239edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cleanup and +prime error table
+RTT table and rank-2 temperaments
Line 5: Line 5:
=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|239}}
{{Harmonics in equal|239}}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve <br>stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 379 -239 }}
| [{{val| 239 379 }}]
| -0.307
| 0.307
| 6.12
|-
| 2.3.5
| {{monzo| 3 -18 11}}, {{monzo| 32 -7 -9 }}
| [{{val| 239 379 555 }}]
| -0.247
| 0.265
| 5.27
|-
| 2.3.5.7
| 2401/2400, 5120/5103, 29360128/29296875
| [{{val| 239 379 555 671 }}]
| -0.204
| 0.241
| 4.80
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 4000/3993, 5632/5625
| [{{val| 239 379 555 671 827 }}]
| -0.220
| 0.218
| 4.34
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 3\239
| 15.06
| 121/120
| [[Yarman I]] (239)
|-
| 1
| 11\239
| 35.15
| 1990656/1953125
| [[Gammic]] (5-limit)
|-
| 1
| 7\239
| 55.23
| 33/32
| [[Escapade]] / [[alphaquarter]]
|-
| 1
| 35\229
| 175.73
| 72/65
| [[Quadrafifths]] (239f)
|-
| 1
| 54\229
| 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)
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]

Revision as of 14:25, 9 March 2022

239edo is the equal division of the octave into 239 parts of 5.0209 cents each. In the 7-limit, it tempers out 2401/2400, 5120/5103, and 29360128/29296875, supporting the hemififths temperament, 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.

239edo is the 52nd prime edo.

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)

Regular temperament properties

Subgroup Comma list Mapping Optimal 8ve
stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
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, 5632/5625 [⟨239 379 555 671 827]] -0.220 0.218 4.34

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 3\239 15.06 121/120 Yarman I (239)
1 11\239 35.15 1990656/1953125 Gammic (5-limit)
1 7\239 55.23 33/32 Escapade / alphaquarter
1 35\229 175.73 72/65 Quadrafifths (239f)
1 54\229 271.13 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)
Retrieved from "https://en.xen.wiki/index.php?title=239edo&oldid=89220"