Talk:Essential tempering comma: Difference between revisions

Mike Battaglia (talk | contribs)
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== Definition still wrong ==
Despite my earlier attempt to frame it for identifying essentially tempered triads (and excluding tetrads), now I find it also fails this task. For example, 121/120 induces essentially tempered triads. One of them is 1-11/8-5/3 with steps 11/8-11/9-6/5. Although 11/10 and 12/11 are interchangeable in the chord construction, the pair of 11/8 and 15/11 isn't since 11/8 is 11-odd-limit and 15/11 isn't, which constitutes the source of the tempering essence.
How about this definition:
# There are three intervals ''i'', ''j'', and ''k'' in S such that ''c'' = ''ij''/''k'', and
# None of ''c<sup>n</sup>i'', ''c<sup>n</sup>j'', and ''c<sup>n</sup>k'' is a member of S, where ''n'' is a nonzero integer.
Can anyone check it out? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:44, 7 January 2022 (UTC)
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