593edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 12: | Line 12: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[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 | ||
| 3.70 | | 3.70 | ||
| Line 24: | Line 33: | ||
| {{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 | ||
| 0.0613 | | 0.0613 | ||
| 3.03 | | 3.03 | ||
| Line 31: | Line 40: | ||
| 4375/4374, 33554432/33480783, 52734375/52706752 | | 4375/4374, 33554432/33480783, 52734375/52706752 | ||
| {{mapping| 593 940 1377 1665 }} | | {{mapping| 593 940 1377 1665 }} | ||
| | | −0.1015 | ||
| 0.0669 | | 0.0669 | ||
| 3.31 | | 3.31 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 68: | Line 84: | ||
| 864/625 | | 864/625 | ||
| [[Whoosh]] | | [[Whoosh]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
Latest revision as of 06:01, 21 February 2025
| ← 592edo | 593edo | 594edo → |
593 equal divisions of the octave (abbreviated 593edo or 593ed2), also called 593-tone equal temperament (593tet) or 593 equal temperament (593et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 593 equal parts of about 2.02 ¢ each. Each step represents a frequency ratio of 21/593, or the 593rd root of 2.
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 | 246\593 | 497.81 | 4/3 | Gary |
| 1 | 277\593 | 560.54 | 864/625 | Whoosh |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct