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Guitar Tuning for Man of La Mancha

🔗Billbrpt@aol.com

7/21/2002 3:31:33 PM

List,

Once again, as I expected would be inevitable, I had to intervene in the
production of Man of La Mancha by our local theater company for the tuning of
the on stage guitar. The company simply could not find a guitarist willing
to attend all of the rehearsals and do everything else that is required. One
of the youngest singers and actors has a guitar however, and is learning to
play it. He offered to do what he can.

He has an electronic tuner for it and a clamp on capo bar. The first few
times he played, I just listened to whatever sound he was getting. He really
is only playing during 2 numbers, the opening Flamenco style chant (some
chords in Bb minor) and for the song, "Little Bird, Little Bird" in which I
am the principal vocalist. He really is exposed in this number, however
because he will be the only instrumentalist heard. There will be no other
orchestra accompaniment. Naturally, I have a vested interest in what kind of
sound will be my accompaniment.

The G major chord he plays for the Little Bird song sounded pretty sour to
me, even more than Equal Temperament is supposed to be. I told him I knew of
a special way to tune that would make it sound much sweeter. He agreed to
have me help him tune it for the next rehearsal. I brought in my Sanderson
Accu-Tuner in which I had set up the Vallotti style Well Tempered Tuning for
guitar that I had designed under very similar circumstances 10 years ago.

I got the very same reaction I have witnessed every single time I have done
this: the jaw drops, the eyes open wide in amazement at the beautiful sound
of the harmony produced by tuning the guitar this way. I then had him clamp
on the capo bar and play the Bb minor chord that goes with the Flamenco style
chant: another look of amazement at the beautifully clear but dark and
disturbing sound of the minor chord in 5 flats in a true, Well Tempered
Tuning. The F Major dominant chord of that key also sounds beautifully clear
and true.

Now, I have written about this before and had any number of people, all
guitarists of high degrees of skill tell me rather specifically and often
quite harshly that this *cannot* be done! Needless to say, I have heard much
the same kinds of hard headed opinions about the way I tune the piano but
obviously, I have never believed in what anyone told me, I have only believed
in what I hear as the results of my work.

Below are the actual figures programed into my Accu-Tuner. They may not look
"right" to you. But ask yourself, has any set of figures for tuning the
piano, regardless of temperament ever looked "right" or logical? They don't
because of the omnipotent presence of the factor known as Inharmonicity. All
of these values are read on Octave 4. That means that the lowest two strings
are read on the 4th partial, the middle three on the 2nd partial and the
highest on its fundamental.

When Inharmonicity is taken into account, it skews everything, making the
numbers appear irrational. These figures were arrived at however, by aural
tuning first, then reading the results with the Accu-Tuner. The figures were
rounded off to convenient whole numbers, much the way I round of my figures
to the nearest 1/2 cent when creating a piano tuning program. The figures
can also be halved which creates a "Victorianized" version of the same idea.

IMPORTANT: All Values are Read on Octave 4

Note Vallotti 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

My piano technology apprentice, Tyler Smith has been to a rehearsal of the
show and heard how the piano tuned in Equal Beating Victorian Temperament
(EBVT) (click on the link to my website for information on that) and saw how
the guitar was tuned. Although he is only 18 years old, he is quite well
read and knowledgeable in many subjects. He was born in 1984 but he has read
George Orwell's novel by that same name as well as other books by the same
author.

I found it interesting that he knows that author and interprets the stories
much the same way I do. The Guild of American Luthiers has a web page which
explains its views on how a guitar should be tuned. My comment about that
writing is that it looks like George Orwell himself had written it. It
basically says that you cannot do what I have done, don't even think about
it. Just do what Big Brother tells you is right and eventually, you'll learn
to like it.

Here is the link to that web page:

http://w3.ime.net/~cygnus/equal_temperament.html

The web page is really meant to instruct guitarists on how not to make the
same basic errors that piano technicians are prone to making by tuning 4ths &
5ths too purely. If the open strings of the guitar are tuned to pure 4ths
(and the A2-E4 octave and 5th made pure), the 3rd, G3-B3 and the 6th, D3-B3
will be far too wide, having a "sour" sound to them and effectively be
Pythagorean 3rds (22 cents wide). The web page teaches the guitar tuner not
to tune the intervals so purely but it also says that there is no other
alternative.

All I do with both of my above arrangements is simply temper the 4ths & 5ths
a little more. The Valotti style temperament has the 4ths and 5ths tempered
exactly twice as much as Equal Temperament. I have learned over the years to
question and prove wrong such iron fisted statements as are made in the
Luthiers Guild web page.

There has been much the same kind of teaching about piano tuning for the last
hundred years but more and more, people are beginning to realize that there
really are some alternatives to Equal Temperament which can and do work
really well with all of the kinds of music the piano is expected to play. I
see no reason this can't be so with the guitar as well. I did once see a
guitarist of the highest caliber from New York who took a lot of time on
stage carefully tuning his guitar in exactly the same way as I describe below.

Here are the aural tuning instructions for accomplishing the Vallotti style
Well Tempered Tuning on a six string guitar.

1. Tune A2 to A-440 fork or other aural pitch source.

2. Tune E4 from A2 a pure octave and 5th first, then flatten E2 until the
Octave and 5th has a lilting beat to it, about 1 beat per second.

3. Tune E2 from A4 a pure 4th first, then flatten E2 until the 4th beats at
2 beats per second. This should create a slightly stretched double octave
from E2-E4. The double octave should have a very slow, roll to it of about
1/2 beat per second.

4. Tune D3 from A2 a pure 4th first, then sharpen D3 until the 4th beats at
2 beats per second.

5. Tune G3 from D3 a pure 4th first, then sharpen G3 until the 4th beats at
2 beats per second.

6. Tune B3 from E4 a pure 4th first, then flatten B3 until the 4th beats at
2 betas per second.

The results of this should be that the 3rd, G3-B3 and the 6th, D3-B3 now also
beat at the same slow, 2 beat per second rate. When all of the 4ths and the
3rd an 6th all beat at the same slow, gentle rate, the tuning is accomplished.

Bill Bremmer RPT
Madison, Wisconsin
<A HREF="http://www.billbremmer.com/">Click here: -=w w w . b i l l b r e m m e r . c o m =-</A>

🔗graham@microtonal.co.uk

7/23/2002 6:56:00 AM

In-Reply-To: <50.eaf03be.2a6c9045@aol.com>
Bill Bremmer wrote:

> I found it interesting that he knows that author and interprets the
> stories much the same way I do. The Guild of American Luthiers has a
> web page which explains its views on how a guitar should be tuned. My
> comment about that writing is that it looks like George Orwell himself
> had written it. It basically says that you cannot do what I have done,
> don't even think about it. Just do what Big Brother tells you is right
> and eventually, you'll learn to like it.

You can optimise the sound of one chord shape, but for all the chords to
sound this good you need to move the frets around.

> All I do with both of my above arrangements is simply temper the 4ths &
> 5ths a little more. The Valotti style temperament has the 4ths and
> 5ths tempered exactly twice as much as Equal Temperament. I have
> learned over the years to question and prove wrong such iron fisted
> statements as are made in the Luthiers Guild web page.

Then it's really a meantone, not a well temperament. You can use a
meantone fretting on a guitar. I find it works well.

Graham

🔗M. Schulter <MSCHULTER@VALUE.NET>

7/24/2002 12:54:36 PM

Please let me quickly try to clear up a possible misunderstanding.

In a Vallotti-Young tuning, six of the fifths are tempered narrow by
1/6-Pythagorean comma (indeed precisely twice as much as in 12-EDO), while
the other six more remote ones are at a pure 3:2.

This indeed produces a 12-note well-temperament with elements of "key
color." In the 18th and early 19th centuries, it could represent a
comparatively "moderate" approach in comparison to Werckmeister III, or to
a scheme like the Earl of Stanhope's with three fifths tempered by
1/3-Pythagorean comma and the rest pure.

A temperament where _all_ the regular fifths are tempered by
1/6-Pythagorean comma would, of course, represent a kind of meantone, also
comparable I might guess to something like 55-EDO.

Most respectfully,

Margo Schulter
mschulter@value.net

🔗Aaron Brick <aaron@lithic.org>

7/24/2002 6:59:29 PM

hello bill,

> When Inharmonicity is taken into account, it skews everything, making the
> numbers appear irrational.

i'd like to read about the concept of inharmonicity. do you have any
relevant reference or link?

thanks,

aaron brick.

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