121edo: Difference between revisions
→Regular temperament properties: 13- to 23-limit notability |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 192 -121 }} | | {{monzo| 192 -121 }} | ||
| {{mapping| 121 192 }} | | {{mapping| 121 192 }} | ||
| | | −0.687 | ||
| 0.687 | | 0.687 | ||
| 6.93 | | 6.93 | ||
| Line 34: | Line 26: | ||
| 15625/15552, {{monzo| 31 -21 1 }} | | 15625/15552, {{monzo| 31 -21 1 }} | ||
| {{mapping| 121 192 281 }} | | {{mapping| 121 192 281 }} | ||
| | | −0.524 | ||
| 0.606 | | 0.606 | ||
| 6.11 | | 6.11 | ||
| Line 41: | Line 33: | ||
| 4000/3969, 6144/6125, 10976/10935 | | 4000/3969, 6144/6125, 10976/10935 | ||
| {{mapping| 121 192 281 340 }} | | {{mapping| 121 192 281 340 }} | ||
| | | −0.667 | ||
| 0.580 | | 0.580 | ||
| 5.85 | | 5.85 | ||
| Line 48: | Line 40: | ||
| 540/539, 896/891, 1375/1372, 4375/4356 | | 540/539, 896/891, 1375/1372, 4375/4356 | ||
| {{mapping| 121 192 281 340 419 }} | | {{mapping| 121 192 281 340 419 }} | ||
| | | −0.768 | ||
| 0.556 | | 0.556 | ||
| 5.61 | | 5.61 | ||
| Line 55: | Line 47: | ||
| 325/324, 352/351, 364/363, 540/539, 625/624 | | 325/324, 352/351, 364/363, 540/539, 625/624 | ||
| {{mapping| 121 192 281 340 419 448 }} | | {{mapping| 121 192 281 340 419 448 }} | ||
| | | −0.750 | ||
| 0.510 | | 0.510 | ||
| 5.14 | | 5.14 | ||
| Line 62: | Line 54: | ||
| 256/255, 325/324, 352/351, 364/363, 375/374, 442/441 | | 256/255, 325/324, 352/351, 364/363, 375/374, 442/441 | ||
| {{mapping| 121 192 281 340 419 448 495 }} | | {{mapping| 121 192 281 340 419 448 495 }} | ||
| | | −0.787 | ||
| 0.480 | | 0.480 | ||
| 4.85 | | 4.85 | ||
| Line 69: | Line 61: | ||
| 190/189, 256/255, 325/324, 352/351, 361/360, 364/363, 375/374 | | 190/189, 256/255, 325/324, 352/351, 361/360, 364/363, 375/374 | ||
| {{mapping| 121 192 281 340 419 448 495 514 }} | | {{mapping| 121 192 281 340 419 448 495 514 }} | ||
| | | −0.689 | ||
| 0.519 | | 0.519 | ||
| 5.23 | | 5.23 | ||
{{comma basis end}} | |||
* 121et (121i val) has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19-, and 23-limit, beating [[111edo|111]] before being superseded by [[130edo|130]] in all those limits except for the 17-limit, where it is superseded by [[140edo|140]]. | * 121et (121i val) has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19-, and 23-limit, beating [[111edo|111]] before being superseded by [[130edo|130]] in all those limits except for the 17-limit, where it is superseded by [[140edo|140]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 187: | Line 173: | ||
|- | |- | ||
| 11 | | 11 | ||
| 50\121<br>(5\121) | | 50\121<br />(5\121) | ||
| 495.87<br>(49.59) | | 495.87<br />(49.59) | ||
| 4/3<br>(36/35) | | 4/3<br />(36/35) | ||
| [[Hendecatonic]] | | [[Hendecatonic]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== 13-limit detempering of 121et == | == 13-limit detempering of 121et == | ||
| Line 200: | Line 186: | ||
== Miscellany == | == Miscellany == | ||
Since 121 is part of the Fibonacci sequence beginning with 5 and 12, 121edo closely approximates [[peppermint]] temperament. This makes it suitable for [[neo-Gothic]] tunings. | Since 121 is part of the Fibonacci sequence beginning with 5 and 12, 121edo closely approximates [[peppermint]] temperament. This makes it suitable for [[neo-Gothic]] tunings. | ||
[[Category:Grendel]] | [[Category:Grendel]] | ||
[[Category:Quintupole]] | [[Category:Quintupole]] | ||