[[19/17]], [[29/26]] | | [[19/17]], [[29/26]] | ||
|vM2 | | vM2 | ||
|vE | | vE | ||
|- | |- | ||
|15 | | 15 | ||
|206.897 | | 206.897 | ||
|[[9/8]] | | [[9/8]] | ||
|[[26/23]] | | [[26/23]] | ||
|M2 | | M2 | ||
|E | | E | ||
|- | |- | ||
|16 | | 16 | ||
|220.690 | | 220.690 | ||
|[[25/22]] | | [[25/22]] | ||
|[[17/15]], [[33/29]] | | [[17/15]], [[33/29]] | ||
|^M2 | | ^M2 | ||
|^E | | ^E | ||
|- | |- | ||
|17 | | 17 | ||
|234.483 | | 234.483 | ||
|[[8/7]] | | [[8/7]] | ||
|[[31/27]] | | [[31/27]] | ||
|^^M2 | | ^^M2 | ||
|^^E | | ^^E | ||
|- | |- | ||
|18 | | 18 | ||
|248.276 | | 248.276 | ||
|[[15/13]] | | [[15/13]] | ||
|[[22/19]], [[38/33]], [[23/20]] | | [[22/19]], [[38/33]], [[23/20]] | ||
|^<sup>3</sup>M2/v<sup>3</sup>m3 | | ^<sup>3</sup>M2/v<sup>3</sup>m3 | ||
|^<sup>3</sup>E/v<sup>3</sup>F | | ^<sup>3</sup>E/v<sup>3</sup>F | ||
|- | |- | ||
|19 | | 19 | ||
|262.089 | | 262.089 | ||
|[[7/6]] | | [[7/6]] | ||
|[[29/25]], [[36/31]] | | [[29/25]], [[36/31]] | ||
|vvm3 | | vvm3 | ||
|vvF | | vvF | ||
|- | |- | ||
|20 | | 20 | ||
|275.862 | | 275.862 | ||
|[[75/64]] | | [[75/64]] | ||
|[[27/23]], [[34/29]] | | [[27/23]], [[34/29]] | ||
|vm3 | | vm3 | ||
|vF | | vF | ||
|- | |- | ||
|21 | | 21 | ||
|289.655 | | 289.655 | ||
|[[32/27]], [[33/28]], [[13/11]] | | [[32/27]], [[33/28]], [[13/11]] | ||
| | | | ||
|m3 | | m3 | ||
|F | | F | ||
|- | |- | ||
|22 | | 22 | ||
|303.448 | | 303.448 | ||
|[[25/21]] | | [[25/21]] | ||
|[[19/16]], [[31/26]] | | [[19/16]], [[31/26]] | ||
|^m3 | | ^m3 | ||
|^F | | ^F | ||
|- | |- | ||
|23 | | 23 | ||
|317.241 | | 317.241 | ||
|[[6/5]] | | [[6/5]] | ||
| | | | ||
|^^m3 | | ^^m3 | ||
|^^F | | ^^F | ||
|- | |- | ||
|24 | | 24 | ||
|331.034 | | 331.034 | ||
|[[40/33]] | | [[40/33]] | ||
|[[23/19]], [[29/24]] | | [[23/19]], [[29/24]] | ||
|vv~3 | | vv~3 | ||
|^<sup>3</sup>F | | ^<sup>3</sup>F | ||
|- | |- | ||
|25 | | 25 | ||
|344.828 | | 344.828 | ||
|[[11/9]], [[39/32]] | | [[11/9]], [[39/32]] | ||
| | | | ||
|v~3 | | v~3 | ||
|^<sup>4</sup>F | | ^<sup>4</sup>F | ||
|- | |- | ||
|26 | | 26 | ||
|358.621 | | 358.621 | ||
|[[27/22]], [[16/13]] | | [[27/22]], [[16/13]] | ||
|[[38/31]] | | [[38/31]] | ||
|^~3 | | ^~3 | ||
|v<sup>4</sup>F# | | v<sup>4</sup>F# | ||
|- | |- | ||
|27 | | 27 | ||
|372.414 | | 372.414 | ||
|[[26/21]] | | [[26/21]] | ||
|[[31/25]], [[36/29]] | | [[31/25]], [[36/29]] | ||
|^^3 | | ^^3 | ||
|v<sup>3</sup>F# | | v<sup>3</sup>F# | ||
|- | |- | ||
|28 | | 28 | ||
|386.207 | | 386.207 | ||
|[[5/4]] | | [[5/4]] | ||
| | | | ||
|vvM3 | | vvM3 | ||
|vvF# | | vvF# | ||
|- | |- | ||
|29 | | 29 | ||
|400.000 | | 400.000 | ||
|[[44/35]] | | [[44/35]] | ||
|[[34/27]], [[24/19]], [[29/23]] | | [[34/27]], [[24/19]], [[29/23]] | ||
|vM3 | | vM3 | ||
|vF# | | vF# | ||
|- | |- | ||
|30 | | 30 | ||
|413.793 | | 413.793 | ||
|[[81/64]], [[14/11]], [[33/26]] | | [[81/64]], [[14/11]], [[33/26]] | ||
|[[19/15]] | | [[19/15]] | ||
|M3 | | M3 | ||
|F# | | F# | ||
|- | |- | ||
|31 | | 31 | ||
|427.586 | | 427.586 | ||
|[[32/25]] | | [[32/25]] | ||
|[[23/18]] | | [[23/18]] | ||
|^M3 | | ^M3 | ||
|^F# | | ^F# | ||
|- | |- | ||
|32 | | 32 | ||
|441.379 | | 441.379 | ||
|[[9/7]], [[35/27]] | | [[9/7]], [[35/27]] | ||
|[[22/17]], [[31/24]], [[40/31]] | | [[22/17]], [[31/24]], [[40/31]] | ||
|^^M3 | | ^^M3 | ||
|^^F# | | ^^F# | ||
|- | |- | ||
|33 | | 33 | ||
|455.172 | | 455.172 | ||
|[[13/10]] | | [[13/10]] | ||
|[[30/23]] | | [[30/23]] | ||
|^<sup>3</sup>M3/v<sup>3</sup>4 | | ^<sup>3</sup>M3/v<sup>3</sup>4 | ||
|^<sup>3</sup>F#/v<sup>3</sup>G | | ^<sup>3</sup>F#/v<sup>3</sup>G | ||
|- | |- | ||
|34 | | 34 | ||
|468.966 | | 468.966 | ||
|[[21/16]] | | [[21/16]] | ||
|[[17/13]], [[25/19]], [[38/29]] | | [[17/13]], [[25/19]], [[38/29]] | ||
|vv4 | | vv4 | ||
|vvG | | vvG | ||
|- | |- | ||
|35 | | 35 | ||
|482.759 | | 482.759 | ||
|[[33/25]] | | [[33/25]] | ||
| | | | ||
|v4 | | v4 | ||
|vG | | vG | ||
|- | |- | ||
|36 | | 36 | ||
|496.552 | | 496.552 | ||
|[[4/3]] | | [[4/3]] | ||
| | | | ||
|P4 | | P4 | ||
|G | | G | ||
|- | |- | ||
|37 | | 37 | ||
|510.345 | | 510.345 | ||
|[[35/26]] | | [[35/26]] | ||
|[[31/23]] | | [[31/23]] | ||
|^4 | | ^4 | ||
|^G | | ^G | ||
|- | |- | ||
|38 | | 38 | ||
|524.138 | | 524.138 | ||
|[[27/20]] | | [[27/20]] | ||
|[[23/17]] | | [[23/17]] | ||
|^^4 | | ^^4 | ||
|^^G | | ^^G | ||
|- | |- | ||
|39 | | 39 | ||
|537.931 | | 537.931 | ||
|[[15/11]] | | [[15/11]] | ||
|[[26/19]], [[34/25]] | | [[26/19]], [[34/25]] | ||
|^<sup>3</sup>4 | | ^<sup>3</sup>4 | ||
|^<sup>3</sup>G | | ^<sup>3</sup>G | ||
|- | |- | ||
|40 | | 40 | ||
|551.724 | | 551.724 | ||
|[[11/8]], [[48/35]] | | [[11/8]], [[48/35]] | ||
| | | | ||
|^<sup>4</sup>4 | | ^<sup>4</sup>4 | ||
|^<sup>4</sup>G | | ^<sup>4</sup>G | ||
|- | |- | ||
|41 | | 41 | ||
|565.517 | | 565.517 | ||
|[[18/13]] | | [[18/13]] | ||
|[[32/23]] | | [[32/23]] | ||
|v<sup>4</sup>A4, vd5 | | v<sup>4</sup>A4, vd5 | ||
|v<sup>4</sup>G#, vAb | | v<sup>4</sup>G#, vAb | ||
|- | |- | ||
|42 | | 42 | ||
|579.310 | | 579.310 | ||
|[[7/5]] | | [[7/5]] | ||
|[[46/33]] | | [[46/33]] | ||
|v<sup>3</sup>A4, d5 | | v<sup>3</sup>A4, d5 | ||
|v<sup>3</sup>G#, Ab | | v<sup>3</sup>G#, Ab | ||
|- | |- | ||
|43 | | 43 | ||
|593.103 | | 593.103 | ||
|[[45/32]] | | [[45/32]] | ||
|[[24/17]], [[38/27]], [[31/22]] | | [[24/17]], [[38/27]], [[31/22]] | ||
|vvA4, ^d5 | | vvA4, ^d5 | ||
|vvG#, ^Ab | | vvG#, ^Ab | ||
|- | |- | ||
|… | | … | ||
|… | | … | ||
|… | | … | ||
|… | | … | ||
|… | | … | ||
|… | | … | ||
|} | |} | ||
| Line 458: | Line 458: | ||
| [[Hanson]] / [[Countercata]] / [[Metakleismic]] | | [[Hanson]] / [[Countercata]] / [[Metakleismic]] | ||
|- | |- | ||
|1 | | 1 | ||
|26\87 | | 26\87 | ||
|358.621 | | 358.621 | ||
|[[16/13]] | | [[16/13]] | ||
|[[Restles]] | | [[Restles]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 507: | Line 507: | ||
==== Mode 8 ==== | ==== Mode 8 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|Overtones | | Overtones | ||
|8 | | 8 | ||
|9 | | 9 | ||
|10 | | 10 | ||
|11 | | 11 | ||
|12 | | 12 | ||
|13 | | 13 | ||
|14 | | 14 | ||
|15 | | 15 | ||
|16 | | 16 | ||
|- | |- | ||
|JI Ratios | | JI Ratios | ||
|1/1 | | 1/1 | ||
|9/8 | | 9/8 | ||
|5/4 | | 5/4 | ||
|11/8 | | 11/8 | ||
|3/2 | | 3/2 | ||
|13/8 | | 13/8 | ||
|7/4 | | 7/4 | ||
|15/8 | | 15/8 | ||
|2/1 | | 2/1 | ||
|- | |- | ||
|… in cents | | … in cents | ||
|0.0 | | 0.0 | ||
|203.9 | | 203.9 | ||
|386.3 | | 386.3 | ||
|551.3 | | 551.3 | ||
|702.0 | | 702.0 | ||
|840.5 | | 840.5 | ||
|968.8 | | 968.8 | ||
|1088.3 | | 1088.3 | ||
|1200.0 | | 1200.0 | ||
|- | |- | ||
|Degrees in 87edo | | Degrees in 87edo | ||
|0 | | 0 | ||
|15 | | 15 | ||
|28 | | 28 | ||
|40 | | 40 | ||
|51 | | 51 | ||
|61 | | 61 | ||
|70 | | 70 | ||
|79 | | 79 | ||
|87 | | 87 | ||
|- | |- | ||
|… in cents | | … in cents | ||
|0.0 | | 0.0 | ||
|206.9 | | 206.9 | ||
|386.2 | | 386.2 | ||
|551.7 | | 551.7 | ||
|703.5 | | 703.5 | ||
|841.4 | | 841.4 | ||
|965.5 | | 965.5 | ||
|1089.7 | | 1089.7 | ||
|1200.0 | | 1200.0 | ||
|} | |} | ||
* The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8. | * The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8. | ||
| Line 566: | Line 566: | ||
==== Mode 16 ==== | ==== Mode 16 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|Odd overtones | | Odd overtones | ||
|17 | | 17 | ||
|19 | | 19 | ||
|21 | | 21 | ||
|23 | | 23 | ||
|25 | | 25 | ||
|27 | | 27 | ||
|29 | | 29 | ||
|31 | | 31 | ||
|- | |- | ||
|JI Ratios | | JI Ratios | ||
|17/16 | | 17/16 | ||
|19/16 | | 19/16 | ||
|21/16 | | 21/16 | ||
|23/16 | | 23/16 | ||
|25/16 | | 25/16 | ||
|27/16 | | 27/16 | ||
|29/16 | | 29/16 | ||
|31/16 | | 31/16 | ||
|- | |- | ||
|… in cents | | … in cents | ||
|105.0 | | 105.0 | ||
|297.5 | | 297.5 | ||
|470.8 | | 470.8 | ||
|628.3 | | 628.3 | ||
|772.6 | | 772.6 | ||
|905.9 | | 905.9 | ||
|1029.6 | | 1029.6 | ||
|1145.0 | | 1145.0 | ||
|- | |- | ||
|Degrees in 87edo | | Degrees in 87edo | ||
|8 | | 8 | ||
|22 | | 22 | ||
|34 | | 34 | ||
|46 | | 46 | ||
|56 | | 56 | ||
|66 | | 66 | ||
|75 | | 75 | ||
|83 | | 83 | ||
|- | |- | ||
|… in cents | | … in cents | ||
|110.3 | | 110.3 | ||
|303.4 | | 303.4 | ||
|469.0 | | 469.0 | ||
|634.5 | | 634.5 | ||
|772.4 | | 772.4 | ||
|910.3 | | 910.3 | ||
|1034.5 | | 1034.5 | ||
|1144.8 | | 1144.8 | ||
|} | |} | ||
* The scale in adjacent steps is 8, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 4, 4, 4. | * The scale in adjacent steps is 8, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 4, 4, 4. | ||