curiosities with dyadic entropy calculator

Following Carl's interesting preference for slightly-better major
thirds at the cost of rather-flat fifths, I have been playing around
with his spreadsheet for dyadic entropy - to be precise the total
entropy of dyads within a triad. Intervals are rounded in cents, which
is why there may be some slightly unexpected values.

If I fix the minor 3rd to be 294c (~32/27) then the minimum total h.e.
is at 0-406-700, with 0-405-699 also making a strong showing.
0-402-696 has higher h.e. even than 0-408-702.

If I fix the m3 to 300, the minimum comes somewhere around 0-399-699
or 0-400-700, which may not be very surprising.

If I fix the M3 to 408, the minimum is for a fifth of either 702 or 703.

For a just 5th the minimum is at 0-387-702.
If I fix the fifth to 696, the minimum occurs for 0-385-696...

I wonder what would happen if one took a given m3 (E-G), divided it
into three equal fifths (G-D-A-E), then found the root C that gave the
major triad of lowest h.e.; then took the resulting m3 A-C and
repeated for F, etc...?
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> Following Carl's interesting preference for slightly-better major
> thirds at the cost of rather-flat fifths, I have been playing around
> with his spreadsheet for dyadic entropy - to be precise the total
> entropy of dyads within a triad. Intervals are rounded in cents,
> which is why there may be some slightly unexpected values.

I may have updated it since you downloaded it
http://lumma.org/stuff/DyadicHarmonicEntropyCalc.xls
it delays rounding an extra step now. But ultimately
it's still looking up h.e. values to the nearest cent,
rather than calculating them on the fly.

-Carl