593edo: Difference between revisions
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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 === | ||
| Line 13: | Line 13: | ||
== 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 | ||
| Line 53: | Line 53: | ||
! 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 | ||
Revision as of 10:42, 7 May 2024
| ← 592edo | 593edo | 594edo → |
Theory
593edo is consistent to the 9-odd-limit. The equal temperament tempers out 4375/4374, 33554432/33480783, 52734375/52706752, and 67108864/66976875 in the 7-limit. It supports vulture and squarschmidt. It is also notable in the 2.3.5.7.17 subgroup, tempering out 2500/2499.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.237 | +0.196 | +0.483 | -0.896 | -0.730 | +0.272 | -0.043 | -0.956 | +0.440 | +0.327 |
| Relative (%) | +0.0 | +11.7 | +9.7 | +23.9 | -44.3 | -36.1 | +13.5 | -2.1 | -47.2 | +21.7 | +16.2 | |
| Steps (reduced) |
593 (0) |
940 (347) |
1377 (191) |
1665 (479) |
2051 (272) |
2194 (415) |
2424 (52) |
2519 (147) |
2682 (310) |
2881 (509) |
2938 (566) | |
Subsets and supersets
593edo is the 108th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [940 -593⟩ | [⟨593 940]] | -0.0748 | 0.0748 | 3.70 |
| 2.3.5 | [24 -21 4⟩, [37 25 -33⟩ | [⟨593 940 1377]] | -0.0780 | 0.0613 | 3.03 |
| 2.3.5.7 | 4375/4374, 33554432/33480783, 52734375/52706752 | [⟨593 940 1377 1665]] | -0.1015 | 0.0669 | 3.31 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 196\593 | 396.63 | 98304/78125 | Squarschmidt |
| 1 | 215\593 | 435.08 | 9/7 | Supermajor |
| 1 | 235\593 | 475.55 | 320/243 | Vulture |
| 1 | 277\593 | 560.54 | 864/625 | Whoosh |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct