3079edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
3079edo is [[consistent]] to the [[9-odd-limit]]. | 3079edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[43046721/43025920]], 1220703125/1219784832 and {{monzo| 51 -13 -1 -10 }} in the 7-limit, [[support]]ing [[acrosextilifourths]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 26: | Line 26: | ||
| {{monzo|-4880 3079}} | | {{monzo|-4880 3079}} | ||
| {{mapping|3079 4880}} | | {{mapping|3079 4880}} | ||
| 0.0122 | | +0.0122 | ||
| 0.0122 | | 0.0122 | ||
| 3.13 | | 3.13 | ||
| Line 33: | Line 33: | ||
| {{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 | ||
| Line 40: | Line 40: | ||
| 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 | ||
| 5.72 | | 5.72 | ||
| Line 61: | Line 61: | ||
| [[Counterschismic]] | | [[Counterschismic]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "mfdreamshoppedfashionforyou" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6paD6q5WZKPjgVW32P81sh Spotify] | [https://francium223.bandcamp.com/track/mfdreamshoppedfashionforyou Bandcamp] | [https://www.youtube.com/watch?v=xPxStKUUpFU YouTube] – | * "mfdreamshoppedfashionforyou" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/6paD6q5WZKPjgVW32P81sh Spotify] | [https://francium223.bandcamp.com/track/mfdreamshoppedfashionforyou Bandcamp] | [https://www.youtube.com/watch?v=xPxStKUUpFU YouTube] – acrosextilifourths[13] in 3079edo tuning | ||
Latest revision as of 20:55, 1 April 2025
| ← 3078edo | 3079edo | 3080edo → |
3079 equal divisions of the octave (abbreviated 3079edo or 3079ed2), also called 3079-tone equal temperament (3079tet) or 3079 equal temperament (3079et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3079 equal parts of about 0.39 ¢ each. Each step represents a frequency ratio of 21/3079, or the 3079th root of 2.
Theory
3079edo is consistent to the 9-odd-limit. As an equal temperament, it tempers out 43046721/43025920, 1220703125/1219784832 and [51 -13 -1 -10⟩ in the 7-limit, supporting acrosextilifourths.
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 distinct