Xenharmonic Wiki

23-limit: Difference between revisions

← Older edit
VisualWikitext
Xenji (talk | contribs)
31 edits
I added an image showing some 23-limit otonal chords. Apologies, I haven't done much editing in recent years. Please feel free to clean this up, if the formatting seems weird, veteran editors. Thank you!
m Sorting and - the pretention that a Wikipedia page exists
 
(8 intermediate revisions by 4 users not shown)
Line 9: Line 9:


== Edo approximation ==
== Edo approximation ==
Here is a list of [[edo]]s with progressively better tunings for 23-limit intervals (decreasing [[TE error]]): {{EDOs| 80, 87, 94, 111, 121i, 130, 140, 152fg, 159, 183, 190g, 193, 217, 243e, 270, 282, 311, 373g, 422, 525, 566g, 581, 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, 1578, 1889, 2000, 2460 }} and so on.  
Here is a list of [[edo]]s with progressively better tunings for 23-limit intervals ([[monotonicity limit]] ≥ 23 and decreasing [[TE error]]): {{EDOs| 58hi, 62, 68e, 72, 94, 111, 121i, 130, 140, 152fg, 159, 183, 190g, 193, 217, 243e, 270, 282, 311, 373g, 422, 525, 566g, 581, 718, 742i, 814, 935, 954h, 1106, 1178, 1308, 1323, 1395, 1506hi, 1578, 1889, 2000, 2460 }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]].  


Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.
Here is a list of edos which provides relatively good tunings for 23-limit intervals ([[TE relative error]] < 5%): {{EDOs| 94, 190g, 193, 217, 243e, 270, 282, 311, 328h, 373g, 388, 422, 436, 460, 525, 540, 566g, 581, 624, 639h, 643i, 653, 692i, 718, 742i, 764(h), 814, 860, 882, 908, 935, 954h, 997, 1012, 1046dgh, 1075, 1106, 1125, 1178, 1205g, 1224, 1236(h), 1258, 1282, 1308, 1323, 1357efhi, 1385, 1395, 1419, 1448(g), 1506hi, 1578, 1600, 1646, 1672h, 1677e, 1696, 1718, 1730(g), 1759, 1768gi, 1817hi, 1821ef, 1889, 1920, 1966, 2000, 2038, 2041, 2072, 2087h, 2103, 2113, 2132eh, 2159, 2217, 2231, 2243e, 2270i, 2311, 2320, 2414, 2460 }} and so on.


: '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "121i" means taking the second closest approximation of harmonics 23.
{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "58hi" means taking the second closest approximations of harmonics 19 and 23. }}


[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.
[[94edo]] is the first [[edo]] to be consistent in the [[23-odd-limit]]. The smallest edo where the [[23-odd-limit]] is distinctly consistent, meaning each element of the tonality diamond is distinguished, is [[282edo]], although [[311edo]] may be preferred for excellent consistency in much larger odd limits, and thus is a good choice if you want the 23-odd-limit to be distinctly consistent and the 27-odd-limit (and higher) to be consistent.


== 23-odd-limit intervals ==
== 23-odd-limit intervals ==
[[File:Some 23-limit otonal chords.png|thumb|15 pentads and 1 hexad, with 23 as the highest odd harmonic, avoiding steps smaller than 23/21.]]
Ratios of 23 in the 23-odd-limit are:
Ratios of 23 in the 23-odd-limit are:


Line 158: Line 160:
| vicesimotertial major seventh
| vicesimotertial major seventh
|}
|}
[[File:Some 23-limit otonal chords.png|thumb|Some 23-limit otonal chords.]]
== 23-Limit Harmony ==
[[File:Some 23-limit otonal chords.png|thumb]]


== Trivia ==
== Trivia ==
Line 172: Line 170:
; [[Francium]]
; [[Francium]]
* "GAY SAPIENS" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/5vILBQgWJduJf2ctGGbyUv Spotify] | [https://francium223.bandcamp.com/track/gay-sapiens Bandcamp] | [https://www.youtube.com/watch?v=DHiwdGuZRII YouTube]
* "GAY SAPIENS" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/5vILBQgWJduJf2ctGGbyUv Spotify] | [https://francium223.bandcamp.com/track/gay-sapiens Bandcamp] | [https://www.youtube.com/watch?v=DHiwdGuZRII YouTube]
; [[Noah Dean Jordan]]
* [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ ''Gracias a Dios''] (2023) for solo jarana (series 23/22, 23/21, …, 23/12)


; {{W|Franz Liszt}}
; {{W|Franz Liszt}}
Line 189: Line 190:
* [https://www.youtube.com/watch?v=m9QaxFOlnYg ''A Hycean World''] (2023)
* [https://www.youtube.com/watch?v=m9QaxFOlnYg ''A Hycean World''] (2023)
* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)
* [https://www.youtube.com/watch?v=jpHylRu6XLM ''ser0tonin circuits in a neural network''] (2023)
 
* [https://www.youtube.com/watch?v=con4DTO8uQs ''Eyes Do More Than See''] (2026)
; {{W|Noah Dean DaSilva Jordan}}
* [https://open.spotify.com/album/2OGG4tT7INfj7iBeN09KDJ Gracias a Dios] (2023) for solo jarana (series 23/22, 23/21....23/12)


[[Category:23-limit| ]] <!-- main article -->
[[Category:23-limit| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/23-limit"