431edo: Difference between revisions

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== Theory ==

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=== Subsets and supersets ===

431edo is the 83rd [[prime edo]].

== Intervals ==

== 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]] (¢)

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| 32805/32768, {{monzo| 7 63 -46 }}

| {{mapping| 431 683 1001 }}

| -0.0230

| −0.0230

| 0.2082

| 7.48

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| 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }}

| {{mapping| 431 683 1001 1210 }}

| -0.0299

| −0.0299

| 0.1803

| 6.48

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| 2401/2400, 5632/5625, 8019/8000, 43923/43904

| {{mapping| 431 683 1001 1210 1491 }}

| -0.0215

| −0.0215

| 0.1621

| 5.82

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| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655

| {{mapping| 431 683 1001 1210 1491 1595 }}

| -0.0318

| −0.0318

| 0.1498

| 5.38

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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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| 498.55

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

|-

| 1

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| [[Ostara]]

|}

<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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* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] | [https://francium223.bandcamp.com/track/take-advantage Bandcamp] | [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]

* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] | [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] | [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]

* "I Will Get You." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1FkxDVzNv6SuSfB5vc8T5y Spotify] | [https://francium223.bandcamp.com/track/i-will-get-you Bandcamp] | [https://www.youtube.com/watch?v=_jioqFrcwz8 YouTube] – in Nordenmarkic, 431edo tuning

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|431}}
+{{ED intro}}
 == Theory ==
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
 edo is the 83rd [[prime edo]].
+== Intervals ==
+{{Main|Table of 431edo intervals}}
 == 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]] (¢)
@@ Line 34: / Line 38: @@
 | 32805/32768, {{monzo| 7 63 -46 }}
 | {{mapping| 431 683 1001 }}
-| -0.0230
+| −0.0230
 | 0.2082
 | 7.48
@@ Line 41: / Line 45: @@
 | 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }}
 | {{mapping| 431 683 1001 1210 }}
-| -0.0299
+| −0.0299
 | 0.1803
 | 6.48
@@ Line 48: / Line 52: @@
 | 2401/2400, 5632/5625, 8019/8000, 43923/43904
 | {{mapping| 431 683 1001 1210 1491 }}
-| -0.0215
+| −0.0215
 | 0.1621
 | 5.82
@@ Line 55: / Line 59: @@
 | 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655
 | {{mapping| 431 683 1001 1210 1491 1595 }}
-| -0.0318
+| −0.0318
 | 0.1498
 | 5.38
@@ Line 62: / Line 66: @@
 === 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 85: / Line 90: @@
 | 498.55
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
 |-
 | 1
@@ Line 93: / Line 98: @@
 | [[Ostara]]
 |}
-<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 99: / Line 104: @@
 * "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] | [https://francium223.bandcamp.com/track/take-advantage Bandcamp] | [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
 * "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] | [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] | [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]
+* "I Will Get You." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1FkxDVzNv6SuSfB5vc8T5y Spotify] | [https://francium223.bandcamp.com/track/i-will-get-you Bandcamp] | [https://www.youtube.com/watch?v=_jioqFrcwz8 YouTube] – in Nordenmarkic, 431edo tuning
+[[Category:Listen]]