2053edo: Difference between revisions

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== Theory ==

2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. ~~The equal temperament~~ is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].

2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. It is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969, and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].

=== 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|3254 -2053}}

| {{mapping|2053 3254}}

| -0.0133

| −0.0133

| 0.0133

| 2.28

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| {{monzo|37 25 -33}}, {{monzo|93 -66 5}}

| {{mapping|2053 3254 4767}}

| -0.0157

| −0.0157

| 0.0114

| 1.95

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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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| [[Whoosh]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2053}}
+{{EDO intro}}
 == Theory ==
-edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. The equal temperament is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].
+edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. It is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969, and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].
 === Prime harmonics ===
@@ Line 13: / 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|3254 -2053}}
 | {{mapping|2053 3254}}
-| -0.0133
+| −0.0133
 | 0.0133
 | 2.28
@@ Line 32: / Line 33: @@
 | {{monzo|37 25 -33}}, {{monzo|93 -66 5}}
 | {{mapping|2053 3254 4767}}
-| -0.0157
+| −0.0157
 | 0.0114
 | 1.95
@@ Line 39: / Line 40: @@
 === 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 52: / Line 54: @@
 | [[Whoosh]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct