1848edo: Difference between revisions
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== Theory == | == Theory == | ||
1848edo is | 1848edo is an extremely strong 11-limit division, having the lowest 11-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[6079edo|6079]]. | ||
In the 5-limit it tempers out the minortone comma, {{monzo| -16 35 -17 }} and the [[atom]], {{monzo| 161 -84 -12 }} and thus tunes the [[atomic]] temperament, for which it also provides the [[optimal patent val]] in the 11-limit. In the 7-limit it tempers out the [[landscape comma]], 250047/250000, so it supports [[domain]] and [[akjayland]]. In the 11-limit it tempers out [[9801/9800]], 151263/151250, [[1771561/1771470]], 3294225/3294172, and the [[spoob]]. | In the 5-limit it tempers out the minortone comma, {{monzo| -16 35 -17 }} and the [[atom]], {{monzo| 161 -84 -12 }} and thus tunes the [[atomic]] temperament, for which it also provides the [[optimal patent val]] in the 11-limit. In the 7-limit it tempers out the [[landscape comma]], 250047/250000, so it supports [[domain]] and [[akjayland]]. In the 11-limit it tempers out [[9801/9800]], 151263/151250, [[1771561/1771470]], 3294225/3294172, and the [[spoob]]. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 41: | Line 32: | ||
| {{monzo| -16 35 -17 }}, {{monzo| 129 -14 -46 }} | | {{monzo| -16 35 -17 }}, {{monzo| 129 -14 -46 }} | ||
| {{mapping| 1848 2929 4291 }} | | {{mapping| 1848 2929 4291 }} | ||
| | | −0.005705 | ||
| 0.011311 | | 0.011311 | ||
| 1.74 | | 1.74 | ||
| Line 48: | Line 39: | ||
| 250047/250000, {{monzo| -4 17 1 -9 }}, {{monzo| 43 -1 -13 -4 }} | | 250047/250000, {{monzo| -4 17 1 -9 }}, {{monzo| 43 -1 -13 -4 }} | ||
| {{mapping| 1848 2929 4291 5188 }} | | {{mapping| 1848 2929 4291 5188 }} | ||
| | | −0.004748 | ||
| 0.009935 | | 0.009935 | ||
| 1.53 | | 1.53 | ||
| Line 55: | Line 46: | ||
| 9801/9800, 151263/151250, 1771561/1771470, 67110351/67108864 | | 9801/9800, 151263/151250, 1771561/1771470, 67110351/67108864 | ||
| {{mapping| 1848 2929 4291 5188 6393 }} | | {{mapping| 1848 2929 4291 5188 6393 }} | ||
| | | −0.002686 | ||
| 0.009797 | | 0.009797 | ||
| 1.51 | | 1.51 | ||
| Line 65: | Line 56: | ||
| 0.029378 | | 0.029378 | ||
| 4.52 | | 4.52 | ||
|- | |- style="border-top: double;" | ||
| 2.3.5.7.11.19 | |||
| 5776/5775, 9801/9800, 10241/10240, 250047/250000, 233744896/233735625 | |||
| {{mapping| 1848 2929 4291 5188 6393 7850 }} | |||
| 0.002094 | |||
| 0.013936 | |||
| +2.15 | |||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 137: | Line 121: | ||
| 975/784<br />(?) | | 975/784<br />(?) | ||
| [[Iridium]] | | [[Iridium]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||