Reply to dante rosati

>I find [Partch's] notion
>that what the ear responds to is ratios (as some kind of abstraction)
>rather than to the overtone series per se interesting but dubious.

Partch did not think of simple ratios as abstractions but appealed to
the regularity of the undulations they produced in the eardrum. He
related the consonance of an interval in a given register with the
shortness of the period of repetition of the waveform resulting from
both notes of the interval. This is not an implausible explanation of
consonance but note that (a) the slightest deviation from just
intonation causes the wave period to increase astronomically, and (b)
adding a higher identity to an otonal chord leaves the period untouched,
or perhaps multiplies it by 1, while adding a higher identity to a
utonal chord multiplies the period by orders of magnitude. (a) is
somewhat in line with Partch's hardcore JI-ism, but is quite silly in
light of the accuracy of actual instruments, instrumentalists, the ear,
and myriad tempering schemes. (b) spells disaster for the otonal/utonal
dualism that Partch espouses, and the inconsistency between this dualism
and the wave-period justification of consonance is probably the most
glaring inconsistency in Partch's theory.

>If it
>were not for overtones, there would be no beating phenomena that make a
>justly tuned interval just in the first place.

That is mostly true, but again, there are some other phenomena that make
otonal chords "special" even in the absence of overtones. Utonal chords
do, however, require harmonic overtones to be "special" -- the other
phenomena are related to the wave period so, as discussed above, do not
favor utonal chords in any way.

>I don't see 4/3 as an abstract utonal generation

Neither would Partch -- three or more notes are necessary to classify a
chord as "otonal" or "utonal".

>or some kind of "three
>limit" interval,

I don't see why you object to that.

>but rather as the interval between the third and fourth
>partial.

The third and fourth partial of what? Of the difference tone between
them? Or is it that the third partial of one note coincides with the
fourth partial of the other note? Both are true, but there are different
theoretical camps based on which fact is deemed more important for
explaining musical effect. These camps will agree that 4/3 is consonant,
but will disagree on issues such as otonal/utonal dualism.

>Alternately it can be thought of as dividing a string in 3 and
>then making another string 4 of those lengths. Or, it is 3/4 of a
string in
>relation to the whole string.

Why would these facts have anything directly to do with our perceptions?

>What I was wondering was does anybody know if someone
>is currently making a guitar with interchangable fretboards? I see a
real
>nice one in Scheider's book "The Contemporary guitar" (1985), that he
says
>is made by Tom Stone of Intonation Systems in Iowa. A search on the net
>turns up nothing, so I dont know if anything like this is being made by
>anyone. The series of fretboards is just what I would drool over -
various
>just, harmonic, historical and cultural intonations. Anybody who can
help
>me out here, I would appreciate it greatly.

Likewise. If you hear anything let me know. I'd like to have lots of
different guitars, but I'm holding out for interchangable fretboards so
I don't blow all my cash.