temperament

[Billbrpt@AOL.COM]

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n a message dated 1/2/01 7:05:11 PM Central Standard Time, 
cneuman@phy.duke.edu (Charles Neuman) writes:


What is the temperament of a guitar? As I understand it, the strings are
tuned to each other in perfect intervals, so it can't be equal
temperament. The frets determine the intervals on each string. Do they
make an equal tempered scale on each string? 

There lots of interesting comments.  Both Richard and Ed I agree with.  What 
I have seen so many people do is to tune the bottom 4 strings pure and the B3 
to the E4 as pure with the E2-E4 double octave pure:  essentially a 
Pythagorean tuning.  Then when the strum the chords they want to ply, it 
sounds terrible so they start trying to make them sound sweeter.  It's as 
simple as that.

Some experienced musicians know how to get what they like more methodically 
than others but in general, they have no concept of a *tempered* interval, 
only a pure one.  Other string players mostly try for pure 4ths or 5th, as 
the case may be.  O good bass player, however knows to tune his 4ths wide.  
In many cases, these "pure" intervals may in fact be tempered just a bit 
haphazardly, and may, in fact, be tempered the wrong way.  It is all in how 
much experience and in depth knowledge the individual musician has.

Here is my take on the guitar:  It is *designed* for Equal Temperament.  
There, aren't you surprised?  I actually admitted that a musical instrument 
was *intended* to be tuned in ET!  However, (and you *knew* I was going to 
say something that would *destroy* the monolithic ideal of ET, didn't you?) a 
true and perfect ET is rarely attained for the same reasons it is difficult 
on the piano.  People don't know enough about how to get the temperament 
truly equal so they make typical errors which are the result of typical but 
misguided tuning habits.

A guitar nicely tuned in ET does not sound bad but it is possible to create 
somewhat of a Well-Tempered sound but only within a narrow range.  It is 
analogous to the Pythagorean type sound you get from tuning pure 4ths.  All 
you have to do is temper your 4ths a little more than for ET and you will 
have a sweeter sounding guitar.  But again, only up to a certain and limited 
point.  You cannot go all the way to 1/4 Syntonic Comma Meantone.  But what 
you can do is get about half way there with what ends up being a Vallotti 
type temperament.

The following is something I saved for some reason from a post I made a year 
and a half ago on this subject.  Be sure to search the archives if you are 
interested.  There are some who claim that only ET will work, otherwise the 
guitar is simply mistuned.  After that, I will post the two schemes which 
represent the two Well-Tempered possibilities there are for the six string 
guitar.


"I have only the most basic skills with a guitar but sometimes "necessity 
is the mother of invention".  I was among the cast of a production of The Man 
of La Mancha when it became apparent to me that I could help the guitarist a 
little by tuning his instrument for him.  The circumstances were that the 
Opera company, with its proverbial limited budget, could not find or afford 
an available well-qualified guitarist.

They did find someone who was a student of Spanish style guitar playing who 
looked good in the costume they had for him.  He not only had trouble tuning 
his instrument but also following the ensemble.  Everyone pitched in to help 
him, including me.  He had a fine guitar.  The fact that the guitar has a 
fret board which serves as a grid for ET is obvious.  I however theorized 
that you could still make a Well Tempered Tuning out of it by slightly 
altering the pitch of the various strings.

Now, the guitar does not have a C string.  The tonality of C is usually the 
center and starting point of all usable HT's.  There is one HT however which 
can easily be tuned from A and still get the proper C tonality, the Vallotti. 
 It is a very easy HT for ET tuners to understand:  All 5ths (or 4ths) 
between two black keys or a black and a white key are pure, the rest of the 
4ths & 5ths between the white keys are tempered exactly twice as much as in 
ET.

I could see how I could temper the strings of the guitar, E-A-D-G-B-E exactly 
the way I would on the piano, twice as much as in ET.  I reasoned that the 
frets then would provide the in between notes exactly the same as they would 
be found in a completely worked out scale.  It apparently worked.

I showed the orchestra conductor the results.  G Major for "Little Bird, 
Little Bird", as sweet as candy.  Then I showed him the difference between 
the serenity of A minor and the dark, disturbing sound of Bb and Ab minor.  
Both keys are found in the score.  The conductor was impressed and I had the 
guitarist tune each of his strings to the program I made for him in my SAT 
each time before he went on.  He ended up having a nice, on-pitch, 
professional sound.

But what I have shown you is about the one and only thing that you can do 
besides tuning in strict ET.  That is the limitation of the guitar.  You 
cannot do any and all other kinds of temperament schemes.  On another 
occaision, I saw a guitarist who, to my surprise, seemed to know how to do 
the very same thing I had experimented with.  The guitarist at the event was 
named Kevin Gallagher.  I hear he is from New York.

It was obvious to me that he knew many different ways in which he could 
manipulate the tuning of his guitar.  He also used some nonstandard tunings 
where he lowered the lowest two strings to make them play entirely different 
notes.  He was adept at pulling on the string to stretch it out and stabilize 
it after having changed the pitch radically.  The audience and other 
musicians waited patiently for him each time he retuned.  I have never seen a 
guitarist tune so meticulously and in such a variety of ways."


Chart for Well-Tempering the Guitar in either the 18th Century (Vallotti 
style) or the late 19th Century Victorian style.

*All values are read on octave 4*  (very important)

18thC  Victorian
E2:  -4.0     -2.0

A2:   0.0      0.0

D3:   2.0      1.0

G3:   4.0      2.0

B3:  -2.0     -1.0

E4:   0.0      0.0


Bill Bremmer RPT
Madison, Wisconsin


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