3-odd-limit: Difference between revisions
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Density of edos consistent to distance d |
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{{ | {{Odd-limit navigation}} | ||
{{Odd-limit intro|3}} | |||
* [[1/1]] | * [[1/1]] | ||
* '''[[4/3]], [[3/2]]''' | * '''[[4/3]], [[3/2]]''' | ||
[[ | {| class="wikitable center-all right-2 left-5" | ||
[[Category: | ! Ratio | ||
! Size ([[cents|¢]]) | |||
! colspan="2" | [[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 there are only two [[pitch class]]es besides the octave. 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 }}. | |||
== See also == | |||
* [[3-limit]] ([[prime limit]]) | |||
[[Category:3-odd-limit| ]] <!-- main article --> | |||
Latest revision as of 09:47, 15 August 2025
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 there are only two pitch classes besides the octave. The density of edos consistent in the 3-odd-limit to distance d is expected to be 1/d for d ≥ 1.