233edo: Difference between revisions

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== Theory ==

233et has a generally flat tendency, in the sense that if the [[octave]] is pure, [[prime harmonic]]s 3 through 17 are all flat. 233edo is accurate for the [[5/1|5th harmonic]] (only 0.0476 ~~cents~~ flat), but less for the [[3/1|third harmonic]] (1.5258 ~~cents~~ flat).

233et has a generally flat tendency, in the sense that if the [[octave]] is pure, [[prime harmonic]]s 3 through 17 are all flat. 233edo is accurate for the [[5/1|5th harmonic]] (only 0.0476{{c}} flat), but less for the [[3/1|third harmonic]] (1.5258{{c}} flat).

The equal temperament [[tempering out|tempers out]] [[78732/78125]] and {{monzo| -53 32 1 }} in the 5-limit; [[2401/2400]], [[65625/65536]], and 177147/175616 in the 7-limit (supporting [[tertiaseptal]] and [[catafourth]]). Using the [[patent val]], it tempers out [[243/242]], [[441/440]], 35937/35840, and 78408/78125 in the 11-limit; [[351/350]], [[1001/1000]], [[1575/1573]], [[4225/4224]], and [[6656/6655]] in the 13-limit.

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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" | [[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]] (%)

|-

| 2.3

| {{~~monzo~~| -369 233 }}

| {{Monzo| -369 233 }}

| {{~~mapping~~| 233 369 }}

| {{Mapping| 233 369 }}

| 0.4813

| +0.4813

| 0.4815

| 9.35

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| 2.3.5

| 78732/78125, {{monzo| -53 32 1 }}

| {{~~mapping~~| 233 369 541 }}

| {{Mapping| 233 369 541 }}

| 0.3277

| +0.3277

| 0.4492

| 8.72

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| 2.3.5.7

| 2401/2400, 65625/65536, 78732/78125

| {{~~mapping~~| 233 369 541 654 }}

| {{Mapping| 233 369 541 654 }}

| 0.2979

| +0.2979

| 0.3924

| 7.62

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| 2.3.5.7.11

| 243/242, 441/440, 540/539, 2401/2400

| {{~~mapping~~| 233 369 541 654 806 }}

| {{Mapping| 233 369 541 654 806 }}

| 0.2525

| +0.2525

| 0.3625

| 7.04

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| 2.3.5.7.11.13

| 243/242, 351/350, 441/440, 540/539, 1001/1000

| {{~~mapping~~| 233 369 541 654 806 862 }}

| {{Mapping| 233 369 541 654 806 862 }}

| 0.2574

| +0.2574

| 0.3311

| 6.43

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| 2.3.5.7.11.13.17

| 351/350, 441/440, 540/539, 561/560, 936/935, 1156/1155

| {{~~mapping~~| 233 369 541 654 806 862 952 }}

| {{Mapping| 233 369 541 654 806 862 952 }}

| 0.2888

| +0.2888

| 0.3161

| 6.14

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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

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| 86\233

| 442.92

| 9/7

| 162/125

| [[~~Sensi~~]]

| [[Sensipent]]

|-

| 1

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| [[Catafourth]]

|}

<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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

== Music ==

; [[Francium]]

* "Cuckoo Cider Mouth" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/7BizYOfoxjMncUJaGEfL0u Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cider-mouth Bandcamp] | [https://www.youtube.com/watch?v=t1hczh8fRQ4 YouTube]

* "goodblucky" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6uq6TWCajp0WueDjfr77ox Spotify] | [https://francium223.bandcamp.com/track/goodblucky Bandcamp] | [https://www.youtube.com/watch?v=4YATiqIwlqE YouTube]

* "Desks For Ladies" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/0tLYtnNlBluBNapUOS322P Spotify] | [https://francium223.bandcamp.com/track/desks-for-ladies Bandcamp] | [https://www.youtube.com/watch?v=MLd7ij1C3kc YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|233}}
+{{ED intro}}
 == Theory ==
-et has a generally flat tendency, in the sense that if the [[octave]] is pure, [[prime harmonic]]s 3 through 17 are all flat. 233edo is accurate for the [[5/1|5th harmonic]] (only 0.0476 cents flat), but less for the [[3/1|third harmonic]] (1.5258 cents flat).
+et has a generally flat tendency, in the sense that if the [[octave]] is pure, [[prime harmonic]]s 3 through 17 are all flat. 233edo is accurate for the [[5/1|5th harmonic]] (only 0.0476{{c}} flat), but less for the [[3/1|third harmonic]] (1.5258{{c}} flat).
 The equal temperament [[tempering out|tempers out]] [[78732/78125]] and {{monzo| -53 32 1 }} in the 5-limit; [[2401/2400]], [[65625/65536]], and 177147/175616 in the 7-limit (supporting [[tertiaseptal]] and [[catafourth]]). Using the [[patent val]], it tempers out [[243/242]], [[441/440]], 35937/35840, and 78408/78125 in the 11-limit; [[351/350]], [[1001/1000]], [[1575/1573]], [[4225/4224]], and [[6656/6655]] in the 13-limit.
@@ Line 15: / Line 15: @@
 == 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]] (%)
 |-
 | 2.3
-| {{monzo| -369 233 }}
+| {{Monzo| -369 233 }}
-| {{mapping| 233 369 }}
+| {{Mapping| 233 369 }}
-| 0.4813
+| +0.4813
 | 0.4815
 | 9.35
@@ Line 33: / Line 34: @@
 | 2.3.5
 | 78732/78125, {{monzo| -53 32 1 }}
-| {{mapping| 233 369 541 }}
+| {{Mapping| 233 369 541 }}
-| 0.3277
+| +0.3277
 | 0.4492
 | 8.72
@@ Line 40: / Line 41: @@
 | 2.3.5.7
 | 2401/2400, 65625/65536, 78732/78125
-| {{mapping| 233 369 541 654 }}
+| {{Mapping| 233 369 541 654 }}
-| 0.2979
+| +0.2979
 | 0.3924
 | 7.62
@@ Line 47: / Line 48: @@
 | 2.3.5.7.11
 | 243/242, 441/440, 540/539, 2401/2400
-| {{mapping| 233 369 541 654 806 }}
+| {{Mapping| 233 369 541 654 806 }}
-| 0.2525
+| +0.2525
 | 0.3625
 | 7.04
@@ Line 54: / Line 55: @@
 | 2.3.5.7.11.13
 | 243/242, 351/350, 441/440, 540/539, 1001/1000
-| {{mapping| 233 369 541 654 806 862 }}
+| {{Mapping| 233 369 541 654 806 862 }}
-| 0.2574
+| +0.2574
 | 0.3311
 | 6.43
@@ Line 61: / Line 62: @@
 | 2.3.5.7.11.13.17
 | 351/350, 441/440, 540/539, 561/560, 936/935, 1156/1155
-| {{mapping| 233 369 541 654 806 862 952 }}
+| {{Mapping| 233 369 541 654 806 862 952 }}
-| 0.2888
+| +0.2888
 | 0.3161
 | 6.14
@@ Line 69: / Line 70: @@
 === 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
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br>ratio*
 ! Temperaments
 |-
@@ Line 103: / Line 105: @@
 | 86\233
 | 442.92
-| 9/7
+| 162/125
-| [[Sensi]]
+| [[Sensipent]]
 |-
 | 1
@@ Line 112: / Line 114: @@
 | [[Catafourth]]
 |}
-<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 forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
+== Music ==
+; [[Francium]]
+* "Cuckoo Cider Mouth" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/7BizYOfoxjMncUJaGEfL0u Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cider-mouth Bandcamp] | [https://www.youtube.com/watch?v=t1hczh8fRQ4 YouTube]
+* "goodblucky" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6uq6TWCajp0WueDjfr77ox Spotify] | [https://francium223.bandcamp.com/track/goodblucky Bandcamp] | [https://www.youtube.com/watch?v=4YATiqIwlqE YouTube]
+* "Desks For Ladies" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/0tLYtnNlBluBNapUOS322P Spotify] | [https://francium223.bandcamp.com/track/desks-for-ladies Bandcamp] | [https://www.youtube.com/watch?v=MLd7ij1C3kc YouTube]
+[[Category:Listen]]