3-odd-limit: Difference between revisions
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All | All [[edo]]s are [[consistent]] in the 3-odd-limit, since every edo maps 3/2 and 4/3 to the nearest step by [[patent val]]. | ||
The {{w|natural density|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap| ''d'' ≥ 1 }}. | The {{w|natural density|density}} of edos consistent in the 3-odd-limit to distance ''d'' is expected to be 1/''d'' for {{nowrap| ''d'' ≥ 1 }}. | ||
Revision as of 05:18, 15 March 2026
The 3-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 3 and k is an integer. To the 1-odd-limit, it adds 1 pairs of octave-reduced interval involving 3.
Below is a list of all octave-reduced intervals in the 3-odd-limit.
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 4/3 | 498.045 | w4 | wa 4th | just perfect fourth |
| 3/2 | 701.955 | w5 | wa 5th | just perfect fifth |
All edos are consistent in the 3-odd-limit, since every edo maps 3/2 and 4/3 to the nearest step by patent val.
The density of edos consistent in the 3-odd-limit to distance d is expected to be 1/d for d ≥ 1.