1583edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|1583}} == Theory == 1583edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 2401/2400, {{monzo|36..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1583}}
{{ED intro}}


== 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]]
! 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
| {{monzo|2509 -1583}}
| {{monzo|2509 -1583}}
| {{mapping|1583 2509}}
| {{mapping|1583 2509}}
| -0.0010
| −0.0010
| 0.0010
| 0.0010
| 0.13
| 0.13
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| {{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
| −0.0429
| 0.0592
| 0.0592
| 7.81
| 7.81
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| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
| {{mapping|1583 2509 3676 4444}}
| {{mapping|1583 2509 3676 4444}}
| -0.0293
| −0.0293
| 0.0564
| 0.0564
| 7.44
| 7.44
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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>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Lafa]]
| [[Lafa]]
|}
|}
<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 />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Music ==
; [[Francium]]
* "BEEFY!" from ''CAPSLOCK'' (2024) &ndash; [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] | [https://francium223.bandcamp.com/track/beefy Bandcamp] | [https://www.youtube.com/watch?v=lked66nkh_A YouTube] &ndash; vili in 1583edo tuning

Latest revision as of 05:56, 21 February 2025

← 1582edo 1583edo 1584edo →
Prime factorization 1583 (prime)
Step size 0.758054 ¢ 
Fifth 926\1583 (701.958 ¢)
Semitones (A1:m2) 150:119 (113.7 ¢ : 90.21 ¢)
Consistency limit 9
Distinct consistency limit 9

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

Approximation of prime harmonics in 1583edo
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

Table of rank-2 temperaments by generator
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

Music

Francium
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