233edo: Difference between revisions

Line 3:

== 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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| {{monzo| -369 233 }}

| {{mapping| 233 369 }}

| 0.4813

| +0.4813

| 0.4815

| 9.35

Line 35:

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

| {{mapping| 233 369 541 }}

| 0.3277

| +0.3277

| 0.4492

| 8.72

Line 42:

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

| {{mapping| 233 369 541 654 }}

| 0.2979

| +0.2979

| 0.3924

| 7.62

Line 49:

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

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

| 0.2525

| +0.2525

| 0.3625

| 7.04

Line 56:

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

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

| 0.2574

| +0.2574

| 0.3311

| 6.43

Line 63:

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

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

| 0.2888

| +0.2888

| 0.3161

| 6.14

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| [[Catafourth]]

|}

<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]]

* "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]

* "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 Bandcamp]

* "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 Bandcamp]

[[Category:Listen]]

@@ Line 3: / Line 3: @@
 == 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 28: / Line 28: @@
 | {{monzo| -369 233 }}
 | {{mapping| 233 369 }}
-| 0.4813
+| +0.4813
 | 0.4815
 | 9.35
@@ Line 35: / Line 35: @@
 | 78732/78125, {{monzo| -53 32 1 }}
 | {{mapping| 233 369 541 }}
-| 0.3277
+| +0.3277
 | 0.4492
 | 8.72
@@ Line 42: / Line 42: @@
 | 2401/2400, 65625/65536, 78732/78125
 | {{mapping| 233 369 541 654 }}
-| 0.2979
+| +0.2979
 | 0.3924
 | 7.62
@@ Line 49: / Line 49: @@
 | 243/242, 441/440, 540/539, 2401/2400
 | {{mapping| 233 369 541 654 806 }}
-| 0.2525
+| +0.2525
 | 0.3625
 | 7.04
@@ Line 56: / Line 56: @@
 | 243/242, 351/350, 441/440, 540/539, 1001/1000
 | {{mapping| 233 369 541 654 806 862 }}
-| 0.2574
+| +0.2574
 | 0.3311
 | 6.43
@@ Line 63: / Line 63: @@
 | 351/350, 441/440, 540/539, 561/560, 936/935, 1156/1155
 | {{mapping| 233 369 541 654 806 862 952 }}
-| 0.2888
+| +0.2888
 | 0.3161
 | 6.14
@@ Line 114: / Line 114: @@
 | [[Catafourth]]
 |}
-<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]]
-* "Cuckoo Cider Mouth" from ''Cursed Cuckoo Creations'' (2024) &ndash; [https://open.spotify.com/track/7BizYOfoxjMncUJaGEfL0u Spotify] | [https://francium223.bandcamp.com/track/cuckoo-cider-mouth Bandcamp] | [https://www.youtube.com/watch?v=t1hczh8fRQ4 YouTube]
+* "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) &ndash; [https://open.spotify.com/track/6uq6TWCajp0WueDjfr77ox Spotify] | [https://francium223.bandcamp.com/track/goodblucky Bandcamp] | [https://www.youtube.com/watch?v=4YATiqIwlqE Bandcamp]
+* "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 Bandcamp]
 [[Category:Listen]]