reply to Herman Miller

>Low integer ratios are useful for explaining traditional Western
harmony,
>but they don't always make sense with other kinds of scales. If you
take a
>two-step interval from Wendy Carlos' alpha scale, for instance, I'd
prefer
>to call it half a minor third than an approximation to 12/11. Some
pelog
>scales have an interval size that has a similar impression to my ear,
>splitting a (roughly) minor third into two parts that are (roughly)
similar
>in size. I'm not sure that it matters much whether it is closer to
11/10,
>12/11, or 13/12, or somewhere in between. In general, my feeling is
that
>the pattern of small and large steps is more relevant to the character
of a
>pelog scale than the integer ratios that approximate those steps.
>Blackwood's faux pelog in his 23-note etude is still recognizable as a
>pelog scale. Similarly, the roughly equal size of the steps of a
slendro
>scale is what gives it its distinctive character.

I totally agree! Look at Arabic scales, like 3 3 4 4 3 3 4 in 24-tET,
for a more familiar example of a minor third being cut in half.

Roughly speaking, low integer ratios matter only when the tones are
being used simulataneously in harmony, and when some sort of "blending"
is the goal. A major exception is that the 2:1 and 3:2 (and 4:3) are
powerful enough that even purely melodic scales tend to have structures
that repeat themselves at these intervals.