1583edo: Difference between revisions

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== 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]].

=== Prime harmonics ===

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== Regular temperament properties ==

{| 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 8ve ~~Stretch~~ (¢)

! rowspan="2" | [[Mapping]]

! colspan="2" |Tuning ~~Error~~

! rowspan="2" | Optimal 8ve stretch (¢)

|-

! colspan="2" | Tuning error

![[TE error|Absolute]] (¢)

|-

![[TE simple badness|Relative]] (%)

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

| {{monzo|2509 -1583}}

| {{mapping|1583 2509}}

| -0.0010

| −0.0010

| 0.0010

| 0.13

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| {{monzo|77 -31 -12}}, {{monzo|-23 57 -29}}

| {{mapping|1583 2509 3676}}

| -0.0429

| −0.0429

| 0.0592

| 7.81

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| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875

| {{mapping|1583 2509 3676 4444}}

| -0.0293

| −0.0293

| 0.0564

| 7.44

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=== Rank-2 temperaments ===

{| 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 per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| [[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) – [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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1583}}
+{{ED intro}}
 == Theory ==
 edo 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 ===
 {{Harmonics in equal|1583}}
@@ Line 12: / Line 13: @@
 == Regular temperament properties ==
 {| 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
 | {{monzo|2509 -1583}}
 | {{mapping|1583 2509}}
-| -0.0010
+| −0.0010
 | 0.0010
 | 0.13
@@ Line 31: / Line 33: @@
 | {{monzo|77 -31 -12}}, {{monzo|-23 57 -29}}
 | {{mapping|1583 2509 3676}}
-| -0.0429
+| −0.0429
 | 0.0592
 | 7.81
@@ Line 38: / Line 40: @@
 | 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
 | {{mapping|1583 2509 3676 4444}}
-| -0.0293
+| −0.0293
 | 0.0564
 | 7.44
@@ Line 45: / Line 47: @@
 === Rank-2 temperaments ===
 {| 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*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 58: / Line 61: @@
 | [[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) – [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) &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