--- In tuning-math@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning-math@yahoogroups.com, "Kalle Aho
<kalleaho@m...>" <kalleaho@m...> wrote:
>
> > How is complexity calculated and why?
>
> I calculated complexity using a rather complicated formula, but
>Paul tells me that Graham complexity would have been better;

actually the representation of the chromatic unison vector comes
into it too.

>evidentally you are interested only in complete tetrads. It is
easy >to compute: take the range in generator steps of the
>representations of
> {1,3,5,7,5/3,7/3,7/5} and multiply by the number of periods in an
>octave.

that's graham's complexity. but you still haven't calculated the
number of complete tetrads.

to do that, you also need to calculate the number of notes in the
scale. first calculate the cardinality per period, by determining
(from the mapping) the number of generators comprising a
49:48 if 25:24 is tempered out, a 25:24 if 49:48 is tempered out,
or either (they'll be the same) if 50:49 is tempered out. then
multiply by the number of periods in an octave.

finally, the number of tetrads will be the graham complexity
minus the number of notes in the scale -- times two (since both
otonal and utonal tetrads count).