ET for Guitar

Billbrpt@AOL.COM Billbrpt@AOL.COM
Thu, 18 Jan 2001 14:47:46 EST


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In a message dated 1/18/01 12:54:58 PM Central Standard Time, 
tunenbww@clear.lakes.com (Paul) writes:


> Bill
> I've played guitar for years and accepted the "normal" way to tune. I very 
> interested in a "better" way. Do you know a better method?

This was discussed not too long ago.  Basically, the document from the 
Luthier Guild says what I have observed, that guitarists tend to tune the 
4ths of a 6 string guitar pure which results in a "Pythagorean" type tuning, 
e.g., the 3rds and 6ths are left very wide and "sour" sounding.  Of course, 
the musician does not like this sound, so he/she attempts to "sweeten" the 
tuning in an uncontrolled, haphazard way.

The document reflects the same belief that has been held since the time of 
Helmholtz: that the *only* solution can be ET.  What I believe, and what I 
have seen a few enlightened musicians do and what I have proved to myself 
many times over is that really for both the piano and the guitar, a *slight* 
tempering in the direction of a Well-Tempered Tuning *is* possible and it 
will result in a more musically pleasing sound.  There is a limit however, 
and the range within you can work is small.  Exceeding that range will result 
in unacceptable sounds as most people believe, fear and want nothing to do 
with.

For the guitar, it simply means that you will temper the 4ths a little more 
than you do for ET.  This produces more gently beating 3rds and 6ths in the 
simple keys and slightly faster, brighter sounds in the remote keys but still 
within a margin that the contemporary ear can accept and also and most 
importantly, in an alignment with the cycle of 5ths that is musically 
*appropriate*.  It does produce more noticeably tempered 5ths and unisons 
which are more imperfect than in ET but just as with the piano, these 
imperfect consonances are not at all troublesome in a real musical context.

This leaves all chords or "forms" as the Luthier Guild document calls them 
*accessible* although they are *not* equal.  That means that traditional Key 
Color is restored.  The document asks you to accept that this is not 
possible.  All I'm saying is that it *is* possible.  The document wants you 
to believe that you must accept the not-so-nice sound of ET chords, telling 
you essentially, "take it, and get used to it, because this is as good as 
you're going to get."  I have heard essentially the same arguments concerning 
ET for piano and I do believe that most people think that way, that the sound 
of ET is as good as can be produced on the piano, so you better get used to 
it and learn to accept that as a beauty of its own.

It all sounds too much like the kind of thought control that was the subject 
of George Orwell's novel, "1984", which is one of my favorite books.  I 
happen to think that Orwell saved much of the world from this kind of tyranny 
by illustrating it so well and powerfully in his story.  Anytime people 
believe there is too much government control in our lives, they cite the "Big 
Brother" image that Orwell created.  His story gives us the hope that we 
*can* resist this kind of domination and that we do not have to accept 
everything that is told to us, written in books or dictated to us by a 
controlling authority.  We do have the right and ability to question such 
statements as "...no further tuning adjustments are permissible."

The following is and excerpt form my post on the subject.  There are numbers 
posted at the bottom which can be used with an electronic tuner.  These 
represent the results of careful listening and tuning of the guitar by ear.

"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 
occasion, 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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