457edo: Difference between revisions

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== Theory ==

457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. ~~The~~ equal temperament [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.

457edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. As an equal temperament, it [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the [[7-limit]]; [[540/539]], [[8019/8000]], and 43923/43904 in the [[11-limit]].

=== Odd harmonics ===

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=== Subsets and supersets ===

457edo is the 88th [[prime edo]].

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

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

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

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

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

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

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

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

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| {{monzo| -724 457 }}

| {{mapping| 457 724 }}

| 0.2716

| +0.2716

| 0.2716

| 10.34

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| {{monzo| -36 11 8 }}, {{monzo| -5 31 -19 }}

| {{mapping| 457 724 1061 }}

| 0.2267

| +0.2267

| 0.2307

| 8.79

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| 19683/19600, 65625/65536, 7381125/7340032

| {{mapping| 457 724 1061 1283 }}

| 0.1609

| +0.1609

| 0.2300

| 8.76

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| 540/539, 8019/8000, 19683/19600, 43923/43904

| {{mapping| 457 724 1061 1283 1581 }}

| 0.1227

| +0.1227

| 0.2194

| 8.36

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| 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923

| {{mapping| 457 724 1061 1283 1581 1691 }}

| 0.1142

| +0.1142

| 0.2012

| 7.66

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| 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224

| {{mapping| 457 724 1061 1283 1581 1691 1868 }}

| 0.0952

| +0.0952

| 0.1920

| 7.31

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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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| [[Tritriple]]

|}

<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 ==

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* "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] | [https://francium223.bandcamp.com/track/less-and-less Bandcamp] | [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]

* "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] | [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] | [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|457}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The equal temperament [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the 7-limit; [[540/539]], [[8019/8000]], and 43923/43904 in the 11-limit.
+edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. As an equal temperament, it [[tempering out|tempers out]] [[19683/19600]] and [[65625/65536]] in the [[7-limit]]; [[540/539]], [[8019/8000]], and 43923/43904 in the [[11-limit]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
 edo is the 88th [[prime edo]].
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 25: / Line 26: @@
 | {{monzo| -724 457 }}
 | {{mapping| 457 724 }}
-| 0.2716
+| +0.2716
 | 0.2716
 | 10.34
@@ Line 32: / Line 33: @@
 | {{monzo| -36 11 8 }}, {{monzo| -5 31 -19 }}
 | {{mapping| 457 724 1061 }}
-| 0.2267
+| +0.2267
 | 0.2307
 | 8.79
@@ Line 39: / Line 40: @@
 | 19683/19600, 65625/65536, 7381125/7340032
 | {{mapping| 457 724 1061 1283 }}
-| 0.1609
+| +0.1609
 | 0.2300
 | 8.76
@@ Line 46: / Line 47: @@
 | 540/539, 8019/8000, 19683/19600, 43923/43904
 | {{mapping| 457 724 1061 1283 1581 }}
-| 0.1227
+| +0.1227
 | 0.2194
 | 8.36
@@ Line 53: / Line 54: @@
 | 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923
 | {{mapping| 457 724 1061 1283 1581 1691 }}
-| 0.1142
+| +0.1142
 | 0.2012
 | 7.66
@@ Line 60: / Line 61: @@
 | 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224
 | {{mapping| 457 724 1061 1283 1581 1691 1868 }}
-| 0.0952
+| +0.0952
 | 0.1920
 | 7.31
@@ Line 67: / Line 68: @@
 === 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 92: / Line 94: @@
 | [[Tritriple]]
 |}
-<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 ==
@@ Line 98: / Line 100: @@
 * "Less and Less" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/5w3K1Q6VhCkUPMXmuh5pVt Spotify] | [https://francium223.bandcamp.com/track/less-and-less Bandcamp] | [https://www.youtube.com/watch?v=y4MGhHE20b4 YouTube]
 * "Porcelain Stoneware" from ''Scoop'' (2024) – [https://open.spotify.com/track/055lRdMBKr37MU8HQqlvus Spotify] | [https://francium223.bandcamp.com/track/porcelain-stoneware Bandcamp] | [https://www.youtube.com/watch?v=bzycN6PYMQQ YouTube]
+[[Category:Listen]]