981edo: Difference between revisions
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== Theory == | == Theory == | ||
981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. | 981edo is a good 13- and 17-limit system, [[consistent]] to the [[17-odd-limit]]. It [[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 === | ||
Line 26: | Line 26: | ||
| {{monzo| 1555 -981 }} | | {{monzo| 1555 -981 }} | ||
| {{mapping| 981 1555 }} | | {{mapping| 981 1555 }} | ||
| | | −0.0586 | ||
| 0.0586 | | 0.0586 | ||
| 4.79 | | 4.79 | ||
Line 33: | Line 33: | ||
| {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }} | | {{monzo| 1 -27 18 }}, {{monzo| 85 -17 -25 }} | ||
| {{mapping| 981 1555 2278 }} | | {{mapping| 981 1555 2278 }} | ||
| | | −0.0722 | ||
| 0.0515 | | 0.0515 | ||
| 4.21 | | 4.21 | ||
Line 40: | Line 40: | ||
| 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }} | | 2401/2400, 4375/4374, {{monzo| 79 -25 -23 5 }} | ||
| {{mapping| 981 1555 2278 2754 }} | | {{mapping| 981 1555 2278 2754 }} | ||
| | | −0.0385 | ||
| 0.0562 | | 0.0562 | ||
| 4.59 | | 4.59 | ||
Line 47: | Line 47: | ||
| 2401/2400, 4375/4374, 131072/130977, 1771561/1771470 | | 2401/2400, 4375/4374, 131072/130977, 1771561/1771470 | ||
| {{mapping| 981 1555 2278 2754 3394 }} | | {{mapping| 981 1555 2278 2754 3394 }} | ||
| | | −0.0630 | ||
| 0.0545 | | 0.0545 | ||
| 4.46 | | 4.46 | ||
Line 54: | Line 54: | ||
| 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 }} | | {{mapping| 981 1555 2278 2754 3394 3630 }} | ||
| | | −0.0453 | ||
| 0.0636 | | 0.0636 | ||
| 5.20 | | 5.20 | ||
Line 61: | Line 61: | ||
| 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 }} | | {{mapping| 981 1555 2278 2754 3394 3630 4010 }} | ||
| | | −0.0473 | ||
| 0.0591 | | 0.0591 | ||
| 4.83 | | 4.83 | ||
Line 88: | Line 88: | ||
| [[Ennealimmal]] / ennealimmia | | [[Ennealimmal]] / ennealimmia | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
[[Category:Ennealimmic]] | [[Category:Ennealimmic]] | ||
[[Category:Ennealimmia]] | [[Category:Ennealimmia]] |