3-odd-limit: Difference between revisions

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-This is a list of 3-odd-limit intervals. To [[1-odd-limit]], it adds 1 additional interval pair involving 3.
+{{Odd-limit navigation|3}}
+{{Odd-limit intro|3}}
-<ul><li>[[4/3|4/3]], [[3/2|3/2]]</li></ul>
+* [[1/1]]
-[[Category:just_interval]]
+* '''[[4/3]], [[3/2]]'''
+The 3-odd-limit can be considered the set of {{W|perfect consonance}}s, containing the unison, octave, perfect fifth, and perfect fourth, which have the simplest [[frequency ratio]]s.
+{| class="wikitable center-all right-2 left-5"
+! 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 [[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 }}.
+== See also ==
+* [[3-limit]] ([[prime limit]])
+[[Category:3-odd-limit| ]] <!-- main article -->