451edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|451}} == Theory == 451et is consistent to the 7-odd-limit. Using the patent val, it tempers out 52734375/52706752, 703125/702464, 65625/6..." |
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== Theory == | == Theory == | ||
451 = 11 × 41, and 451edo shares its [[3/2|fifth]] with [[41edo]]. Unlike 41, however, 451 is only [[consistent]] to the [[7-odd-limit]], though it has a reasonable approximation up to the [[13-limit]] using the [[patent val]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[65625/65536]], [[703125/702464]], [[2100875/2097152]], and 390625000/387420489 in the 7-limit; [[6250/6237]], 42592/42525, 42875/42768, 43923/43904 in the 11-limit; and [[625/624]], [[2080/2079]], [[2200/2197]], [[4096/4095]], [[4225/4224]], 4459/4455, and 17303/17280 in the 13-limit. It [[support]]s [[tertiaseptal]], [[tertiseptisix]], and [[hemermacomp]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
451 factors into 11 × 41, | Since 451 factors into 11 × 41, 451edo has [[11edo]] and [[41edo]] as its subsets. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3.5 | |||
| {{monzo| 3 -18 11 }}, {{monzo| -59 5 22 }} | |||
| {{mapping| 451 715 1047 }} | |||
|2.3.5 | |||
|{{monzo|3 -18 11}}, {{monzo|-59 5 22}} | |||
|{{mapping|451 715 1047}} | |||
| -0.0294 | | -0.0294 | ||
| 0.2144 | | 0.2144 | ||
| 8.06 | | 8.06 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, | | 2401/2400, 65625/65536, 390625000/387420489 | ||
|{{mapping|451 715 1047 | | {{mapping| 451 715 1047 126 6}} | ||
| +0.0057 | | +0.0057 | ||
| 0.1953 | | 0.1953 | ||
| 7.34 | | 7.34 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|2401/2400, 6250/6237, 42592/42525, 43923/43904 | | 2401/2400, 6250/6237, 42592/42525, 43923/43904 | ||
|{{mapping|451 715 1047 1266 1560}} | | {{mapping| 451 715 1047 1266 1560 }} | ||
| +0.0359 | | +0.0359 | ||
| 0.1849 | | 0.1849 | ||
| 6.95 | | 6.95 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| | | 625/624, 2080/2079, 2200/2197, 2401/2400, 17303/17280 | ||
|{{mapping|451 715 1047 1266 1560 1669}} | | {{mapping| 451 715 1047 1266 1560 1669 }} | ||
| +0.0177 | | +0.0177 | ||
| 0.1736 | | 0.1736 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|29\451 | | 29\451 | ||
|77.16 | | 77.16 | ||
|256/245 | | 256/245 | ||
|[[Tertiaseptal]] | | [[Tertiaseptal]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||