RE: [tuning] Re: plethora of pentatonics

Hi Jason, and thanks for taking a look at this.

>I have to look closer at the list. At first glance there are a lot of
>intervals between common JI/meantone intervals, but as we go further down,
>there are some interesting anamolies. The first scale with disc. 40.01 is
>do re mi fa so in meantone, except the third is flat by 3 cents. The minor
>version below it also has a flat major third. Looks like the optimizer
>prefers a just minor to a either a just major third or a comprimize between
>the two in this scale, because this give the widest minor second. From a
>musical standpoint that sounds like a bogous reason, and I think it
>partially vindicates John's observation about the seconds being
>overweighted as harmonic elements, although you can't solve that by leaving
>the seconds out of consideration.

Hmm . . . well, I wouldn't take 3 cents too seriously, so I would just call
this "pseudo-meantone", but I see your point. Again, the only "musical
standpoint" that is addressed here is that of all intervals in the scale
getting equal playing time. If you want to ask a different question, that's
fine, and the answers will correspondingly be different. I happen to agree
that in real music one wants to allow the dissonant intervals to be as
dissonant as they care to be in order to make the consonant intervals more
consonant. However, that presupposes a decision about _which_ intervals
(i.e., which entries in the interval matrix) are dissonant and which aren't,
a decision which might cause this search to leave out some interesting
possibilities.

All your other comments are good ones too.

-Paul