1583edo: Difference between revisions
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== Theory == | == Theory == | ||
1583edo is consistent to the [[9-odd-limit]]. Using the patent val, it [[tempering out|tempers out]] [[2401/2400]], {{monzo|36 -16 -7 2}} and {{monzo|9 21 -17 -1}} in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It [[support]]s [[empress]] and [[vili]]. | 1583edo is consistent to the [[9-odd-limit]]. Using the patent val, it [[tempering out|tempers out]] [[2401/2400]], {{monzo|36 -16 -7 2}} and {{monzo|9 21 -17 -1}} in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It [[support]]s [[empress]] and [[vili]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1583}} | {{Harmonics in equal|1583}} | ||
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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" |[[Comma list|Comma List]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning Error | ! rowspan="2" | Optimal<br />8ve Stretch (¢) | ||
|- | ! colspan="2" | Tuning Error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Lafa]] | | [[Lafa]] | ||
|} | |} | ||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "BEEFY!" from ''CAPSLOCK'' (2024) | * "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 | ||
Revision as of 01:02, 16 November 2024
| ← 1582edo | 1583edo | 1584edo → |
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 |