Delta centauri: Difference between revisions

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There is a clear strong extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up. This provides a simpler interpretation of several intervals in the MOS scales. This extension sacrifices a little bit of accuracy and has [[damage]] of around 1-2 cents on 11/9 and 17/9 in CWE tuning, but it's still decent accuracy.

One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions in that subgroup aren't very good because they seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b15 & 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).

One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions in that subgroup aren't very good because they seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b15 & 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 weak extension b15 & b71 (which splits [[5/1]] into two 739/325s).

== Interval chain ==

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 There is a clear strong extension to 3.5.11.17, by tempering out [[1377/1375]] and mapping [[17/9]] to 12 generators up. This provides a simpler interpretation of several intervals in the MOS scales. This extension sacrifices a little bit of accuracy and has [[damage]] of around 1-2 cents on 11/9 and 17/9 in CWE tuning, but it's still decent accuracy.
-One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions in that subgroup aren't very good because they seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b15 & 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).
+One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 [[isoharmonic]] chord, however most extensions in that subgroup aren't very good because they seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b15 & 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 weak extension b15 & b71 (which splits [[5/1]] into two 739/325s).
 == Interval chain ==