OTC 2L ns: Difference between revisions

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<ul><li>P(3) = P(5)+1 = P(7)+2</li><li>P(6) = P(8)+1 = P(10)+2 = P(12a)+3</li><li>P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4</li><li>P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5</li><li>P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5</li><li>etc.</li></ul>These groups appear to share generators and temperaments.

For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[~~EDO|~~EDO]]s that represent 4/3 and 3/2 with relatively high accuracy.

For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[EDO]]s that represent 4/3 and 3/2 with relatively high accuracy.

{| class="wikitable"

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===See also===

<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>

[[Category:Omnitetrachordal]]

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 <ul><li>P(3) = P(5)+1 = P(7)+2</li><li>P(6) = P(8)+1 = P(10)+2 = P(12a)+3</li><li>P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4</li><li>P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5</li><li>P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5</li><li>etc.</li></ul>These groups appear to share generators and temperaments.
-For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[EDO|EDO]]s that represent 4/3 and 3/2 with relatively high accuracy.
+For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[EDO]]s that represent 4/3 and 3/2 with relatively high accuracy.
 {| class="wikitable"
@@ Line 318: / Line 318: @@
 ===See also===
 <ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
+[[Category:Omnitetrachordal]]