hi John Chalmers

Hi John --

I was wondering if you could help in understanding your triangular
tetrachord graphs.

I would like to use the same thing for triads but of course then the sum of
the three intervals (when appropriately signed) is not 500 but 0.

Please be as mathematical as you like.

This would be immensely helpful.

Thanks,
Paul

Hi John:

>I understand your math but not the point of summing the triadic
>intervals to 0. I think simply plotting the lower by the upper intervals
>would be sufficient.

I assume you had a point in using 120-degree rather than 90-degree angles in
your tetrachord plots, didn't you? The reasons I see are (a) symmetry, and
(b) distance between triads being meaningfully reflected by distance on the
plot. The latter is crucial if we are going to superimpose a bell-shaped
distribution over the graph.