Dan, Dave, experience, entropy

[let's have all future discussion on this topic referred to the harmonic
entropy list, OK]

Basically, the definition of "small" in Dave Keenan's "Small Whole-number
Frequency Ratios" is a fuzzy thing, both in Dan Stearns' experience, and in
the predictions of harmonic entropy.

Take a look at
/tuning/files/perlich/stearns.jpg.

Now the simplest ratios for which product rule and harmonic entropy (s=1.5%)
give different rankings are 7/2 and 5/3. Entropy says 5/3 should be more
consonant, while product says 7/2 (7*2 = 14 < 5*3 = 15). So it looks like in
applying the "rule of thumb" we'll have to reduce the thumb from 99 to 14,
not 98 (assuming this particular value of s is relevant in the situation at
hand; and, needless to say, that the harmonic entropy model correctly
predicts experience).

But the general correlation between product and entropy continues on up to
about a product of 35, after which it begins to "unravel". By far the worst
exception below 100 is 11/9, at the end of an extremely anomalous "arm" that
includes 18/5 and 12/7. 11/9 has a product of 99, and 18/5 a product of 90,
but both have an entropy lower than that of 8/5 (product 40).

[let's _really_ have all future discussion on this topic referred to the
harmonic entropy list, OK]

Here's the same thing with about eight times more ratios seeding the entropy
calculation:

/tuning/files/perlich/stearns2.jpg

You can see that 11/9 is still ranked as more consonant than 8/5 when s=1.5,
despite other small changes in the rankings.