Delta centauri: Difference between revisions

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One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b51 & b28, which maps [[13/9]] to 5 generators up, but this will make 13/9 very flat (18 cents of [[damage]] in CWE tuning). There is also the high-complexity weak extension b15 & b99 (which has a period of [[13/9]] and tempers out [[2197/2187]]) and the high-complexity strong extension b15 & b71 (which splits [[5/1]] into two 739/325s).

There is a clear extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up.

There is a clear strong extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up.

== Interval chain ==

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 One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b51 & b28, which maps [[13/9]] to 5 generators up, but this will make 13/9 very flat (18 cents of [[damage]] in CWE tuning). There is also the high-complexity weak extension b15 & b99 (which has a period of [[13/9]] and tempers out [[2197/2187]]) and the high-complexity strong extension b15 & b71 (which splits [[5/1]] into two 739/325s).
-There is a clear extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up.
+There is a clear strong extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up.
 == Interval chain ==