593edo: Difference between revisions
m add links |
Preserve the distinction between ET and edo. "Supporting speric" can be better worded as tempering out 2500/2499 in the 2.3.5.7.17 subgroup, same for garischismic and decovulture |
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== Theory == | == Theory == | ||
593edo is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[4375/4374]], [[33554432/33480783]], 52734375/52706752, and 67108864/66976875 in the 7-limit. It [[support]]s [[vulture]] and [[squarschmidt]]. It is also notable in the 2.3.5.7.17 [[subgroup]], tempering out [[2500/2499]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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== 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 | | 2.3 | ||
|{{monzo|940 -593}} | | {{monzo| 940 -593 }} | ||
|{{mapping|593 940}} | | {{mapping| 593 940 }} | ||
| -0.0748 | | -0.0748 | ||
| 0.0748 | | 0.0748 | ||
| 3.70 | | 3.70 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|24 -21 4}}, {{monzo|37 25 -33}} | | {{monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }} | ||
|{{mapping|593 940 1377}} | | {{mapping| 593 940 1377 }} | ||
| -0.0780 | | -0.0780 | ||
| 0.0613 | | 0.0613 | ||
| 3.03 | | 3.03 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 52734375/52706752 | | 4375/4374, 33554432/33480783, 52734375/52706752 | ||
|{{mapping|593 940 1377 1665}} | | {{mapping| 593 940 1377 1665 }} | ||
| -0.1015 | | -0.1015 | ||
| 0.0669 | | 0.0669 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|196\593 | | 196\593 | ||
|396.63 | | 396.63 | ||
|98304/78125 | | 98304/78125 | ||
|[[Squarschmidt]] | | [[Squarschmidt]] | ||
|- | |- | ||
|1 | | 1 | ||
|215\593 | | 215\593 | ||
|435.08 | | 435.08 | ||
|9/7 | | 9/7 | ||
|[[Supermajor]] | | [[Supermajor]] | ||
|- | |- | ||
|1 | | 1 | ||
|235\593 | | 235\593 | ||
|475.55 | | 475.55 | ||
|320/243 | | 320/243 | ||
|[[Vulture]] | | [[Vulture]] | ||
|- | |- | ||
|1 | | 1 | ||
|277\593 | | 277\593 | ||
|560.54 | | 560.54 | ||
|864/625 | | 864/625 | ||
|[[Whoosh]] | | [[Whoosh]] | ||
|} | |} | ||
<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 |