383edo: Difference between revisions
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== 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 | 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 the 76th [[prime edo]]. | 383edo is the 76th [[prime edo]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|383|columns=11}} | ||
== 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|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 66: | Line 66: | ||
{| 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 | ! Periods<br>per Octave | ||
! Generator<br>( | ! Generator<br>(Reduced) | ||
! Cents<br>( | ! Cents<br>(Reduced) | ||
! Associated<br> | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
|- | |||
| 1 | |||
| 53\383 | |||
| 166.06 | |||
| 11/10 | |||
| [[Countertertiaschis]] | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 79: | Line 85: | ||
|- | |- | ||
| 1 | | 1 | ||
| 133\ | | 133\383 | ||
| 416.71 | | 416.71 | ||
| 14/11 | | 14/11 | ||
| Line 93: | Line 99: | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
[[Category:Countertertiaschis]] | |||
Revision as of 21:26, 31 August 2022
| ← 382edo | 383edo | 384edo → |
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 equal division of the octave into 383 parts of about 3.13 cents each.
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 the 76th prime edo.
Prime harmonics
| 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) | |
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
| Periods per Octave |
Generator (Reduced) |
Cents (Reduced) |
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 |