383edo: Difference between revisions
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. | '''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]] | ||