183edo: Difference between revisions
→Regular temperament properties: 13- to 23-limit notability |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 36: | Line 28: | ||
| 32805/32768, {{val| 10 23 -20 }} | | 32805/32768, {{val| 10 23 -20 }} | ||
| {{mapping| 183 290 425 }} | | {{mapping| 183 290 425 }} | ||
| | | −0.0157 | ||
| 0.182 | | 0.182 | ||
| 2.78 | | 2.78 | ||
| Line 43: | Line 35: | ||
| 6144/6125, 16875/16807, 19683/19600 | | 6144/6125, 16875/16807, 19683/19600 | ||
| {{mapping| 183 290 425 514 }} | | {{mapping| 183 290 425 514 }} | ||
| | | −0.1601 | ||
| 0.296 | | 0.296 | ||
| 4.51 | | 4.51 | ||
| Line 50: | Line 42: | ||
| 540/539, 1375/1372, 5632/5625, 8019/8000 | | 540/539, 1375/1372, 5632/5625, 8019/8000 | ||
| {{mapping| 183 290 425 514 633 }} | | {{mapping| 183 290 425 514 633 }} | ||
| | | −0.0993 | ||
| 0.291 | | 0.291 | ||
| 4.44 | | 4.44 | ||
| Line 57: | Line 49: | ||
| 351/350, 540/539, 676/675, 1375/1372, 4096/4095 | | 351/350, 540/539, 676/675, 1375/1372, 4096/4095 | ||
| {{mapping| 183 290 425 514 633 677 }} | | {{mapping| 183 290 425 514 633 677 }} | ||
| | | −0.0295 | ||
| 0.308 | | 0.308 | ||
| 4.70 | | 4.70 | ||
| Line 64: | Line 56: | ||
| 351/350, 442/441, 540/539, 561/560, 1375/1372, 4096/4095 | | 351/350, 442/441, 540/539, 561/560, 1375/1372, 4096/4095 | ||
| {{mapping| 183 290 425 514 633 677 748 }} | | {{mapping| 183 290 425 514 633 677 748 }} | ||
| | | −0.0240 | ||
| 0.286 | | 0.286 | ||
| 4.36 | | 4.36 | ||
{{comma basis end}} | |||
* 183et has lower absolute errors in the 13-, 17-, 19-, and 23-limit than any previous equal temperaments, after [[130edo|130]], [[171edo|171]], [[161edo|161]], and [[159edo|159]], respectively. In the 13-, 19-, and 23-limit it is superseded by [[190edo|190g]]. In the 17-limit, where it is the strongest, by [[217edo|217]]. | * 183et has lower absolute errors in the 13-, 17-, 19-, and 23-limit than any previous equal temperaments, after [[130edo|130]], [[171edo|171]], [[161edo|161]], and [[159edo|159]], respectively. In the 13-, 19-, and 23-limit it is superseded by [[190edo|190g]]. In the 17-limit, where it is the strongest, by [[217edo|217]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 140: | Line 126: | ||
|- | |- | ||
| 3 | | 3 | ||
| 38\183<br>(23\183) | | 38\183<br />(23\183) | ||
| 249.18<br>(150.82) | | 249.18<br />(150.82) | ||
| 15/13<br>(12/11) | | 15/13<br />(12/11) | ||
| [[Hemiterm]] | | [[Hemiterm]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 76\183<br>(15\183) | | 76\183<br />(15\183) | ||
| 498.36<br>(98.36) | | 498.36<br />(98.36) | ||
| 4/3<br>(200/189) | | 4/3<br />(200/189) | ||
| [[Term]] / terminator | | [[Term]] / terminator | ||
|- | |- | ||
| 61 | | 61 | ||
| 38\183<br>(2\183) | | 38\183<br />(2\183) | ||
| 249.18<br>(13.11) | | 249.18<br />(13.11) | ||
| 13750/11907<br>(?) | | 13750/11907<br />(?) | ||
| [[Promethium]] | | [[Promethium]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[birdshite stalactite]] | ; [[birdshite stalactite]] | ||
* from ''meticulous clutter'' (2022) | * from ''meticulous clutter'' (2022) | ||
** "cursed owl windchimes" | ** "cursed owl windchimes" – [https://open.spotify.com/track/0A9z6gw5HuNWS7eYjvtCa1 Spotify] | [https://birdshitestalactite.bandcamp.com/track/cursed-owl-windchimes Bandcamp] | [https://www.youtube.com/watch?v=vyTbwHhdoXE YouTube] – madagascar[19] in 183edo tuning | ||
** "octopus bones" | ** "octopus bones" – [https://open.spotify.com/track/6TUm7uXjVaO6MGACWswoL7 Spotify] | [https://birdshitestalactite.bandcamp.com/track/octopus-bones Bandcamp] | [https://www.youtube.com/watch?v=ej80dEpC-DQ YouTube] – madagascar[19] in 183edo tuning and parakleismic[19] in 61edo tuning | ||
* "lemon drizzle" from ''tropical nosebleed'' (2023) | * "lemon drizzle" from ''tropical nosebleed'' (2023) – [https://open.spotify.com/track/3dBXs1KjzTjSWJ7KF4BjlK Spotify] | [https://birdshitestalactite.bandcamp.com/track/lemon-drizzle Bandcamp] | [https://www.youtube.com/watch?v=VJ_bAvWB8W0 YouTube] | ||
[[Category:Borneo]] | [[Category:Borneo]] | ||
Revision as of 05:39, 16 November 2024
| ← 182edo | 183edo | 184edo → |
The 183 equal divisions of the octave (183edo), or the 183(-tone) equal temperament (183tet, 183et) when viewed from a regular temperament perspective, divides the octave into 183 equal parts of about 6.56 cents each, a size close to 243/242, the rastma.
Theory
183edo is notable as a higher-limit system, distinctly consistent in the 17-odd-limit, or the no-19 no-31 33-odd-limit. The equal temperament tempers out the schisma in the 5-limit. In the 7-limit, it tempers out porwell, 6144/6125, cataharry, 19683/19600 and mirkwai, 16875/16807. In the 11-limit, it tempers out 540/539, 1375/1372, 3025/3024, 5632/5625, and 8019/8000; in the 13-limit, 351/350, 676/675, 729/728, 1001/1000, 1573/1568, 2080/2079, 4096/4095, 4225/4224, and 6656/6655; in the 17-limit 442/441, 561/560, 715/714, 936/935, 1089/1088, and 1156/1155; and in the 19-limit 456/455. It is the optimal patent val for 13- and 17-limit mirkat, the 72 & 111 temperament, and an excellent tuning for the rank-3 temperaments madagascar and borneo. It allows essentially tempered chord including ratwolfsmic chords, swetismic chords, squbemic chords, sinbadmic chords, and lambeth chords in the 13-odd-limit, in addition to island chords in the 15-odd-limit.
It is even stronger if 7 is left out of the picture. As a no-7 temperament, it tempers out 5632/5625, 8019/8000, 676/675, 4225/4224, 6656/6655, 936/935, 1089/1088, and 1377/1375.
Prime harmonics
In the range of edos from 100 to 200, 183edo is notable as having especially low error in all prime limits from 11 to 29, compared using a variety of prime error punishments, although it has a bad 19 and fails to be consistent in the 19-odd-limit. It is however a strong no-19's 29-limit system with an essentially perfectly accurate prime 43. It can also be considered to model the 2.17.29.43 subgroup with extreme accuracy.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.32 | +0.57 | +1.67 | -0.50 | -1.18 | -0.04 | -2.43 | +1.23 | -0.07 | +2.51 |
| Relative (%) | +0.0 | -4.8 | +8.7 | +25.4 | -7.6 | -18.0 | -0.6 | -37.1 | +18.8 | -1.1 | +38.2 | |
| Steps (reduced) |
183 (0) |
290 (107) |
425 (59) |
514 (148) |
633 (84) |
677 (128) |
748 (16) |
777 (45) |
828 (96) |
889 (157) |
907 (175) | |
Subsets and supersets
Since 183 factors into 3 × 61, 183edo contains 3edo and 61edo as its subsets.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-290 183⟩ | [⟨183 290]] | +0.0996 | 0.100 | 1.52 |- | 2.3.5 | 32805/32768, ⟨10 23 -20] | [⟨183 290 425]] | −0.0157 | 0.182 | 2.78 |- | 2.3.5.7 | 6144/6125, 16875/16807, 19683/19600 | [⟨183 290 425 514]] | −0.1601 | 0.296 | 4.51 |- | 2.3.5.7.11 | 540/539, 1375/1372, 5632/5625, 8019/8000 | [⟨183 290 425 514 633]] | −0.0993 | 0.291 | 4.44 |- | 2.3.5.7.11.13 | 351/350, 540/539, 676/675, 1375/1372, 4096/4095 | [⟨183 290 425 514 633 677]] | −0.0295 | 0.308 | 4.70 |- | 2.3.5.7.11.13.17 | 351/350, 442/441, 540/539, 561/560, 1375/1372, 4096/4095 | [⟨183 290 425 514 633 677 748]] | −0.0240 | 0.286 | 4.36 Template:Comma basis end
- 183et has lower absolute errors in the 13-, 17-, 19-, and 23-limit than any previous equal temperaments, after 130, 171, 161, and 159, respectively. In the 13-, 19-, and 23-limit it is superseded by 190g. In the 17-limit, where it is the strongest, by 217.
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 10\183
| 65.57
| 27/26
| Luminal
|-
| 1
| 17\183
| 111.48
| 16/15
| Stockhausenic
|-
| 1
| 38\183
| 249.18
| 15/13
| Hemischis
|-
| 1
| 58\183
| 380.33
| 56/45
| Quanharuk
|-
| 1
| 59\183
| 386.89
| 5/4
| Grendel
|-
| 1
| 76\183
| 498.36
| 4/3
| Helmholtz
|-
| 1
| 77\183
| 504.92
| 104976/78125
| Countermeantone
|-
| 3
| 21\183
| 137.70
| 13/12
| Avicenna
|-
| 3
| 24\183
| 157.38
| 35/32
| Nessafof
|-
| 3
| 28\183
| 183.61
| 10/9
| Mirkat
|-
| 3
| 38\183
(23\183)
| 249.18
(150.82)
| 15/13
(12/11)
| Hemiterm
|-
| 3
| 76\183
(15\183)
| 498.36
(98.36)
| 4/3
(200/189)
| Term / terminator
|-
| 61
| 38\183
(2\183)
| 249.18
(13.11)
| 13750/11907
(?)
| Promethium
Template:Rank-2 end
Template:Orf