233edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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 | 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. | 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 14: | Line 14: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -369 233 }} | ||
| {{ | | {{Mapping| 233 369 }} | ||
| 0.4813 | | +0.4813 | ||
| 0.4815 | | 0.4815 | ||
| 9.35 | | 9.35 | ||
| Line 25: | Line 34: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, {{monzo| -53 32 1 }} | | 78732/78125, {{monzo| -53 32 1 }} | ||
| {{ | | {{Mapping| 233 369 541 }} | ||
| 0.3277 | | +0.3277 | ||
| 0.4492 | | 0.4492 | ||
| 8.72 | | 8.72 | ||
| Line 32: | Line 41: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 65625/65536, 78732/78125 | | 2401/2400, 65625/65536, 78732/78125 | ||
| {{ | | {{Mapping| 233 369 541 654 }} | ||
| 0.2979 | | +0.2979 | ||
| 0.3924 | | 0.3924 | ||
| 7.62 | | 7.62 | ||
| Line 39: | Line 48: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 243/242, 441/440, 540/539, 2401/2400 | | 243/242, 441/440, 540/539, 2401/2400 | ||
| {{ | | {{Mapping| 233 369 541 654 806 }} | ||
| 0.2525 | | +0.2525 | ||
| 0.3625 | | 0.3625 | ||
| 7.04 | | 7.04 | ||
| Line 46: | Line 55: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 243/242, 351/350, 441/440, 540/539, 1001/1000 | | 243/242, 351/350, 441/440, 540/539, 1001/1000 | ||
| {{ | | {{Mapping| 233 369 541 654 806 862 }} | ||
| 0.2574 | | +0.2574 | ||
| 0.3311 | | 0.3311 | ||
| 6.43 | | 6.43 | ||
| Line 53: | Line 62: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 351/350, 441/440, 540/539, 561/560, 936/935, 1156/1155 | | 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 | | 0.3161 | ||
| 6.14 | | 6.14 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 89: | Line 105: | ||
| 86\233 | | 86\233 | ||
| 442.92 | | 442.92 | ||
| | | 162/125 | ||
| [[ | | [[Sensipent]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 97: | Line 113: | ||
| 250/189 | | 250/189 | ||
| [[Catafourth]] | | [[Catafourth]] | ||
|} | |||
<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 == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Cuckoo Cider Mouth" from ''Cursed Cuckoo Creations'' (2024) | * "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) | * "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]] | [[Category:Listen]] | ||