What temperament is a guitar tuned? (still more)

[Billbrpt@aol.com]

In a message dated 6/2/98 5:56:52 PM Central Daylight Time,
tkeenan@kermode.net writes:

<<the two (simplest) ways I have just mentioned on your hypothetical
instruments would not work.
  Tim Keenan >>

I thank you for your time but I can only reiterate  what I said in the
previous post.  Before you declare something impossible, you should at least
try it first.

While I am pleased that you are not one of those who is eager to jump on my
back   insisting that ET is the only, always was and always shall be the only,
possible and useful temperament,  I must respectfully say that there is
something wrong with your conclusions.  Unfortunately, it sounds a little too
much like all the things I've heard about pianos and how such and such
temperament "couldn't work" and  "wouldn't work" yet when real music is played
with it, it turns out to be a fascinating enhancement.

I have given those guitar specifications to many people and none have said
what you did.  They only said how good it sounded.

If you, as a guitarist, alter your tunings a bit from strictly ET so that
certain harmonies sound sweeter, you are essentially doing what I described
here.  You have to remember that in order to be "equal" you cannot have any
variation of any kind. If you claim that what I hypothesized "wouldn't work"
then you would have to say that whatever you do "wouldn't work" either. Yes,
there is a limit to how far one could alter the guitar's tempering before
normal playing would become unacceptable but I don't think my figures are at
that limit.

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. It seems logical to them but it, in fact, creates a Pythagorean
style tuning in which all the 3rds and 6ths are very wide. Some Country &
Western performers,  especially the Cajuns in Louisiana like that kind of
sound.

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:

Tune A2 to the fork.
Tune E4 to A2 first a pure 12th, then flatten E4 until it beats at 1 strong
beat per  second.
Tune E2, a double octave to E4, as wide as possible without creating a
noticeable beat.                                                     
Check the 4th, E2-A2 for about 2 beats per second.
Tune D3 to A2 first a pure 4th, then sharpen D3 until it beats 2 beats per
second.
Tune B3 to E4 first a pure 4th, then flatten B3 until it beats 2 beats per
second.
Listen to the 6th, D3-B3. It should beat gently, 3-4 beats per second.
Tune G3 to D3 first a pure 4th, then sharpen G3 until it beats 2 beats per
second.
Check the 3rd, G3-B3.  It should beat gently, 3-4 beats per second, exactly
the same as
     the 6th, D3-B3.  If these checks don't agree, tweek your intervals,
evening them out 
     until they do.

Now, as a musical test, play your favorite music normally.  Avoid trying to
"prove" that this will "not work" (the way piano tuners like to "prove" that a
WT or other HT "won't work" by "banging" on the intervals they think sound
"sour").  In other words, play normal musical contexts,whatever they might
be,donot try to find obscure intervals and play them out of context.  Even in
ET,you cannot have a pure unison on a fretted six-string guitar unless you
tune in Pythagorean intonation.  Absolute purety of a  unison or octave does
not have the same importance or value on the guitar as it does on the piano.
It doesn't between other intruments or voices either. 

I think you will find that a real musical context will indeed work.  If you
think this idea is perhaps good but simply goes too far, you can try the
"Victorian" version.  As you can see by the digital information, all of the
tempereing is cut in half from the 1/6 ditonic comma WT. Your 12th and 4ths
will beat just a little more than in ET.  Your 3rd and 6th will beat more
gently than in ET, a slightly "sweeter" sound.

I hope you discover something that really pleases your ear.

Bill Bremmer RPT
Madison,Wisconsin