379edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|379}}  
{{ED intro}}
==Theory==
 
379 tempers out 4096000/4084101, [[5120/5103]] and [[2401/2400]] in the 7-limit; 2097152/2096325, 1953125/1951488, [[6250/6237]], 42875/42768, 5767168/5764801, 180224/180075, [[5632/5625]], 537109375/536870912, 422576/421875, 9453125/9437184, 166375/165888, 67110351/67108864, 3294225/3294172, 43923/43904, 102487/102400, 20614528/20588575, 644204/643125 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the [[subneutral]] temperament.
== 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 [[hemififths]] and [[subneutral]].
 
=== Odd harmonics ===
{{Harmonics in equal|379}}
 
=== Subsets and supersets ===
379edo is the 75th [[prime edo]].
379edo is the 75th [[prime edo]].
{{Harmonics in equal|379}}
 
==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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo| 601 -379}}
| {{monzo| 601 -379 }}
|{{val| 379 601}}
| {{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 }}
|{{val| 379​ 601 ​880}}
| {{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 }}
|{{val| 379​ 601​ 880​ 1064​}}
| {{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, 166375/165888
| 2401/2400, 5120/5103, 5632/5625, 14641/14580
|{{val| 379 ​601 ​880​ 1064 ​1311​}}
| {{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
|{{val| 379 ​601 ​880​ 1064 ​1311​ 1402}}
| {{mapping| 379 ​601 ​880​ 1064 ​1311​ 1402 }} (379)
| -0.014
| −0.014
|0.2969
| 0.2969
|9.38
| 9.38
|}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|110\379
| 61\379
|348.28
| 193.14
|57344/46875
| 262144/234375
|Subneutral
| [[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]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Scales ==
* [[Subneutral31]]
== Music ==
; [[Francium]]
* [https://www.youtube.com/watch?v=SDE2Nb7crIU ''Subneutral Funk''] (2023)
* "Blindfolded, Ordinary" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/0Ron6qIepdAdTfAnKaKPfS Spotify] | [https://francium223.bandcamp.com/track/blindfolded-ordinary Bandcamp] | [https://www.youtube.com/watch?v=uuFcSrCfA00 YouTube]
* "Bread That Was Brought To Life" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/2mVUbNEBX6FPRqjTJ3fyMh Spotify] | [https://francium223.bandcamp.com/track/bread-that-was-brought-to-life Bandcamp] | [https://www.youtube.com/watch?v=bfw1PUNV930 YouTube] – bronxic in 379edo


==Scales==
[[Category:Listen]]
*[[Subneutral31]]

Latest revision as of 12:39, 21 February 2025

← 378edo 379edo 380edo →
Prime factorization 379 (prime)
Step size 3.16623 ¢ 
Fifth 222\379 (702.902 ¢)
Semitones (A1:m2) 38:27 (120.3 ¢ : 85.49 ¢)
Consistency limit 7
Distinct consistency limit 7

379 equal divisions of the octave (abbreviated 379edo or 379ed2), also called 379-tone equal temperament (379tet) or 379 equal temperament (379et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 379 equal parts of about 3.17 ¢ each. Each step represents a frequency ratio of 21/379, or the 379th root of 2.

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 hemififths and subneutral.

Odd harmonics

Approximation of odd harmonics in 379edo
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, 14641/14580 [⟨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

Table of rank-2 temperaments by generator
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

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Scales

Music

Francium
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