1583edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" Tags: Mobile edit Mobile web edit |
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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|2509 -1583}} | | {{monzo|2509 -1583}} | ||
| {{mapping|1583 2509}} | | {{mapping|1583 2509}} | ||
| | | −0.0010 | ||
| 0.0010 | | 0.0010 | ||
| 0.13 | | 0.13 | ||
| Line 24: | Line 33: | ||
| {{monzo|77 -31 -12}}, {{monzo|-23 57 -29}} | | {{monzo|77 -31 -12}}, {{monzo|-23 57 -29}} | ||
| {{mapping|1583 2509 3676}} | | {{mapping|1583 2509 3676}} | ||
| | | −0.0429 | ||
| 0.0592 | | 0.0592 | ||
| 7.81 | | 7.81 | ||
| Line 31: | Line 40: | ||
| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875 | | 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875 | ||
| {{mapping|1583 2509 3676 4444}} | | {{mapping|1583 2509 3676 4444}} | ||
| | | −0.0293 | ||
| 0.0564 | | 0.0564 | ||
| 7.44 | | 7.44 | ||
|} | |||
=== 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 44: | Line 60: | ||
| {{monzo|-32 13 5}} | | {{monzo|-32 13 5}} | ||
| [[Lafa]] | | [[Lafa]] | ||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] | [https://francium223.bandcamp.com/track/beefy Bandcamp] | [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning | * "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] | [https://francium223.bandcamp.com/track/beefy Bandcamp] | [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning | ||
Latest revision as of 13:33, 13 March 2026
| ← 1582edo | 1583edo | 1584edo → |
1583 equal divisions of the octave (abbreviated 1583edo or 1583ed2), also called 1583-tone equal temperament (1583tet) or 1583 equal temperament (1583et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1583 equal parts of about 0.758 ¢ each. Each step represents a frequency ratio of 21/1583, or the 1583rd root of 2.
Theory
1583edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 2401/2400, [36 -16 -7 2⟩ and [9 21 -17 -1⟩ in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It supports empress and vili.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.003 | +0.294 | -0.032 | -0.212 | +0.155 | -0.344 | -0.356 | +0.153 | -0.139 | -0.374 |
| Relative (%) | +0.0 | +0.4 | +38.8 | -4.3 | -28.0 | +20.4 | -45.4 | -46.9 | +20.1 | -18.4 | -49.3 | |
| Steps (reduced) |
1583 (0) |
2509 (926) |
3676 (510) |
4444 (1278) |
5476 (727) |
5858 (1109) |
6470 (138) |
6724 (392) |
7161 (829) |
7690 (1358) |
7842 (1510) | |
Subsets and supersets
1583edo is the 250th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [2509 -1583⟩ | [⟨1583 2509]] | −0.0010 | 0.0010 | 0.13 |
| 2.3.5 | [77 -31 -12⟩, [-23 57 -29⟩ | [⟨1583 2509 3676]] | −0.0429 | 0.0592 | 7.81 |
| 2.3.5.7 | 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875 | [⟨1583 2509 3676 4444]] | −0.0293 | 0.0564 | 7.44 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 341\1583 | 258.497 | [-32 13 5⟩ | Lafa |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct