The results of my 53-tone "experiment"

And I came up with nothing new. It works like this. There are five
columns. The central colums are only 3-limit intervals covering the whole
circle of fifths (I used some half-sharps and half-flats instead of triple
and quadruple sharps and flats). When natural thirds (5-limit) are figured
in, the two columns on either side displace the note down one scale degree
(numerator) or up (denominator). When we go to 7-limit, the outer colums
involve displacement of two scale degrees, again down for numerator and up
for denominator. A rougher approximation of 11- and 13-limit can be
expressed in the central column, as either the double diminished fifth and
double augmented fifth, or a half-sharp fourth or a half-flat sixth.

Then 17-limit means 1/12 of an octave, 19-limit octave 1/4 of an octave, and
23-limit half of an octave (23/16 is a good tritone like 7/5). I forgot how
29- and 31-limits work out.

~DaW~

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