2081edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2081edo is consistent to the 7-odd-limit, tempering out 2460375/2458624, 1312993546389/1310720000000 and {{monzo|24 13 -18 -1}}. It is strong in the 2.5.7.11.17.19 subgroup, tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625. === Odd harmonics === {{Harmonics in equal|2081}} === Subsets and supersets === 2081edo is the 313th prime edo. == Regular tempera..." |
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<nowiki />* [[Normal | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | |||
; [[Francium]] | |||
* "Fluffy Pants" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/19RLlJT3xTUmnIk9u9p1dT Spotify] | [https://francium223.bandcamp.com/track/fluffy-pants Bandcamp] | [https://www.youtube.com/watch?v=nNQjh8ZUtVc YouTube] | |||
Latest revision as of 13:44, 13 March 2026
| ← 2080edo | 2081edo | 2082edo → |
2081 equal divisions of the octave (abbreviated 2081edo or 2081ed2), also called 2081-tone equal temperament (2081tet) or 2081 equal temperament (2081et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2081 equal parts of about 0.577 ¢ each. Each step represents a frequency ratio of 21/2081, or the 2081st root of 2.
Theory
2081edo is consistent to the 7-odd-limit, tempering out 2460375/2458624, 1312993546389/1310720000000 and [24 13 -18 -1⟩. It is strong in the 2.5.7.11.17.19 subgroup, tempering out 10241/10240, 495635/495616, 184877/184832, 163498496/163480075 and 244248928/244140625.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.177 | +0.039 | -0.061 | +0.223 | -0.045 | +0.222 | -0.138 | -0.006 | +0.036 | -0.238 | +0.270 |
| Relative (%) | -30.7 | +6.8 | -10.6 | +38.6 | -7.7 | +38.5 | -23.9 | -1.0 | +6.3 | -41.3 | +46.8 | |
| Steps (reduced) |
3298 (1217) |
4832 (670) |
5842 (1680) |
6597 (354) |
7199 (956) |
7701 (1458) |
8130 (1887) |
8506 (182) |
8840 (516) |
9140 (816) |
9414 (1090) | |
Subsets and supersets
2081edo is the 313th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-3298 2081⟩ | [⟨2081 3298]] | 0.0558 | 0.0558 | 9.68 |
| 2.3.5 | [-68 18 17⟩, [-30 79 -41⟩ | [⟨2081 3298 4832]] | 0.0316 | 0.0570 | 9.88 |
| 2.3.5.7 | 2460375/2458624, [-24 13 -7 7⟩, [24 13 -18 -1⟩ | [⟨2081 3298 4832 5842]] | 0.0291 | 0.0496 | 8.60 |
| 2.3.5.7.11 | 160083/160000, 2460375/2458624, 3750705/3748096, 204073344/203809375 | [⟨2081 3298 4832 5842 7199]] | 0.0259 | 0.0448 | 7.77 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 194\2081 | 111.869 | 16/15 | Vavoom |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct