What temperament is a guitar tuned? (still more)

[Tim Keenan & Rebecca Counts]

Bill and List:

To quote Boss Caine in "Cool Hand Luke", "what we have heah is a failyuh 
to communicate."

First, I am uncomfortable with the word temperament here, because the 
intervals are fixed in one dimension, and cannot be tempered. The only 
intervals that can be tempered are those among the open strings.

I don't think you [Bill] have answered my one central problem.  Let me 
try to state it another way.  In any temperament system on a 
single-voiced keyboard intrument, once you have set a temperament, every 
occurrance of a given note, let us use A as an example, is tuned to the A 
in the temperament octave, except for a little stretching. There is only 
one key, integer, which locates a given pitch. 

On a guitar, a cartesian co-ordinate system locates the pitches, with 
strings along the y axis and frets along the x axis.  and there are 
several solutions for all but the lowest and highest notes; that is, I 
can produce the (theoretically)identical  pitch using several different 
fret/string combinations.

I attempted to show that for 1 solution in each case, the result would be 
an intolerable octave. But even if it is not intolerable, the point is 
that in any given temperament on a keyboard the same interval (say A-C#) 
has the same character or colour, in any register,  and that cannot hold 
true on a guitar.  On the contrary, all *parallel* intervals formed by 
moving that shape up the neck on the same pair of strings will have the 
same character (A#-D, B-D#, C-E# etc) whereas the interval A-C# will have 
a *different* character using any other combination of strings and frets.

>I must respectfully say that there is
> something wrong with your conclusions. 

I must respectfully ask you to tell me what that might be.  

>If you claim that what I hypothesized "wouldn't work"
> then you would have to say that whatever you do "wouldn't work" either. 

No, I just claim that a different "temperament" is required for most 
keys. 

> I did not comment on the other styles of tuning you mentioned because they did
> not involve the issue of ET vs. WT.  I have observed that many people tune
> their guitars by making solid unisons with a fret and open string as you
> describe.

On the contrary, I think you must have misunderstood what I was talking 
about. An open tuning is one in which all the strings on the guitar form 
a chord when played unstopped, or "open". Temperament is most certainly 
relevant to open tunings, and non-equal temperaments are probably 
particularly apt, because there are fewer different chord voicings 
used--mostly single note or double-stopped melody lines within a more or 
less fixed harmonic framework.
> 
> If you do not have an SAT and would like to approximate the 1/6 comma ditonic
> WT by ear, here is how you would do it:

I will certainly try it.  Never let it be said that I don't have an open 
mind.

Tim Keenan
Terrace, BC