9-odd-limit: Difference between revisions

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-This is a list of 9-odd-limit intervals. To [[7-odd-limit]], it adds 3 additional interval pairs involving 9.
+{{odd-limit navigation}}
+{{odd-limit intro|9}}
-<ul><li>[[10/9|10/9]], [[9/5|9/5]]</li><li>[[9/8|9/8]], [[16/9|16/9]]</li><li>[[8/7|8/7]], [[7/4|7/4]]</li><li>[[7/6|7/6]], [[12/7|12/7]]</li><li>[[6/5|6/5]], [[5/3|5/3]]</li><li>[[5/4|5/4]], [[8/5|8/5]]</li><li>[[9/7|9/7]], [[14/9|14/9]]</li><li>[[4/3|4/3]], [[3/2|3/2]]</li><li>[[7/5|7/5]], [[10/7|10/7]]</li></ul>
+* [[1/1]]
-[[Category:just_interval]]
+* '''[[10/9]], [[9/5]]'''
+* '''[[9/8]], [[16/9]]'''
+* [[8/7]], [[7/4]]
+* [[7/6]], [[12/7]]
+* [[6/5]], [[5/3]]
+* [[5/4]], [[8/5]]
+* '''[[9/7]], [[14/9]]'''
+* [[4/3]], [[3/2]]
+* [[7/5]], [[10/7]]
+{| class="wikitable center-all right-2 left-5"
+! Ratio
+! Size ([[cents|¢]])
+! colspan="2" | [[Color name]]
+! Name(s)
+|-
+| [[10/9]]
+| 182.404
+| y2
+| yo 2nd
+| classic whole tone <br>minor whole tone
+|-
+| [[9/8]]
+| 203.910
+| w2
+| wa 2nd
+| Pythagorean whole tone <br>major whole tone
+|-
+| [[9/7]]
+| 435.084
+| r3
+| ru 3rd
+| septimal supermajor third
+|-
+| [[14/9]]
+| 764.916
+| z6
+| zo 6th
+| septimal subminor sixth
+|-
+| [[16/9]]
+| 996.090
+| w7
+| wa 7th
+| Pythagorean minor seventh
+|-
+| [[9/5]]
+| 1017.596
+| g7
+| gu 7th
+| classic minor seventh
+|}
+The smallest [[equal division of the octave]] which is [[consistent]] in the 9-odd-limit is [[5edo]]; that which is distinctly consistent in the same is [[41edo]]. The {{w|natural density|density}} of edos consistent in the 9-odd-limit is 1/4<ref group="note">Provable in a similar method to the one for the 5-odd-limit.</ref>.
+== See also ==
+* [[Diamond9]] – as a scale
+== Notes ==
+<references group="note"/>
+[[Category:9-odd-limit| ]] <!-- main article -->