383edo: Difference between revisions

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'''383EDO''' is the [[EDO|equal division of the octave]] into 383 parts of 3.13316 [[cent]]s each. It is distinctly consistent through the 15-limit, and tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 6250/6237, 4000/3993 and 3025/3024 in the 11-limit;  and 625/624, 1575/1573 and 2080/2079 in the 13-limit and it supports [[Schismatic_family#Sesquiquartififths|sesquiquartififths]].
{{Infobox ET}}
{{ED intro}}


383EDO is the 76th [[prime EDO]].
== Theory ==
383edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the [[11-limit]]; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limits.


[[Category:Edo]]
=== Prime harmonics ===
[[Category:Prime EDO]]
{{Harmonics in equal|383}}
 
=== Subsets and supersets ===
383edo is the 76th [[prime edo]].
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! 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
| {{monzo| -607 383 }}
| {{mapping| 383 607 }}
| +0.0402
| 0.0402
| 1.28
|-
| 2.3.5
| 32805/32768, {{monzo| -8 -55 41}}
| {{mapping| 383 607 889 }}
| +0.1610
| 0.1741
| 5.55
|-
| 2.3.5.7
| 2401/2400, 32805/32768, 68359375/68024448
| {{mapping| 383 607 889 1075 }}
| +0.1813
| 0.1548
| 4.94
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 4000/3993, 32805/32768
| {{mapping| 383 607 889 1075 1325 }}
| +0.1382
| 0.1631
| 5.20
|-
| 2.3.5.7.11.13
| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976
| {{mapping| 383 607 889 1075 1325 1417 }}
| +0.1531
| 0.1525
| 4.87
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 53\383
| 166.06
| 11/10
| [[Countertertiaschis]]
|-
| 1
| 56\383
| 175.46
| 448/405
| [[Sesquiquartififths]]
|-
| 1
| 133\383
| 416.71
| 14/11
| [[Unthirds]]
|-
| 1
| 159\383
| 498.17
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Music ==
; [[Francium]]
* "Mark A Player" from ''I Want To'' (2025) – [https://open.spotify.com/track/1M3LmqPfXRjpxuuTRgEufN Spotify] | [https://francium223.bandcamp.com/track/mark-a-player Bandcamp] | [https://www.youtube.com/watch?v=ePR_S5cNZvI YouTube] – in Marconic, 383edo tuning
 
[[Category:Countertertiaschis]]

Latest revision as of 02:30, 17 April 2025

← 382edo 383edo 384edo →
Prime factorization 383 (prime)
Step size 3.13316 ¢ 
Fifth 224\383 (701.828 ¢)
Semitones (A1:m2) 36:29 (112.8 ¢ : 90.86 ¢)
Consistency limit 15
Distinct consistency limit 15

383 equal divisions of the octave (abbreviated 383edo or 383ed2), also called 383-tone equal temperament (383tet) or 383 equal temperament (383et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 383 equal parts of about 3.13 ¢ each. Each step represents a frequency ratio of 21/383, or the 383rd root of 2.

Theory

383edo is distinctly consistent through the 15-odd-limit with a flat tendency. As an equal temperament, it tempers out 32805/32768 (schisma) in the 5-limit; 2401/2400 in the 7-limit; 3025/3024, 4000/3993 and 6250/6237 in the 11-limit; and 625/624, 1575/1573 and 2080/2079 in the 13-limit. It provides the optimal patent val for the countertertiaschis temperament, and a good tuning for sesquiquartififths in the higher limits.

Prime harmonics

Approximation of prime harmonics in 383edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.13 -0.94 -0.68 +0.12 -0.84 -1.56 +0.14 +1.49 +1.23 -1.43
Relative (%) +0.0 -4.1 -29.8 -21.7 +3.8 -26.8 -49.8 +4.4 +47.6 +39.3 -45.7
Steps
(reduced) 		383
(0) 		607
(224) 		889
(123) 		1075
(309) 		1325
(176) 		1417
(268) 		1565
(33) 		1627
(95) 		1733
(201) 		1861
(329) 		1897
(365)

Subsets and supersets

383edo is the 76th prime edo.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-607 383⟩ [⟨383 607]] +0.0402 0.0402 1.28
2.3.5 32805/32768, [-8 -55 41⟩ [⟨383 607 889]] +0.1610 0.1741 5.55
2.3.5.7 2401/2400, 32805/32768, 68359375/68024448 [⟨383 607 889 1075]] +0.1813 0.1548 4.94
2.3.5.7.11 2401/2400, 3025/3024, 4000/3993, 32805/32768 [⟨383 607 889 1075 1325]] +0.1382 0.1631 5.20
2.3.5.7.11.13 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976 [⟨383 607 889 1075 1325 1417]] +0.1531 0.1525 4.87

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 53\383 166.06 11/10 Countertertiaschis
1 56\383 175.46 448/405 Sesquiquartififths
1 133\383 416.71 14/11 Unthirds
1 159\383 498.17 4/3 Helmholtz

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

Music

Francium
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