Choosing a Temperament

Billbrpt@AOL.COM Billbrpt@AOL.COM
Mon, 9 Aug 1999 21:03:41 EDT


Dear List,

I am glad to see that these issues are still of interest.  I would like to 
relay some recent experiences and also comment on recent points made on the 
List.

<<From what I remember Barbour did not believe even in 1934 that many tuners 
acheived ET. >>

<>

In my early years as a tuner, the 1070s I learned from a 4ths & 5ths 
temperament too.  I was instructed that 3rds should have a very rapid beat 
but that was all, nothing about progressions and certainly nothing about the 
4:5 ratio of contiguous 3rds.  I believed that what I was tuning was ET too 
but later realized that what I really was tuning was a crude form of a 
Well-Temperament.

In my understanding of what has been written about late 19th Century tuners, 
they believed in the concept of ET and were gravitating away from the very 
unequal kinds of temperaments such as 1/4 Comma Meantone and even the very 
unequal Well-Temperaments like Kirnburger's and Werkmeister's but still 
somehow retained an alignment with the Cycle of 5ths that produced true key 
color, defined as different sizes and speeds of the Rapidly Beating Intervals 
(RBI) (the 3rds, 6ths, 10ths & 17ths) that corresponded to the key signature. 
 This alignment satisfied Werkmeister's Rules for Well-Temperament and that 
is why the late 19th Century temperaments more closely fit Werkmeister's idea 
for temperament than what we expect from ET today.

They were tuning the different variations of what we call today the Victorian 
and Quasi-Equal Temperaments but may have at the same time thought of them 
and believed them to be "equal" temperament.  I don't see how this is any 
less logical or less mistaken than the perception we hear today that a little 
variation in the 3rds is of no importance or consequence, it is still somehow 
"equal" regardless, as long as the intent and belief in ET is there, the 
results are accepted as ET.  It is also no less logical than to believe that 
ET which by its very nature and definition is bereft of tonal distinction, 
still retains some kind of "color".

For the past three weekends, I had the privilege of being the concert tuner 
for a chamber music series at the Frank Lloyd Wright estate in Spring Green, 
Wisconsin, about 40 miles West of Madison.  Ever since I auditioned for and 
made the cast for a new Opera that was written about the famous architect, I 
have been inspired by this great man's work and ideals.

The name of the estate is, "Taliesin", (pronounced "tally-EH-sin"), a Welsh 
language word which reportedly means, "Radiant Brow".  It was what they 
called a Medieval poet who was known to be very wise and a clairvoyant.  His 
face and forehead were said to have had a glow about them, I suppose much 
like we imagine a saint to have had a halo.  Apparently, it was a Welsh 
tradition to give one's home a name.  So when Frank Lloyd Wright built his 
beautiful home in the brow of a hill south of the village of Spring Green, he 
named it "Taliesin".

The conceivers of the new opera dubbed it "Shining Brow", an Americanization 
of the usual translation, "Radiant Brow".  As a member of the cast, I was 
required to study a lot about the man and his works.  He was quite the 
individual and was very arrogant.  He was once quoted in an interview as 
saying about his arrogance that he preffered "honest arrogance rather than 
phony humility".  It was plainly obvious that he did not care what his 
critics thought of him.  Many even considered him unethical and immoral.  He 
rarely if ever apologized for anything that went wrong but continued to 
challenge himself to create architectural masterpieces that have had a 
profound and lasting impact worldwide.

I have taken care of the pianos at that estate for many years, even before 
the opera was commissioned.  When called upon to tune the piano(s) used for 
the rehearsals of the opera, I studied the score.  It used many different 
keys for different moods and characters.  It also occasionally used 
polyphony, that is, two unrelated keys at once.  I decided not to go with 
what I knew to be conventional wisdom, ET,  but to try the Victorian idea 
which is to be as close to ET as possible but still retain a distinct color 
for each and every key, in an alignment with the cycle of 5ths.

Owen Jorgensen's Book, Tuning had not yet been published but he had given a 
preview of the Usual Broadwood Temperament and also the idea that one could 
use one's "own personal taste" to alter or modify any temperament to suit 
one's needs.  I could not follow the instructions for the Victorian well 
though because there were only theoretical beat speeds given, all 
"irrational" numbers and no compensation for inharmonicity.  Somehow, I felt 
divinely inspired and came up with an idea that has worked for me ever since. 
 I used the concept of Equal-Beating to greatly mitigate a Modified Meantone 
Temperament from Owen's second publication, the "Handbook".

The people at Taliesin and the Opera conductor and music director were always 
and continue to be supportive of my goals.  It fit their philosophy and it 
gave some individuality and diversity, two things which Wright thought were 
important, to their work and environment.  The piano used in the Hillside 
Theater at Taliesin is a 100 year old Bechstein 9 foot grand which has all of 
the original strings but which has had the action replaced with new Renner 
parts and hammers.  The strings have been cleaned.

During this chamber music series, the theme of which was "The Killer Bees"  
(all of the composers names begin with the letter, "B"), I once again used 
the Equal Beating Victorian Temperament (EBVT).  It served J. S. Bach, C. P. 
E. Bach, Beethoven and Brahms well, as you might expect but most notably, it 
served more modern music such as the Irish Folk song, "Down in the Sally 
Gardens" for flute and piano played in six flats.  There was no "sour" sound, 
only a vibrant "humming" sound that was very pleasing to the ear when that 
beautiful melody was played on the flute accompanied by the piano.

It also served the music of Samuel Barber, Leonard Bernstein and Bela Bartok 
but my favorite was a quintet by Ernest Bloch (1880-1859), a multi-tonal, 
modern, extended harmony piece which ended on a gently decaying C major 
chord.  Ironically, the Beethoven Trio in C minor also ended on virtually the 
same chord, leaving behind the inevitable sad sound of the minor key to the 
pleasant and quiet stillness of C Major.

The EBVT contains several instances of triads which contain equally beating 
RBI's.  These have a "canceling out" effect which make extended chords played 
in those keys sound much purer than they really are.  This effect is not 
possible in a true ET. The conservative tempering at the top of the Cycle of 
5ths also allows me to have RBI's at the bottom of the Cycle of 5ths:  Ab, 
Db, F#, B (which sound too harsh for many people in most HT's) that are well 
below the threshold of tolerance for today's listeners, no more than 18 or 19 
cents wide at the most.  (Not quite as "sharp" as the ear can well bear).

The powerful and extensive Brahms Quintet in F minor sounded lush with the 
different colors.  There were times when you could hear the seemingly still 
chords and others when you heard full and rich vibrancy but never once could 
you hear anything that any listener of today, even a piano technician, would 
find harsh, objectionable or out of tune sounding.

But the last performance had what I considered to be the most interesting and 
intriguing, and it had nothing to do with the piano, it was the guitar.  
Consider these statements made recently on the List:

<<But the point is that lutes and fretted instruments being tuned in ET means 
that
people were hearing ET in music in 1637. Actually  a case can be made that the
best sounding lutes, guitars, etc can only have their frets arranged in equal
proportions.    The concept of ET or if you will mathematical predictions of 
ET have
existed at least since Mersenne. As to when ET was heard on strung keyboards, 
well
Barbour was still skeptical of tuners in 1934. Mersenne tries to give 
instructions
for tuning ET but in the end says it is the "secret of the masters"  It is 
not even
possible to draw conclusions from Mersenne that keyboards were actually tuned 
in ET,
but he sure gives indications that it was a goal, that it was something music 
could
look forward to. (Marin Mersenne _Harmonie Universelle_  trans Roger E. 
Chapman,
pub. Martinus Nijhoff / The Hague, 1957.) 
>  
> >The problem it seems is that ET was a goal, but no one knew how to tune
> >it. >>

Several months ago, I wrote that I had once figured out a way to tune the 
guitar in what I called a Well Tempered Tuning.  I immediately got responses 
that said the figures I gave "wouldn't work".  This being by an accomplished 
guitarist who did not even bother to try what I had said but who "proved" his 
statement by showing that the unisons would be "out of tune".  Another 
guitarist tried the figures and said that his guitar had sounded better just 
being plain out of tune than the way I had specified.

Well, I knew what the guitar sounded like in the performances of "The Man of 
La Mancha" in which the tuning was used and I also have seen the expression 
of delight many times when I have tuned the guitar for someone.  However, I 
can only strum basic chords, I am not an accomplished guitarist, so even I 
have had my doubts until last night when I heard a true master of the 
instrument perform on the guitar, in a Well Tempered Tuning.

I did not know this man, had never heard of him before and did not speak to 
him either before nor after the performance.  But what I did notice was that 
before each and every selection that he played in, in took plenty of time to 
very carefully tune his instrument.  When he was supposed to make some 
comments but had forgotten to do so about the "Fandango" by Luigi Boccherini, 
he apologized saying that he had been concentrating on the tuning of his 
guitar for this piece.

I could hear that the tempering that he put in his 4ths was much more than ET 
would require and that made his 3rds much slower.  He had many different ways 
to pluck the strings for different sound qualities and he knew all of the 
"geography" of the fret board.  When he played unisons, there was a distinct 
beat in them.  But this beating seemed to have the right musical quality to 
it.  I also heard other intervals that were much more tempered than what you 
usually hear.

Most professional guitarists these days have an electronic tuner based on ET. 
 They tune the string until the tuner indicates that it is right and they 
accept that as being correct.  Some will tweak that tuning a little bit but 
most play it just that way. This man was different and tuned just the way he 
wanted each time and very carefully.  I think it is an example of someone not 
blindly accepting conventional wisdom and actually going against it only to 
end up creating something far more beautiful because of it.

Some people who try to tune the guitar mistakenly tune all of its 4ths pure 
or they fret unisons and tune them pure.  This gives the guitar a 
"Pythagorean Tuning".  The open intervals are pure which, of course, sounds 
pleasing to the ear but the 3rds and 6ths are thus very harshly wide, 22 
cents.  So even if fret boards have been evenly divided for centuries, does 
it necessarily follow that *everyone* or even most people *always* tuned 
these fretted instruments in a strict ET?  I really don't think so.  I would 
require proof to be convinced.

So, for anyone interested, here is my "honestly arrogant" set of figures for 
tuning a guitar so that it will sound more beautiful than the usual way in ET:

All values are read on Octave 4:

E2: -4.0   A2: 0.0   D3: 2.0   G3:  4.0   B3:  -2.0   E4:  0.0

You can also do a "Victorianized" version of it which is milder:

E2: -2.0   A2: 0.0   D3: 1.0   G3:  2.0   B3:  -1.0   E4:  0.0

Don't ask any questions or say it won't work, just do it!  (and enjoy the 
beautiful chords).

Yours truly,

Bill Bremmer RPT
Madison, Wisconsin


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