In a message dated 98-01-30 06:49:13 EST, you write:
<< Greetings,
(I'm changing thread titles, hoping to focus the subject more closely, >>
Thanks, Ed for introducing a new title. I think the temperature under our
collars has cooled off enough and that we can now continue with a
constructive, civil discussion that sticks to the issue and does not have to
contend with scurrilous accusations of unethical, illegal or "abnormal"
practices.
Tom posted earlier;
<< Since a pianist does not have the capability to adjust intonation when a
modulation occurs, I submit that a "neutral" tuning is a very desirable.(snip)
I'm not against HTs per se but think that, for most situations, an instrument
that is called upon for playing such a vast array of music needs to have the
most versatile tuning possible. (snip) How do you choose a temperament? I've
got 57 programmed into my machine and I'm confused. (snip)The instrument
should be transparent to the music. >>
These, I recognize is the most commonly held beliefs and they do seem
logical on the surface. From the time of Bach, tunings gravitated towards ET
being that composers wished to be able to use all 24 major & minor keys. From
today's perspective, it seems only logical to go to the point of neutrality
and be done with it. Why regress and create something that will inevitably
prove unuseable at some point or another?
We must not ignore the fact that ET had always been a consideration.
Helmholz did not invent it. Dr. Wm. Braide White was not the first to tune it
or propose that it be used. It was tried and rejected because in the early
days, it sounded very bad to the people of that time. It sounded bad on
harpsichords, fortepianos and organs. Those instruments have entirely
different characteristics than the modern piano. The music of the Baroque and
Classical periods was "geared" towards using those instruments.
Tuning at the time was "geared" to the music that was actually being
written and to make those instruments sound pleasing to the ear and to
contemporary taste. As the piano developed, so did musical complexity. The
piano that Chopin used was far different from what Bach and Mozart had.
Chopin chose to write primarily in the remote keys because he craved the
energy and brilliance he derived from them on his piano. The simpler keys
just sounded too "dull" with poor leading tones.
Since keyboards have always, and still are the tools of composers who
write music, the character that a certain key has, because of the way the
instrument is tuned, has become part of music as we know it. Strangely
enough, this concept of character has persisted to the present in spite of ET.
I personally believe this to be true because of two things: traditions in
harmonic concepts that have never been lost and the fact that since it is so
very difficult to actually truly neutralize a scale, especially by ear alone,
piano tuners, by and large, never really did until very recently, even though
they may well have believed that they were tuning ET and that ET had been in
use since the time of Bach.
Indeed, as soon as the Well-Tempered Tunings were developed, where the
restriction of the "wolf" was eliminated, the tunings were called "equal"
because now all 24 major and minor keys were equally accessible although they
were most definitely not equal in character (color) or equally tempered. As
some have already pointed out in this discussion, those earlier instruments
were very unstable compared to ours today. Even if someone were trying to
tune a true ET, it might not have held up through a single movement as such.
What many of today do not realize is that the "errors" or inequalities
that may be in the temperament do matter very much. If one's temperament is
not truly equal, then the speed of the 3rds and the tempering (or purity) of
the 5ths introduce color to the temperament where there is supposed to be no
distinction. If that color is in line with the Cycle of 5ths, it will
actually enhance the way the piano sounds and is a good thing as I will
explain futher on. If it is at random or in opposition to the cycle of 5ths,
then it is actually destructive because it runs contrary to the way virtually
all music since the early Baroque and into the present (with very, very few
exceptions) has been conceived. Tragically, I'm afraid that common practices
often to result in this kind of "Reverse-Well" temperament and this fact is
not realized and/or ignored. The belief remains that the temperament is
"equal" and any small errors don't matter.
What was far more practical in the early days was to give the keys their
character (color) based upon the cycle of 5ths. Any instability could be
tolerated until the instrument was out of tune enough to require a complete
tuning. So, even though there were all of these numerous small variations in
bearing plans and small resultant character (color) differences between them
and even though so many people had their own ideas about which temperament was
best, none of these small differences had much real effect on the outcome of
the music at the time. It was all cycle of 5ths based and every temperament
had the same basic characteristic: Tonality progressed through the cycle of
5ths from smooth and harmonious at the top to brilliant and strident at the
bottom. (I am ignoring for the purpose of this discussion any of the odd
tuning concepts that were never widely used, I am speaking of the meantones,
the modified meantones and the Well-Temperaments).
Composers always chose to write in a key that reflected the character they
wished to create. There have always been 2 basic kinds of major tonalities
and 2 basic kinds of minor. If you truly tune a keyboard in ET, you quite
effectively reduce your choices of basic character from 4 to 2. In doing so,
you create 2 new types that never existed before.
Tom Cole asserts...
<<You might even say that the piece and the temperament are integral. Of
course, that same logic could be applied to works written since ET. >>
There was only one very brief period, in the early 20th Century when music
writing theory truly went atonal. As I said in my humor piece, "...it is
rarely, if ever played. It's really awful, in my opinion. It has no harmony,
no melody, no good beat to it or anything". Owen Jorgensen adds his own
light humored observation to this in his lectures, "To introduce key color to
this kind of music would be to introduce something that was not designed or
intended, not to say that it might not help that kind of music actually sound
better!"
So now, what do we do with the modern piano, a versitile instrument, far
different in character from its ancestors and on which we wish to play
virtually all music from all periods?
Tom Cole adds...
>An ill-chosen temperament would detract from a performance but a >well-
chosen
and well-executed HT tuning might very well enhance a >composition.
Ed Foote answers...
An ill-chosen temperament is precisely what I hope technicians will learn
to recognize. A well-executed HT *will* enhance a composition written for
it. ( and a poorly chosen one will ruin a performance!)
Instead of looking to ET, which totally eliminates the character provided
by Cycle of 5ths based temperaments, I think we need to develop a body or
repertoire of temperaments that we can consider to be universally acceptable,
the way ET is thought to be. A few years ago, I was calling this concept, a
"Universally Acceptable Alternative Temperament" or UAAT (as in "Where y'at
wit' yo" UAAT's?") Marshall Hawkins admonished that he didn't like that word,
"alternative". It does make it sound like a liberal idea when in actuality,
the preservation of HT's might well be considered conservative.
I don't think there will ever be a one and only or "Holy Grail" as some
have called the concept. The obvious place to start however is with the
Victorian Temperaments which represent the very last Cycle of 5ths based
temperaments before tuning actually began gravitating towards true ET. There
are the Quasi-Equal Temperaments ("quasi" meaning "almost") but they are by
design not cycle of 5ths oriented and thus do not provide for the 4 distinct
modes that I mentioned earlier.
I have used for 6 years now a Victorian temperament that I have come to
call Equal-Beating Victorian. There are no set rules or in my view, any
"authentic" Victorian. There is a description as a very mild Well-Tempered
Tuning and several historically documented very small variations in how tuners
were tuning in the late 19th Century. While working on the Victorian style, I
came to notice that I could get a significant amount of the "Equal-Beating"
phenomonen that is associated with so many of the meantone and Well-
Temperaments. It is a very important feature. It lends harmoniousness and a
clean, clear, "in-tune" sound to a tuning that is not possible in ET.
There are, of course other tunings that can be in this repertoire. The
Thomas Young #1, the Vallotti, the Handel and the 1/7 Comma Meantone. There
are bound to be many more that will work and there are bound to be
contemporary technicians who will develop their own, as I and my friend Paul
Bailey RPT have. Remember that in 1982, Steve Fairchild came up with the same
idea as Antonio Franceso Vallotti did in the 18th Century. It's a very good
temperament. I've used it for piano concertos and would again, given the
right occasion.
Let's also not lose sight of the idea that we can tune a particular
temperament for a particular occasion. We can have concerts where there are
two or more pianos, each with a different character of its own and each with a
different tuning that reflects that character. This will present an expanded
business opportunity for us. All we need to do is get people used to and
interested in the idea.
I so often hear, "We couldn't do that!" "We have to have a piano you can
play in ALL the keys!" "Nobody can tell difference in all those
temperaments!" "We have to have consistency!" "We can't be jerking the piano
all around, ya know!" "We're lucky to be able to have ONE piano, let alone
TWO!" "ET is the BEST temperament, Bach invented it HUNDREDS of years ago
(sic) and it's been used ever since!" "I wouldn't want any MEAN tones coming
out of MY piano!", and so on, all negativity, all leading nowhere, all putting
the piano ultimately in jeopardy of extinction.
Here are some figures you can try on virtually any piano if you have an
SAT. They were the actual figures I came up with when I was presented with
the opportunity of tuning a Steinway B for the rehearsals of a newly
commissioned opera about the famous architect, Frank Lloyd Wright who lived at
one time in Madison and was born nearby. I still take care of the pianos at
his estate and tune every one of them with this temperament. The name of the
Opera was, "Shining Brow". It is an American English translation of the Welch
word, "Taliesin". This was the name Wright gave to his great house and estate
in Spring Green, Wisconsin. It is now a National Landmark.
For a time, this temperament was known as the "Shining Brow" temperament.
It was what I later developed into the Equal-Beating Victorian. If for no
other reason, I dropped the "Shining Brow" name because I did not want to risk
any copyright infringement of a name already legally claimed.
All values are read on octave 5. You must reset the SAT at note C4 so that it
stores the values on octave 5 and not 6 as it will do automatically. These
values can be used on virtually any piano, there will only be a slight
difference in the outcome from one piano to the next due to the individual
piano's inharmonicity. These are NOT deviations for an FAC program. You must
create your own octaves.
F3: 2.0 F#3: -2.5 G3: 2.0 G#3: 1.0 A3: 0.0 A#3: 1.0 B3: -2.0
C4: 2.5 C#4: -2.0 D4: 0.0 D#4: 1.5 E4: -2.5 F4: 2.5
Notice that there is no deviation from theoretical ET greater than 2.5.
This means that there is no note that is even 1 cycle deviant from theoretical
ET. It is completely compatible with any and all other instruments and can be
used to play any and all music from early to contemporary while leaving in the
inherent character (color) of the cycle of 5ths. There are NO WOLVES. There
are NO PYTHAGOREAN 3rds. There is virtually no sound that a contemporary
musician will find that seems out of character for the modern piano.
With all due respect to my colleagues and their concerns, I believe that
is within the bounds of ethics to use a temperament such as this with or
without explanation to the customer. While I would like to be able to explain
and inform each and every customer about it, there are indeed times when it is
not a good idea to talk about the work to be done, sometimes there is no one
to talk to.
At the end of this post is a copy of a set of instructions I had written a
couple of years ago on a Smith-Corona Word Processor for an aurally
constructed Equal-Beating Victorian. The most difficult part is in the 1st 3
notes where some estimating is required, as it is in ET. I figured out how to
do that with consistency with an SAT and wrote to Jim Coleman a month or so
ago on how to do it. If you'd like to construct the EBVic by scratch and
store it in the SAT, follow the instructions for the first three notes, then
do the aural instructions and enter the results as you go. You can use the
direct interval method for the 4 pure 5ths that are part of the temperament.
To sample the effect of this temperament however, simply use the values for
the temperament listed above which is from where the below was derived.
The most difficult part of the temperament is the first three notes (as they
are in ET). If you are using an SAT, your F3-F4 octave must all be read on
the 5th octave. I use the same partial selection as the RPT Exam does. The
3rd, 4th & 5th octaves are all read on the 5th octave. In this way, I can
make my numerical values more rational. The manual tells how to change the
partial selection to accomplish this.
If you are using the SAT to assist, first, you need to sample the
inharmonicity the old "Stretch Factor" way (explained in the Manual) by
reading the difference in value between the 5th and 6th octave on note F4. A
reading of 4.5 or below is considered "low". A reading of 4.6 to 5.9 is
considered "moderate" and a reading beyond 6 is considered "high"
inharmonicity.
Next, tune A3 to 0.0 (read on the 5th octave). Then go to E4 (read on E5).
If the Inharmonicity (I) is low, dial in -2.5 and store. If the I is
moderate, store -2.0, if it is high, store -1.5. Next, by direct interval,
tune a 3rd down from E4 to C4. (See the Manual for Direct Interval tuning).
If the I is low, tune a 6.5 cent 3rd and store C4 at that value on C5. If
the I is moderate, tune a 7.0 cent 3rd, if it is high, tune a 7.5 cent 3rd and
store C4.
Now you have your 1st 3 notes. Proceed with the aural instructions and
use the Direct interval method for tuning the pure 4ths and 5ths that are
indicated and store the resutls of aural equal beating intervals as you go.
My usual method for stretching is outlined at the end of the instructions.
Equal Beating Victorian Temperament
(Equal Beating Victorianized Modified Meantone Temperament)
Instructions for Aural Tuning
1. Tune A4 to A-440 pitch source.
2. Tune A3 to A4, a 6:3 type octave.
3. Temper E4 from A3, a narrow 5th, at 1 beat per second.
4. Temper C4 from E4, a wide Major 3rd to beat at 6 beats per second.
5. Temper G3 from E4, a wide Major 6th so that it beats exactly the same
as the C4-E4 3rd.
6. Temper B3 from G3, a wide Major 3rd so that it beats exactly the same
as both the C4-E4 3rd and the G3-E4 6th.
7. Temporarily tune D4 a pure 4th from A4 then notice the strong beat
in the 5th G3-D4 and sharpen D4 until the beat is exactly the same
in both the G3-D4 5th and the A3-D4 4th.
8. Tune F3 a pure 5th from C4. To check this interval, use G#2 as the
test note and prove that the Ab2-F3 6th beats exactly the same as
the Ab2-C4 10th.
9. Tune F4 a pure 4th from C4. To check this interval, use G#3 as the
test note and prove that the 3rd Ab3-C4 beats exactly the same as the
Ab3-F4 6th.
10. Verify the F3-F4 octave. Using the test for a pure 5th which chooses
the lowest coincident partial of F3 & C4 and the test for the pure 4th
C4-F4 will yield a properly stretched octave, usually a compromise
between a 4:2 & 6:3 type.
11. Tune Bb3 a pure 5th from F4. Use the test note C#3 to prove that the
Db3-Bb3 6th beats exactly the same as the Db3-F4 10th.
12. Listen to the resultant 3rd, Bb3-D4. Temper C#4 so that the A3-C#4
3rd beats exactly the same as the Bb3-D4 3rd.
13. Tune F#3 a pure 5th from C#4. Use the test note A2 to prove that the
A2-F#3 6th beats exactly the same as the A2-C#4 10th.
14. Tune G#3 a pure 4th from C#4. Use the test note E3 to prove that the
E3-G#3 3rd beats exactly the same as the E3-C#4 6th. The Ab3-C4 3rd
will beat exactly the same as the F#3-A#3 3rd.
15. Temporarily tune D#4 a pure 5th from G#3 then notice the strong beat
between D#4 & A#3 and flatten D#4 until the G#3-D#4 5th beats exactly
the same as the A#3-D#4 4th. The B3-D#4 3rd will beat very rapidly,
at least as fast as the F#3-A#3 & Ab3-C4 3rds below and similar to
but perhaps not quite as fast as the D#4-F4 3rd above.
16. When expanding the octaves do so in a manner which will cause the
2nd inversion major triads of C, G, D, A, E, & B to have the 3rd & 6th
beat exactly the same.
17. When expanding the outer octaves, try to reconcile the double octave
and the octave and a 5th (12th) so that the double octave and the 12th
beat exactly the same. This will naturally result in octaves which
vary slightly in size up and down the keyboard.
Bill Bremmer RPT
Madison, Wisconsin
P.S. Tom Cole says in summation...
<<This discussion of temperaments reminds me of our endless arguments over
membership categories. >>
There is a similarity. Many are perfectly content with ET as the standard
and do not want any change. Many others recognize that ET is not perfect, it
does not suit all requirements but feel it is still the best compromise they
know of and until somebody comes up with something else that is seriously
credible, they will stick with it. Then there are those (like me) who are
constantly asserting the wrongness of the way things are and are vigorously
trying to find something that people will pay attention to, consider and
accept.
What do you think?
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