4349edo: Difference between revisions
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== Regular temperament properties == | == 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 | | 2.3 | ||
| Line 55: | Line 64: | ||
| 0.0089 | | 0.0089 | ||
| 3.23 | | 3.23 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 65: | Line 81: | ||
| 8388608/7381125 | | 8388608/7381125 | ||
| [[Fortune]] | | [[Fortune]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
Revision as of 13:10, 16 November 2024
| ← 4348edo | 4349edo | 4350edo → |
Theory
4349edo is consistent to the 29-odd-limit, tempering out 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 123201/123200, 76545/76544, 47125/47124 and 25840/25839. It supports counterquectismic, chalmersic, tritomere and girardic. Essentially tempered chords available in 4349et include vicetertismic chords.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.001 | -0.018 | -0.051 | -0.019 | -0.059 | -0.104 | -0.065 | +0.008 | -0.099 | +0.055 |
| Relative (%) | +0.0 | -0.2 | -6.5 | -18.7 | -6.8 | -21.2 | -37.6 | -23.7 | +2.9 | -35.9 | +20.0 | |
| Steps (reduced) |
4349 (0) |
6893 (2544) |
10098 (1400) |
12209 (3511) |
15045 (1998) |
16093 (3046) |
17776 (380) |
18474 (1078) |
19673 (2277) |
21127 (3731) |
21546 (4150) | |
Subsets and supersets
4349edo is the 594th prime EDO.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-6893 4349⟩ | [⟨4349 6893]] | +0.0002 | 0.0002 | 0.07 |
| 2.3.5 | [-107 47 14⟩, [-35 -79 69⟩ | [⟨4349 6893 10098]] | +0.0027 | 0.0036 | 1.30 |
| 2.3.5.7 | 78125000/78121827, [-1 -18 -3 13⟩, [-52 17 12 -1⟩ | [⟨4349 6893 10098 12209]] | +0.0066 | 0.0074 | 2.68 |
| 2.3.5.7.11 | 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752 | [⟨4349 6893 10098 12209 15045]] | +0.0064 | 0.0067 | 2.43 |
| 2.3.5.7.11.13 | 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928 | [⟨4349 6893 10098 12209 15045 16093]] | +0.0079 | 0.0070 | 2.54 |
| 2.3.5.7.11.13.17 | 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096 | [⟨4349 6893 10098 12209 15045 16093 17776]] | +0.0104 | 0.0089 | 3.23 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 803\4349 | 221.5682 | 8388608/7381125 | Fortune |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct