383edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
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.
{{EDO intro|383}}


== 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. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.
383edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. The equal temperament [[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 limit.
 
383edo is the 76th [[prime edo]].


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|383|columns=11}}
{{Harmonics in equal|383|columns=11}}
=== Subsets and supersets ===
383edo is the 76th [[prime edo]].


== Regular temperament properties ==
== Regular temperament properties ==
Line 23: Line 24:
| 2.3
| 2.3
| {{monzo| -607 383 }}
| {{monzo| -607 383 }}
| [{{val| 383 607 }}]
| {{mapping| 383 607 }}
| +0.0402
| +0.0402
| 0.0402
| 0.0402
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| 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
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| 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 44: Line 45:
| 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
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| 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
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{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per Octave
! Periods<br>per 8ve
! Generator<br>(Reduced)
! Generator*
! Cents<br>(Reduced)
! Cents*
! Associated<br>Ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Helmholtz]]
| [[Helmholtz]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
[[Category:Countertertiaschis]]
[[Category:Countertertiaschis]]

Revision as of 14:03, 9 November 2023

← 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

Template:EDO intro

Theory

383edo is distinctly consistent through the 15-odd-limit with a flat tendency. The equal temperament 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 limit.

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 it is distinct

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