3079edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|3079}} == Theory == 3079et is consistent to the 9-odd-limit. The equal temperament tempers out 43046721/43025920, 1220703125/1219784832..." |
+regular temperament properties |
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=== Subsets and supersets === | === Subsets and supersets === | ||
3079edo is the 440th [[prime EDO]]. | 3079edo is the 440th [[prime EDO]]. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|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|-4880 3079}} | |||
|{{mapping|3079 4880}} | |||
| 0.0122 | |||
| 0.0122 | |||
| 3.13 | |||
|- | |||
|2.3.5 | |||
|{{monzo|-69 45 -1}}, {{monzo|-50 -71 70}} | |||
|{{mapping|3079 4880 7149}} | |||
| 0.0203 | |||
| 0.0151 | |||
| 3.87 | |||
|- | |||
|2.3.5.7 | |||
|43046721/43025920, 1220703125/1219784832, {{monzo|51 -13 -1 -10}} | |||
|{{mapping|3079 4880 7149 8644}} | |||
| 0.0099 | |||
| 0.0223 | |||
| 5.72 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>Ratio* | |||
! Temperaments | |||
|- | |||
|1 | |||
|1278\3079 | |||
|498.084 | |||
|4/3 | |||
|[[Counterschismic]] | |||
|} | |||
<nowiki>*</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 12:20, 14 May 2024
| ← 3078edo | 3079edo | 3080edo → |
Theory
3079et is consistent to the 9-odd-limit. The equal temperament tempers out 43046721/43025920, 1220703125/1219784832 and [51 -13 -1 -10⟩ in the 7-limit. It supports acrosextilififths.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.039 | -0.084 | +0.060 | +0.160 | +0.135 | -0.116 | -0.144 | -0.018 | +0.108 | +0.012 |
| Relative (%) | +0.0 | -10.0 | -21.7 | +15.4 | +41.0 | +34.6 | -29.8 | -36.9 | -4.7 | +27.7 | +3.0 | |
| Steps (reduced) |
3079 (0) |
4880 (1801) |
7149 (991) |
8644 (2486) |
10652 (1415) |
11394 (2157) |
12585 (269) |
13079 (763) |
13928 (1612) |
14958 (2642) |
15254 (2938) | |
Subsets and supersets
3079edo is the 440th prime EDO.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-4880 3079⟩ | [⟨3079 4880]] | 0.0122 | 0.0122 | 3.13 |
| 2.3.5 | [-69 45 -1⟩, [-50 -71 70⟩ | [⟨3079 4880 7149]] | 0.0203 | 0.0151 | 3.87 |
| 2.3.5.7 | 43046721/43025920, 1220703125/1219784832, [51 -13 -1 -10⟩ | [⟨3079 4880 7149 8644]] | 0.0099 | 0.0223 | 5.72 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 1278\3079 | 498.084 | 4/3 | Counterschismic |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct