383edo: Difference between revisions

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{{Infobox ET
{{Infobox ET}}
| Prime factorization = 383 (prime)
{{ED intro}}
| Step size = 3.13316¢
| Fifth = 224\383 (701.83¢)
| Semitones = 36:29 (112.79¢ : 90.86¢)
| Consistency = 15
}}
The '''383 equal divisions of the octave''' ('''383edo'''), or the '''383(-tone) equal temperament''' ('''383tet''', '''383et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 383 parts of about 3.13 [[cent]]s each.


== Theory ==
== Theory ==
383edo is distinctly [[consistent]] through the [[15-odd-limit]] with a flat tendency. It tempers out 32805/32768 ([[schisma]]) 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 [[support]]s [[sesquiquartififths]].
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.


=== Prime harmonics ===
{{Harmonics in equal|383}}
=== Subsets and supersets ===
383edo is the 76th [[prime edo]].
383edo is the 76th [[prime edo]].
=== Prime harmonics ===
{{Primes in edo|383}}


== 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]]
! rowspan="2" | [[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
|-
|-
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| 2.3
| 2.3
| {{monzo| -607 383 }}
| {{monzo| -607 383 }}
| [{{val| 383 607 }}]
| {{mapping| 383 607 }}
| +0.0402
| +0.0402
| 0.0402
| 0.0402
Line 36: Line 32:
| 2.3.5
| 2.3.5
| 32805/32768, {{monzo| -8 -55 41}}
| 32805/32768, {{monzo| -8 -55 41}}
| [{{val| 383 607 889 }}]
| {{mapping| 383 607 889 }}
| +0.1610
| +0.1610
| 0.1741
| 0.1741
Line 43: Line 39:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 32805/32768, 68359375/68024448
| 2401/2400, 32805/32768, 68359375/68024448
| [{{val| 383 607 889 1075 }}]
| {{mapping| 383 607 889 1075 }}
| +0.1813
| +0.1813
| 0.1548
| 0.1548
Line 50: Line 46:
| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 3025/3024, 4000/3993, 32805/32768
| 2401/2400, 3025/3024, 4000/3993, 32805/32768
| [{{val| 383 607 889 1075 1325 }}]
| {{mapping| 383 607 889 1075 1325 }}
| +0.1382
| +0.1382
| 0.1631
| 0.1631
Line 57: Line 53:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976
| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976
| [{{val| 383 607 889 1075 1325 1417 }}]
| {{mapping| 383 607 889 1075 1325 1417 }}
| +0.1531
| +0.1531
| 0.1525
| 0.1525
Line 65: Line 61:
=== 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 octave
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
| 1
| 53\383
| 166.06
| 11/10
| [[Countertertiaschis]]
|-
|-
| 1
| 1
Line 79: Line 82:
|-
|-
| 1
| 1
| 133\373
| 133\383
| 416.71
| 416.71
| 14/11
| 14/11
Line 88: Line 91:
| 498.17
| 498.17
| 4/3
| 4/3
| [[Helmholtz]]
| [[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:Equal divisions of the octave]]
[[Category:Countertertiaschis]]
[[Category:Prime EDO]]

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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