36edo: Difference between revisions
m Fixed non-standard bold, slightly rewrote beginning. |
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<b>36edo</b>, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33⅓ cents. | <b>36edo</b>, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33⅓ cents. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | Degree | ! rowspan="2"| Degree | ||
! | Size | ! colspan="3"| Size | ||
in | in | ||
! | Approximate | ! rowspan="2"| Approximate | ||
ratios of 2.3.7 | ratios of 2.3.7 | ||
! | Additional ratios | ! rowspan="2"| Additional ratios | ||
of 2.3.7.13.17 | of 2.3.7.13.17 | ||
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs ]][[Ups_and_Downs_Notation|notation]] | ! colspan="3" rowspan="2" | [[Ups_and_Downs_Notation|ups and downs]] [[Ups_and_Downs_Notation|notation]] | ||
|- | |||
![[cent|cents]] | |||
!pions | |||
!7mus | |||
|- | |- | ||
| style="text-align:center;" | 0 | | style="text-align:center;" | 0 | ||
| style="text-align:right;" | 0.00 | | colspan="3" style="text-align:right;" | 0.00 | ||
| style="text-align:center;" | 1/1 | | style="text-align:center;" | 1/1 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 122: | Line 127: | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:right;" | 33.33 | | style="text-align:right;" | 33.33 | ||
|35.33 | |||
|42.67 (2A.AB<sub>16</sub>) | |||
| style="text-align:center;" | 64/63, [[49/48|49/48]] | | style="text-align:center;" | 64/63, [[49/48|49/48]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 129: | Line 136: | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:right;" | 66.67 | | style="text-align:right;" |66.67 | ||
|70.67 | |||
|85.33 (55.55<sub>16</sub>) | |||
| style="text-align:center;" | [[28/27|28/27]] | | style="text-align:center;" | [[28/27|28/27]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 137: | Line 146: | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:right;" | 100 | | style="text-align:right;" | 100 | ||
|106 | |||
|128 (80<sub>16</sub>) | |||
| style="text-align:center;" | 256/243 | | style="text-align:center;" | 256/243 | ||
| style="text-align:center;" | [[17/16|17/16]], [[18/17|18/17]] | | style="text-align:center;" | [[17/16|17/16]], [[18/17|18/17]] | ||
| Line 146: | Line 157: | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:right;" | 133.33 | | style="text-align:right;" | 133.33 | ||
|141.33 | |||
|170.67 (AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | 243/224 | | style="text-align:center;" | 243/224 | ||
| style="text-align:center;" | [[14/13|14/13]], [[13/12|13/12]] | | style="text-align:center;" | [[14/13|14/13]], [[13/12|13/12]] | ||
| Line 154: | Line 167: | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:right;" | 166.67 | | style="text-align:right;" | 166.67 | ||
|176.67 | |||
|213.33 (D5.55<sub>16</sub>) | |||
| style="text-align:center;" | [[54/49|54/49]] | | style="text-align:center;" | [[54/49|54/49]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 161: | Line 176: | ||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:right;" | 200 | | style="text-align:right;" | 200 | ||
|212 | |||
|256 (100<sub>16</sub>) | |||
| style="text-align:center;" | [[9/8|9/8]] | | style="text-align:center;" | [[9/8|9/8]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 170: | Line 187: | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:right;" | 233.33 | | style="text-align:right;" | 233.33 | ||
|247.33 | |||
|298.67 (12A.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[8/7|8/7]] | | style="text-align:center;" | [[8/7|8/7]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 178: | Line 197: | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:right;" | 266.67 | | style="text-align:right;" | 266.67 | ||
|282.67 | |||
|341.33 (155.55<sub>16</sub>) | |||
| style="text-align:center;" | [[7/6|7/6]] | | style="text-align:center;" | [[7/6|7/6]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 185: | Line 206: | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
| style="text-align:right;" | 300 | | style="text-align:right;" | 300 | ||
|318 | |||
|384 (180<sub>16</sub>) | |||
| style="text-align:center;" | [[32/27|32/27]] | | style="text-align:center;" | [[32/27|32/27]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 194: | Line 217: | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
| style="text-align:right;" | 333.33 | | style="text-align:right;" | 333.33 | ||
|353.33 | |||
|426.67 (1AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | 98/81 | | style="text-align:center;" | 98/81 | ||
| style="text-align:center;" | [[17/14|17/14]] | | style="text-align:center;" | [[17/14|17/14]] | ||
| Line 202: | Line 227: | ||
| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:right;" | 366.67 | | style="text-align:right;" | 366.67 | ||
|388.67 | |||
|469.33 (1D5.55<sub>16</sub>) | |||
| style="text-align:center;" | 243/196 | | style="text-align:center;" | 243/196 | ||
| style="text-align:center;" | [[16/13|16/13]], [[26/21|26/21]], [[21/17|21/17]] | | style="text-align:center;" | [[16/13|16/13]], [[26/21|26/21]], [[21/17|21/17]] | ||
| Line 209: | Line 236: | ||
|- | |- | ||
| style="text-align:center;" | 12 | | style="text-align:center;" | 12 | ||
| style="text-align:right;" | 400 | | style="text-align:right;" | 400 | ||
|424 | |||
|512 (200<sub>16</sub>) | |||
| style="text-align:center;" | [[81/64|81/64]] | | style="text-align:center;" | [[81/64|81/64]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 218: | Line 247: | ||
| style="text-align:center;" | 13 | | style="text-align:center;" | 13 | ||
| style="text-align:right;" | 433.33 | | style="text-align:right;" | 433.33 | ||
|459.33 | |||
|554.67 (22A.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[9/7|9/7]] | | style="text-align:center;" | [[9/7|9/7]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 226: | Line 257: | ||
| style="text-align:center;" | 14 | | style="text-align:center;" | 14 | ||
| style="text-align:right;" | 466.67 | | style="text-align:right;" | 466.67 | ||
|494.67 | |||
|597.33 (255.55<sub>16</sub>) | |||
| style="text-align:center;" | [[64/49|64/49]], [[21/16|21/16]] | | style="text-align:center;" | [[64/49|64/49]], [[21/16|21/16]] | ||
| style="text-align:center;" | [[17/13|17/13]] | | style="text-align:center;" | [[17/13|17/13]] | ||
| Line 234: | Line 267: | ||
| style="text-align:center;" | 15 | | style="text-align:center;" | 15 | ||
| style="text-align:right;" | 500.00 | | style="text-align:right;" | 500.00 | ||
|530 | |||
|640 (280<sub>16</sub>) | |||
| style="text-align:center;" | [[4/3|4/3]] | | style="text-align:center;" | [[4/3|4/3]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 242: | Line 277: | ||
| style="text-align:center;" | 16 | | style="text-align:center;" | 16 | ||
| style="text-align:right;" | 533.33 | | style="text-align:right;" | 533.33 | ||
|565.33 | |||
|682.67 (2AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[49/36|49/36]] | | style="text-align:center;" | [[49/36|49/36]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 250: | Line 287: | ||
| style="text-align:center;" | 17 | | style="text-align:center;" | 17 | ||
| style="text-align:right;" | 566.67 | | style="text-align:right;" | 566.67 | ||
|600.67 | |||
|725.33 (2D5.55<sub>16</sub>) | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | [[18/13|18/13]] | | style="text-align:center;" | [[18/13|18/13]] | ||
| Line 257: | Line 296: | ||
|- | |- | ||
| style="text-align:center;" | 18 | | style="text-align:center;" | 18 | ||
| style="text-align:right;" | 600 | | style="text-align:right;" | 600 | ||
|636 | |||
|768 (300<sub>16</sub>) | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 266: | Line 307: | ||
| style="text-align:center;" | 19 | | style="text-align:center;" | 19 | ||
| style="text-align:right;" | 633.33 | | style="text-align:right;" | 633.33 | ||
|671.33 | |||
|810.67 (32A.AB<sub>16</sub>) | |||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | [[13/9|13/9]] | | style="text-align:center;" | [[13/9|13/9]] | ||
| Line 274: | Line 317: | ||
| style="text-align:center;" | 20 | | style="text-align:center;" | 20 | ||
| style="text-align:right;" | 666.67 | | style="text-align:right;" | 666.67 | ||
|706.67 | |||
|853.33 (355.55<sub>16</sub>) | |||
| style="text-align:center;" | 72/49 | | style="text-align:center;" | 72/49 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 281: | Line 326: | ||
|- | |- | ||
| style="text-align:center;" | 21 | | style="text-align:center;" | 21 | ||
| style="text-align:right;" | 700 | | style="text-align:right;" | 700 | ||
|742 | |||
|896 (380<sub>16</sub>) | |||
| style="text-align:center;" | [[3/2|3/2]] | | style="text-align:center;" | [[3/2|3/2]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 290: | Line 337: | ||
| style="text-align:center;" | 22 | | style="text-align:center;" | 22 | ||
| style="text-align:right;" | 733.33 | | style="text-align:right;" | 733.33 | ||
|777.33 | |||
|938.67 (3AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[49/32|49/32]], [[32/21|32/21]] | | style="text-align:center;" | [[49/32|49/32]], [[32/21|32/21]] | ||
| style="text-align:center;" | [[26/17|26/17]] | | style="text-align:center;" | [[26/17|26/17]] | ||
| Line 298: | Line 347: | ||
| style="text-align:center;" | 23 | | style="text-align:center;" | 23 | ||
| style="text-align:right;" | 766.67 | | style="text-align:right;" | 766.67 | ||
|812.67 | |||
|981.33 (3D5.55<sub>16</sub>) | |||
| style="text-align:center;" | [[14/9|14/9]] | | style="text-align:center;" | [[14/9|14/9]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 305: | Line 356: | ||
|- | |- | ||
| style="text-align:center;" | 24 | | style="text-align:center;" | 24 | ||
| style="text-align:right;" | 800 | | style="text-align:right;" | 800 | ||
|848 | |||
|1024 (400<sub>16</sub>) | |||
| style="text-align:center;" | [[128/81|128/81]] | | style="text-align:center;" | [[128/81|128/81]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 314: | Line 367: | ||
| style="text-align:center;" | 25 | | style="text-align:center;" | 25 | ||
| style="text-align:right;" | 833.33 | | style="text-align:right;" | 833.33 | ||
|883.33 | |||
|1066.67 (42A.AB<sub>16</sub>) | |||
| style="text-align:center;" | 392/243 | | style="text-align:center;" | 392/243 | ||
| style="text-align:center;" | [[13/8|13/8]], [[21/13|21/13]], [[34/21|34/21]] | | style="text-align:center;" | [[13/8|13/8]], [[21/13|21/13]], [[34/21|34/21]] | ||
| Line 322: | Line 377: | ||
| style="text-align:center;" | 26 | | style="text-align:center;" | 26 | ||
| style="text-align:right;" | 866.67 | | style="text-align:right;" | 866.67 | ||
|919.67 | |||
|1109.33 (455.55<sub>16</sub>) | |||
| style="text-align:center;" | 81/49 | | style="text-align:center;" | 81/49 | ||
| style="text-align:center;" | [[28/17|28/17]] | | style="text-align:center;" | [[28/17|28/17]] | ||
| Line 329: | Line 386: | ||
|- | |- | ||
| style="text-align:center;" | 27 | | style="text-align:center;" | 27 | ||
| style="text-align:right;" | 900 | | style="text-align:right;" | 900 | ||
|954 | |||
|1152 (480<sub>16</sub>) | |||
| style="text-align:center;" | [[27/16|27/16]] | | style="text-align:center;" | [[27/16|27/16]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 338: | Line 397: | ||
| style="text-align:center;" | 28 | | style="text-align:center;" | 28 | ||
| style="text-align:right;" | 933.33 | | style="text-align:right;" | 933.33 | ||
|989.33 | |||
|1194.67 (4AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[12/7|12/7]] | | style="text-align:center;" | [[12/7|12/7]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 346: | Line 407: | ||
| style="text-align:center;" | 29 | | style="text-align:center;" | 29 | ||
| style="text-align:right;" | 966.67 | | style="text-align:right;" | 966.67 | ||
|1024.67 | |||
|1237.33 (4D5.55<sub>16</sub>) | |||
| style="text-align:center;" | [[7/4|7/4]] | | style="text-align:center;" | [[7/4|7/4]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 353: | Line 416: | ||
|- | |- | ||
| style="text-align:center;" | 30 | | style="text-align:center;" | 30 | ||
| style="text-align:right;" | 1000 | | style="text-align:right;" | 1000 | ||
|1060 | |||
|1280 (500<sub>16</sub>) | |||
| style="text-align:center;" | [[16/9|16/9]] | | style="text-align:center;" | [[16/9|16/9]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 362: | Line 427: | ||
| style="text-align:center;" | 31 | | style="text-align:center;" | 31 | ||
| style="text-align:right;" | 1033.33 | | style="text-align:right;" | 1033.33 | ||
|1095.33 | |||
|1332.67 (52A.AB<sub>16</sub>) | |||
| style="text-align:center;" | 49/27 | | style="text-align:center;" | 49/27 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 370: | Line 437: | ||
| style="text-align:center;" | 32 | | style="text-align:center;" | 32 | ||
| style="text-align:right;" | 1066.67 | | style="text-align:right;" | 1066.67 | ||
|1131.67 | |||
|1365.33 (555.55<sub>16</sub>) | |||
| style="text-align:center;" | 448/243 | | style="text-align:center;" | 448/243 | ||
| style="text-align:center;" | [[13/7|13/7]], [[24/13|24/13]] | | style="text-align:center;" | [[13/7|13/7]], [[24/13|24/13]] | ||
| Line 377: | Line 446: | ||
|- | |- | ||
| style="text-align:center;" | 33 | | style="text-align:center;" | 33 | ||
| style="text-align:right;" | 1100 | | style="text-align:right;" | 1100 | ||
|1166 | |||
|1408 (580<sub>16</sub>) | |||
| style="text-align:center;" | [[243/128|243/128]] | | style="text-align:center;" | [[243/128|243/128]] | ||
| style="text-align:center;" | [[32/17|32/17]], [[17/9|17/9]] | | style="text-align:center;" | [[32/17|32/17]], [[17/9|17/9]] | ||
| Line 386: | Line 457: | ||
| style="text-align:center;" | 34 | | style="text-align:center;" | 34 | ||
| style="text-align:right;" | 1133.33 | | style="text-align:right;" | 1133.33 | ||
|1201.33 | |||
|1440.67 (5AA.AB<sub>16</sub>) | |||
| style="text-align:center;" | [[27/14|27/14]] | | style="text-align:center;" | [[27/14|27/14]] | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 394: | Line 467: | ||
| style="text-align:center;" | 35 | | style="text-align:center;" | 35 | ||
| style="text-align:right;" | 1166.67 | | style="text-align:right;" | 1166.67 | ||
|1236.67 | |||
|1483.33 (5D5.55<sub>16</sub>) | |||
| style="text-align:center;" | 63/32, 96/49 | | style="text-align:center;" | 63/32, 96/49 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 402: | Line 477: | ||
| style="text-align:center;" | 36 | | style="text-align:center;" | 36 | ||
| style="text-align:right;" | 1200.00 | | style="text-align:right;" | 1200.00 | ||
|1272 | |||
|1536 (600<sub>16</sub>) | |||
| style="text-align:center;" | 2/1 | | style="text-align:center;" | 2/1 | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 412: | Line 489: | ||
=Music= | =Music= | ||
<ul><li><span style="">[https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo?in=overtoneshock/sets/xenharmonic-microtonal Exponentially More Lost and Forgetful] by [https://soundcloud.com/overtoneshock Stephen Weigel] played by flautists Orlando Cela and Wei Zhao</span></li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 Something]</span> by [[Herman_Klein|Herman Klein]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3 Hay]</span> by [[Joe_Hayseed|Joe Hayseed]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 Boomers]</span> by [[Ivan_Bratt|Ivan Bratt]]</li><li>[http://micro.soonlabel.com/36edo/20120418-36edo.mp3 Thoughts in Legolas Tuning] by [[Chris_Vaisvil|Chris Vaisvil]]</li></ul> [[Category:edo]] | <ul><li><span style="">[https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo?in=overtoneshock/sets/xenharmonic-microtonal Exponentially More Lost and Forgetful] by [https://soundcloud.com/overtoneshock Stephen Weigel] played by flautists Orlando Cela and Wei Zhao</span></li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 Something]</span> by [[Herman_Klein|Herman Klein]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3 Hay]</span> by [[Joe_Hayseed|Joe Hayseed]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 Boomers]</span> by [[Ivan_Bratt|Ivan Bratt]]</li><li>[http://micro.soonlabel.com/36edo/20120418-36edo.mp3 Thoughts in Legolas Tuning] by [[Chris_Vaisvil|Chris Vaisvil]]</li></ul> | ||
[[Category:edo]] | |||
[[Category:listen]] | [[Category:listen]] | ||
[[Category:melpomene]] | [[Category:melpomene]] | ||