239edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve <br>Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 379 -239 }}
| {{monzo| 379 -239 }}
| {{mapping| 239 379 }}
| {{mapping| 239 379 }}
| -0.307
| &minus;0.307
| 0.307
| 0.307
| 6.12
| 6.12
Line 32: Line 24:
| {{monzo| 3 -18 11}}, {{monzo| 32 -7 -9 }}
| {{monzo| 3 -18 11}}, {{monzo| 32 -7 -9 }}
| {{mapping| 239 379 555 }}
| {{mapping| 239 379 555 }}
| -0.247
| &minus;0.247
| 0.265
| 0.265
| 5.27
| 5.27
Line 39: Line 31:
| 2401/2400, 5120/5103, 29360128/29296875
| 2401/2400, 5120/5103, 29360128/29296875
| {{mapping| 239 379 555 671 }}
| {{mapping| 239 379 555 671 }}
| -0.204
| &minus;0.204
| 0.241
| 0.241
| 4.80
| 4.80
Line 46: Line 38:
| 2401/2400, 3025/3024, 4000/3993, 5120/5103
| 2401/2400, 3025/3024, 4000/3993, 5120/5103
| {{mapping| 239 379 555 671 827 }}
| {{mapping| 239 379 555 671 827 }}
| -0.220
| &minus;0.220
| 0.218
| 0.218
| 4.34
| 4.34
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 119: Line 105:
| 7/5
| 7/5
| [[Neptune]] (7-limit)
| [[Neptune]] (7-limit)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "thatyounglighthouseboi" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/2dGpklZpWAYSRDHtjc3nDs Spotify] | [https://francium223.bandcamp.com/track/thatyounglighthouseboi Bandcamp] | [https://www.youtube.com/watch?v=nAdJncpsOlk YouTube]
* "thatyounglighthouseboi" from ''albumwithoutspaces'' (2024) &ndash; [https://open.spotify.com/track/2dGpklZpWAYSRDHtjc3nDs Spotify] | [https://francium223.bandcamp.com/track/thatyounglighthouseboi Bandcamp] | [https://www.youtube.com/watch?v=nAdJncpsOlk YouTube]
* "Bath And A Nice Dream" from ''You Are A...'' (2024) – [https://open.spotify.com/track/3RJ77kQEsnkjfgjjUFk9DH Spotify] | [https://francium223.bandcamp.com/track/bath-and-a-nice-dream Bandcamp] | [https://www.youtube.com/watch?v=3eBYJM6cRPA YouTube]
* "Bath And A Nice Dream" from ''You Are A...'' (2024) &ndash; [https://open.spotify.com/track/3RJ77kQEsnkjfgjjUFk9DH Spotify] | [https://francium223.bandcamp.com/track/bath-and-a-nice-dream Bandcamp] | [https://www.youtube.com/watch?v=3eBYJM6cRPA YouTube]


[[Category:Alphaquarter]]
[[Category:Hemififths]]
[[Category:Hemififths]]
[[Category:Listen]]
[[Category:Quasiorwell]]
[[Category:Quasiorwell]]
[[Category:Alphaquarter]]

Revision as of 03:57, 16 November 2024

← 238edo 239edo 240edo →
Prime factorization 239 (prime)
Step size 5.02092 ¢ 
Fifth 140\239 (702.929 ¢)
Semitones (A1:m2) 24:17 (120.5 ¢ : 85.36 ¢)
Consistency limit 11
Distinct consistency limit 11

Template:EDO intro

Theory

239edo has a sharp tendency, with prime harmonics 3 through 11 all tuned sharp. The equal temperament tempers out 2401/2400, 5120/5103, and 29360128/29296875 in the 7-limit, supporting the hemififths temperament and providing an excellent tuning. It also supports and provides a good tuning for quasiorwell and alphaquarter. In the 11-limit, it tempers out 3025/3024, 4000/3993, 5632/5625, and 12005/11979.

Prime harmonics

Approximation of prime harmonics in 239edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.97 +0.30 +0.21 +0.98 -2.03 +0.48 -1.28 -0.66 -0.29 -0.27
Relative (%) +0.0 +19.4 +5.9 +4.2 +19.6 -40.5 +9.6 -25.5 -13.1 -5.7 -5.3
Steps
(reduced) 		239
(0) 		379
(140) 		555
(77) 		671
(193) 		827
(110) 		884
(167) 		977
(21) 		1015
(59) 		1081
(125) 		1161
(205) 		1184
(228)

Subsets and supersets

239edo is the 52nd prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [379 -239⟩ | [⟨239 379]] | −0.307 | 0.307 | 6.12 |- | 2.3.5 | [3 -18 11⟩, [32 -7 -9⟩ | [⟨239 379 555]] | −0.247 | 0.265 | 5.27 |- | 2.3.5.7 | 2401/2400, 5120/5103, 29360128/29296875 | [⟨239 379 555 671]] | −0.204 | 0.241 | 4.80 |- | 2.3.5.7.11 | 2401/2400, 3025/3024, 4000/3993, 5120/5103 | [⟨239 379 555 671 827]] | −0.220 | 0.218 | 4.34 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 3\239 | 15.06 | 121/120 | Yarman I (239) |- | 1 | 7\239 | 35.15 | 1990656/1953125 | Gammic (5-limit) |- | 1 | 9\239 | 45.19 | 250/243 | Quartonic (5-limit) |- | 1 | 11\239 | 55.23 | 33/32 | Escapade / alphaquarter |- | 1 | 35\239 | 175.73 | 72/65 | Quadrafifths (239f) |- | 1 | 54\239 | 271.13 | 90/77 | Quasiorwell (239) |- | 1 | 70\239 | 351.46 | 49/40 | Hemififths (7-limit) |- | 1 | 79\239 | 396.65 | 44/35 | Squarschmidt |- | 1 | 83\239 | 416.74 | 14/11 | Unthirds (239f) |- | 1 | 116\239 | 582.43 | 7/5 | Neptune (7-limit) Template:Rank-2 end Template:Orf

Music

Francium
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