RE:

Justin White wrote,

>PS. Despite my mentioning of the 21st and 27th identies I have ear tested
>them and prefer the 11th and 13th harmonics in these circumstances.

OK!

>So I
>will probably venture further north and south and further north east and
>south west in my periodicity blocks [ie more 5 and 7 less 3]

11 and 13 are distinct primes and you'll never get them by combining any
number of 5s and 7s. So perhaps we should look at 13-limit periodicity
blocks -- or did I misunderstand you?

By the way, on a guitar, there are additional great advantages to using
equal temperaments -- same notes appear on all strings and frets go straight
across . . . . 41-tone equal temperament is consistent and very accurate
through the 13-limit. If you find the 41-tET approximations to your chords
acceptable, you will have access to an _infinite_ expanse of the
5-dimensional 13-limit lattice -- i.e., there will be no restrictions on
what kind of 13-limit consonant chord you can construct on any note of any
previous consonant chord . . . and then there are all kinds of intermediate
possibilities between 13-limit JI and 41-tET, just as meantone is
intermediate between 5-limit JI and 12-tET . . .