Tuning ranges of regular temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) clarify eigenmonzo and provide unchanged-interval as alternative |
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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/ | * 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 | ||