3079edo: Difference between revisions
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== Theory == | == Theory == | ||
3079edo is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[43046721/43025920]], 1220703125/1219784832 and {{monzo|51 -13 -1 -10}} in the 7-limit. It [[support]]s [[acrosextilififths]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
3079edo is the 440th [[prime | 3079edo is the 440th [[prime edo]]. | ||
== 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|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-4880 3079}} | | {{monzo|-4880 3079}} | ||
|{{mapping|3079 4880}} | | {{mapping|3079 4880}} | ||
| 0.0122 | | 0.0122 | ||
| 0.0122 | | 0.0122 | ||
| 3.13 | | 3.13 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-69 45 -1}}, {{monzo|-50 -71 70}} | | {{monzo| -69 45 -1 }}, {{monzo| -50 -71 70 }} | ||
|{{mapping|3079 4880 7149}} | | {{mapping| 3079 4880 7149 }} | ||
| 0.0203 | | 0.0203 | ||
| 0.0151 | | 0.0151 | ||
| 3.87 | | 3.87 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|43046721/43025920, 1220703125/1219784832, {{monzo|51 -13 -1 -10}} | | 43046721/43025920, 1220703125/1219784832, {{monzo| 51 -13 -1 -10 }} | ||
|{{mapping|3079 4880 7149 8644}} | | {{mapping| 3079 4880 7149 8644 }} | ||
| 0.0099 | | 0.0099 | ||
| 0.0223 | | 0.0223 | ||
| Line 53: | Line 53: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|1278\3079 | | 1278\3079 | ||
|498.084 | | 498.084 | ||
|4/3 | | 4/3 | ||
|[[Counterschismic]] | | [[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 | <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 12:25, 15 May 2024
| ← 3078edo | 3079edo | 3080edo → |
Theory
3079edo 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