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]]. 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]]. 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
| 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
| −0.0722
| 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
| −0.0385
| 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
| −0.0630
| 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
| −0.0453
| 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
| −0.0473
| 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 it is distinct
<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]]