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It can sometimes be useful to look not just at "indirect" prime-based mappings, but also add extra "direct" mappings for important rationals -- deliberately inconsistent with the indirect ones -- for which the indirect mapping is subpar.

A good example of this is in 16-EDO, which ~~has a perfectly good~~ 9/8 at 225 cents, ~~but which does not agree with the mapping of~~ 3/2 at 675 cents. In this instance, the associated "2.3.5.9" sval would be <math>\langle 16\, 25\, 37\, 51|</math>, where it is seen that the mapping of 51 steps for 9 is "inconsistent" with the mapping of 25 steps for 3.

A good example of this is 16-EDO, in which 9/8 is mapped to 225 cents, while 3/2 is mapped to 675 cents. In this instance, the associated "2.3.5.9" sval would be <math>\langle 16\, 25\, 37\, 51|</math>, where it is seen that the mapping of 51 steps for 9 is "inconsistent" with the mapping of 25 steps for 3.

Note that there is no mapping for 3 at all which will map 9/1 to 51 steps, since 51 is an odd number, so it is useful to have both mappings: the regular 9/1, for use in chords such as the "[[Mavila]]" major 9 chord of 0-375-675-1050-1350, so that the 1350 cent 9/4 is a stack of two ~675 cent 3/2's, and the tempered 4:7:9 at 0-975-1425, which need not have any 3/2 at all.

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 It can sometimes be useful to look not just at "indirect" prime-based mappings, but also add extra "direct" mappings for important rationals -- deliberately inconsistent with the indirect ones -- for which the indirect mapping is subpar.
-A good example of this is in 16-EDO, which has a perfectly good 9/8 at 225 cents, but which does not agree with the mapping of 3/2 at 675 cents. In this instance, the associated "2.3.5.9" sval would be <math>\langle 16\, 25\, 37\, 51|</math>, where it is seen that the mapping of 51 steps for 9 is "inconsistent" with the mapping of 25 steps for 3.
+A good example of this is 16-EDO, in which 9/8 is mapped to 225 cents, while 3/2 is mapped to 675 cents. In this instance, the associated "2.3.5.9" sval would be <math>\langle 16\, 25\, 37\, 51|</math>, where it is seen that the mapping of 51 steps for 9 is "inconsistent" with the mapping of 25 steps for 3.
 Note that there is no mapping for 3 at all which will map 9/1 to 51 steps, since 51 is an odd number, so it is useful to have both mappings: the regular 9/1, for use in chords such as the "[[Mavila]]" major 9 chord of 0-375-675-1050-1350, so that the 1350 cent 9/4 is a stack of two ~675 cent 3/2's, and the tempered 4:7:9 at 0-975-1425, which need not have any 3/2 at all.