Tuning ranges of regular temperaments: Difference between revisions

Cmloegcmluin (talk | contribs)
clarify eigenmonzo and provide unchanged-interval as alternative
Inthar (talk | contribs)
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* If 8/5 is the eigenmonzo, that's equivalent to 5/4 being the eigenmonzo and leads to the same tuning.
* If 8/5 is the eigenmonzo, that's equivalent to 5/4 being the eigenmonzo and leads to the same tuning.
* If 6/5 is the eigenmonzo, then 12/5 is also tuned pure so the fourth (the generator) is (12/5)^(1/3). Therefore the tuning is [2/1, (12/5)^(1/3)], or third-comma meantone.
* If 6/5 is the eigenmonzo, then 12/5 is also tuned pure so the fourth (the generator) is (12/5)^(1/3). Therefore the tuning is [2/1, (12/5)^(1/3)], or third-comma meantone.
* If 5/3 is the eigenmonzo, that's equivalent to 6/3 being the eigenmonzo.
* If 5/3 is the eigenmonzo, that's equivalent to 6/5 being the eigenmonzo.
These lead to three distinct tunings:
These lead to three distinct tunings:
* [2/1, 4/3] or Pythagorean - 4/3 and 3/2 are pure
* [2/1, 4/3] or Pythagorean - 4/3 and 3/2 are pure