383edo: Difference between revisions

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Cleanup; +prime error table
+RTT table and rank-2 temperaments
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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-odd-limit, and 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 supports [[Schismatic family #Sesquiquartififths|sesquiquartififths]].
'''383edo''' is the [[EDO|equal division of the octave]] into 383 parts of 3.13316 [[cent]]s each.  
 
== Theory ==
383edo is distinctly consistent through the 15-odd-limit, and 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 supports [[Schismatic family #Sesquiquartififths|sesquiquartififths]].


383edo is the 76th [[prime edo]].
383edo is the 76th [[prime edo]].
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=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|383}}
{{Primes in edo|383}}
== 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 }}
| [{{val| 383 607 }}]
| +0.0402
| 0.0402
| 1.28
|-
| 2.3.5
| 32805/32768, {{monzo| -8 -55 41}}
| [{{val| 383 607 889 }}]
| +0.1610
| 0.1741
| 5.55
|-
| 2.3.5.7
| 2401/2400, 32805/32768, 68359375/68024448
| [{{val| 383 607 889 1075 }}]
| +0.1813
| 0.1548
| 4.94
|-
| 2.3.5.7.11
| 2401/2400, 3025/3024, 4000/3993, 32805/32768
| [{{val| 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
| [{{val| 383 607 889 1075 1325 1417 }}]
| +0.1531
| 0.1525
| 4.87
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 56\383
| 175.46
| 448/405
| [[Sesquiquartififths]]
|-
| 1
| 133\373
| 416.71
| 14/11
| [[Unthirds]]
|-
| 1
| 159\383
| 498.17
| 4/3
| [[Helmholtz]]
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 18:52, 9 January 2022

383edo is the equal division of the octave into 383 parts of 3.13316 cents each.

Theory

383edo is distinctly consistent through the 15-odd-limit, and 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 supports sesquiquartififths.

383edo is the 76th prime edo.

Prime harmonics

Script error: No such module "primes_in_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 octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 56\383 175.46 448/405 Sesquiquartififths
1 133\373 416.71 14/11 Unthirds
1 159\383 498.17 4/3 Helmholtz
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