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== Theory == | == Theory == | ||
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| [[Luna]] | | [[Luna]] | ||
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<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]] | |||
* "Slow Down Or Die" from ''I Want To'' (2025) – [https://open.spotify.com/track/2vzrMXihetN2DhUWBLUcZs Spotify] | [https://francium223.bandcamp.com/track/slow-down-or-die Bandcamp] | [https://www.youtube.com/watch?v=7lPwEesZbsI YouTube] | |||
[[Category:Luna]] | [[Category:Luna]] | ||
Latest revision as of 13:31, 13 March 2026
| ← 732edo | 733edo | 734edo → |
733 equal divisions of the octave (abbreviated 733edo or 733ed2), also called 733-tone equal temperament (733tet) or 733 equal temperament (733et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 733 equal parts of about 1.64 ¢ each. Each step represents a frequency ratio of 21/733, or the 733rd root of 2.
Theory
733edo is consistent to the 11-odd-limit, tempering out 3025/3024, 19712/19683, 180224/180075 and 1953125/1951488. It supports hemiluna and French decimal.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.364 | +0.044 | +0.342 | +0.387 | -0.691 | -0.181 | +0.441 | +0.375 | +0.164 | -0.697 |
| Relative (%) | +0.0 | +22.2 | +2.7 | +20.9 | +23.7 | -42.2 | -11.0 | +26.9 | +22.9 | +10.0 | -42.6 | |
| Steps (reduced) |
733 (0) |
1162 (429) |
1702 (236) |
2058 (592) |
2536 (337) |
2712 (513) |
2996 (64) |
3114 (182) |
3316 (384) |
3561 (629) |
3631 (699) | |
Subsets and supersets
733edo is the 130th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1162 -733⟩ | [⟨733 1162]] | −0.1149 | 0.1149 | 7.02 |
| 2.3.5 | [38 -2 -15⟩, [42 -47 14⟩ | [⟨733 1162 1702]] | −0.0829 | 0.1042 | 6.36 |
| 2.3.5.7 | 420175/419904, 67108864/66976875, 48828125/48771072 | [⟨733 1162 1702 2058]] | −0.0926 | 0.0918 | 5.61 |
| 2.3.5.7.11 | 3025/3024, 19712/19683, 180224/180075, 1953125/1951488 | [⟨733 1162 1702 2058 2536]] | −0.0965 | 0.0824 | 5.03 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 118\733 | 193.179 | 262144/234375 | Luna |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct