User:M1k1 H2tsun2/Exploring on another way to avoid wolf intervals problem

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Revision as of 12:06, 5 April 2026 by M1k1 H2tsun2 (talk | contribs) (Traditional just scales is fine but it is create wolf intervals problem, and how to remove them, 7-pitch scale in the octave are fit in 3-limit tuning, meantone temperament. but not fit in 5-limit tuning, such as 9/8 to 5/3, 4/3 to 9/5. to do that, remove one or the other. as the 6-pitch scale in the octave.)
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This article it is for pratical reason rather than only theoretical things.

Most of these scales has wolf intervals, for example:

1/1 9/8 5/4 4/3 3/2 5/3 15/8

1/1 9/8 6/5 4/3 3/2 8/5 9/5

9/8 to 5/3 is wolf fifth, and 5/3 to 9/4 is wolf fourth, how to avoid it? well, you might say to tempered out 81/80 to make fifths narrow a bit, In my opinion, yes, but there are another solutions here:

1/1 9/8 5/4 4/3 3/2 15/8

1/1 5/4 4/3 3/2 5/3 15/8

1/1 9/8 6/5 3/2 8/5 9/5

These scales does not include any wolf interval, so when the scale has wolf intervals, the best way it is to remove it. In major, we will remove 9/8 or 5/3 as the solution, and in minor, we only remove 4/3 as the solution.