981edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table |
Adopt template: Factorization; misc. cleanup |
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== Theory == | == Theory == | ||
981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2080/2079]], [[2401/2400]], 2431/2430, [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and 4914/4913 in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095. | 981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. The equal temperament [[Tempering out|tempers out]] [[2080/2079]], [[2401/2400]], [[2431/2430]], [[4096/4095]], [[4225/4224]], [[4375/4374]], 4459/4455 and [[4914/4913]] in the 17-limit. It provides the [[optimal patent val]] for 13-limit [[ennealimmic]], the rank-3 temperament tempering out 2080/2079, 2401/2400, and 4375/4374, and for 13-limit [[ennealimmia]], which also tempers out 4096/4095. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 981 = | Since 981 = {{factorization|981}}, 981edo has subset edos 3, 9, 109, and 327. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 24: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 1555 -981 }} | | {{monzo| 1555 -981 }} | ||
| | | {{mapping| 981 1555 }} | ||
| -0.0586 | | -0.0586 | ||
| 0.0586 | | 0.0586 | ||
| Line 31: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }} | | {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }} | ||
| | | {{mapping| 981 1555 2278 }} | ||
| -0.0722 | | -0.0722 | ||
| 0.0515 | | 0.0515 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }} | | 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }} | ||
| | | {{mapping| 981 1555 2278 2754 }} | ||
| -0.0385 | | -0.0385 | ||
| 0.0562 | | 0.0562 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470 | | 2401/2400, 4375/4374, 131072/130977, 1771561/1771470 | ||
| | | {{mapping| 981 1555 2278 2754 3394 }} | ||
| -0.0630 | | -0.0630 | ||
| 0.0545 | | 0.0545 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470 | | 2080/2079, 2401/2400, 4096/4095, 4375/4374, 1771561/1771470 | ||
| | | {{mapping| 981 1555 2278 2754 3394 3630 }} | ||
| -0.0453 | | -0.0453 | ||
| 0.0636 | | 0.0636 | ||
| Line 59: | Line 59: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913 | | 2080/2079, 2401/2400, 2431/2430, 4096/4095, 4375/4374, 4914/4913 | ||
| | | {{mapping| 981 1555 2278 2754 3394 3630 4010 }} | ||
| -0.0473 | | -0.0473 | ||
| 0.0591 | | 0.0591 | ||
| Line 70: | Line 70: | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 77: | Line 77: | ||
| 500.306 | | 500.306 | ||
| 8192/6137 | | 8192/6137 | ||
| [[ | | [[Protolangwidge]] | ||
|- | |- | ||
| 9 | | 9 | ||