379edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|379}} | {{EDO intro|379}} | ||
==Theory== | |||
== Theory == | |||
Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2401/2400]], [[5120/5103]], and [[10976/10935]] in the 7-limit; [[5632/5625]], [[6250/6237]], [[14641/14580]], 42875/42768, and 43923/43904 in the 11-limit. It [[support]]s the [[subneutral]] temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|379}} | |||
=== Subsets and supersets === | |||
379edo is the 75th [[prime edo]]. | 379edo is the 75th [[prime edo]]. | ||
==Regular temperament properties== | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo| 601 -379}} | | {{monzo| 601 -379 }} | ||
|{{ | | {{mapping| 379 601 }} | ||
| -0.2989 | | -0.2989 | ||
|0.2988 | | 0.2988 | ||
|9.43 | | 9.43 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo| 35 -25 2}}, {{monzo| 38 -2 -15}} | | {{monzo| 35 -25 2 }}, {{monzo| 38 -2 -15 }} | ||
|{{ | | {{mapping| 379 601 880 }} | ||
| -0.1944 | | -0.1944 | ||
|0.2852 | | 0.2852 | ||
|9.01 | | 9.01 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|5120/5103, 2401/2400, {{monzo| -23 -11 15 2}} | | 5120/5103, 2401/2400, {{monzo| -23 -11 15 2 }} | ||
|{{ | | {{mapping| 379 601 880 1064} } | ||
| -0.1493 | | -0.1493 | ||
|0.2591 | | 0.2591 | ||
|8.18 | | 8.18 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|5120/5103, 5632/5625 | | 2401/2400, 5120/5103, 5632/5625, 166375/165888 | ||
|{{ | | {{mapping| 379 601 880 1064 1311 }} | ||
| -0.0967 | | -0.0967 | ||
|0.2545 | | 0.2545 | ||
|8.04 | | 8.04 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|325/324, 1001/1000, 1716/1715, 5120/5103, 6656/6655 | | 325/324, 1001/1000, 1716/1715, 5120/5103, 6656/6655 | ||
|{{ | | {{mapping| 379 601 880 1064 1311 1402 }} (379) | ||
| -0.014 | | -0.014 | ||
|0.2969 | | 0.2969 | ||
|9.38 | | 9.38 | ||
|} | |} | ||
| Line 56: | Line 62: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br> | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|61\379 | | 61\379 | ||
|193.14 | | 193.14 | ||
|262144/234375 | | 262144/234375 | ||
|[[Luna]] | | [[Luna]] | ||
|- | |- | ||
|1 | | 1 | ||
|110\379 | | 110\379 | ||
|348.28 | | 348.28 | ||
|57344/46875 | | 57344/46875 | ||
|[[Subneutral]] | | [[Subneutral]] | ||
|- | |- | ||
|1 | | 1 | ||
|111\379 | | 111\379 | ||
|351.45 | | 351.45 | ||
|49/40 | | 49/40 | ||
|[[Hemififths]] | | [[Hemififths]] | ||
|- | |- | ||
|1 | | 1 | ||
|143\379 | | 143\379 | ||
|452.77 | | 452.77 | ||
|162/125 | | 162/125 | ||
|[[Maja]] | | [[Maja]] (5-limit) | ||
|- | |- | ||
|1 | | 1 | ||
|221\379 | | 221\379 | ||
|699.74 | | 699.74 | ||
|8192/6137 | | 8192/6137 | ||
|[[Langwidge]] | | [[Langwidge]] | ||
|} | |} | ||
==Scales== | == Scales == | ||
*[[Subneutral31]] | * [[Subneutral31]] | ||
==Music== | == Music == | ||
*[https://www.youtube.com/watch?v=SDE2Nb7crIU Subneutral Funk] | ; [[User:Francium|Francium]] | ||
* [https://www.youtube.com/watch?v=SDE2Nb7crIU ''Subneutral Funk''] (2023) | |||
Revision as of 14:23, 9 November 2023
| ← 378edo | 379edo | 380edo → |
Theory
Using the patent val, the equal temperament tempers out 2401/2400, 5120/5103, and 10976/10935 in the 7-limit; 5632/5625, 6250/6237, 14641/14580, 42875/42768, and 43923/43904 in the 11-limit. It supports the subneutral temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.95 | -0.03 | +0.04 | -1.27 | -0.39 | -1.48 | +0.91 | -0.47 | +0.11 | +0.99 | -1.36 |
| Relative (%) | +29.9 | -1.1 | +1.2 | -40.2 | -12.5 | -46.7 | +28.8 | -14.8 | +3.5 | +31.2 | -43.0 | |
| Steps (reduced) |
601 (222) |
880 (122) |
1064 (306) |
1201 (64) |
1311 (174) |
1402 (265) |
1481 (344) |
1549 (33) |
1610 (94) |
1665 (149) |
1714 (198) | |
Subsets and supersets
379edo is the 75th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [601 -379⟩ | [⟨379 601]] | -0.2989 | 0.2988 | 9.43 |
| 2.3.5 | [35 -25 2⟩, [38 -2 -15⟩ | [⟨379 601 880]] | -0.1944 | 0.2852 | 9.01 |
| 2.3.5.7 | 5120/5103, 2401/2400, [-23 -11 15 2⟩ | 379 601 880 1064} } | -0.1493 | 0.2591 | 8.18 |
| 2.3.5.7.11 | 2401/2400, 5120/5103, 5632/5625, 166375/165888 | [⟨379 601 880 1064 1311 ]] | -0.0967 | 0.2545 | 8.04 |
| 2.3.5.7.11.13 | 325/324, 1001/1000, 1716/1715, 5120/5103, 6656/6655 | [⟨379 601 880 1064 1311 1402]] (379) | -0.014 | 0.2969 | 9.38 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 61\379 | 193.14 | 262144/234375 | Luna |
| 1 | 110\379 | 348.28 | 57344/46875 | Subneutral |
| 1 | 111\379 | 351.45 | 49/40 | Hemififths |
| 1 | 143\379 | 452.77 | 162/125 | Maja (5-limit) |
| 1 | 221\379 | 699.74 | 8192/6137 | Langwidge |
Scales
Music
- Subneutral Funk (2023)