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In a message dated 9/16/02 7:49:41 PM Central Daylight Time,
kswafford@earthlink.net writes:
> I'm looking forward to seeing these figures. I have long thought that
> the problem with developing these figures has been the irregularity of
> lower partials about which Ron K is reminding us.
>
>
Thank you very much for your interest. As much as I know about the practical
matter of tuning, I know absolutely nothing about how to do this. I have
seen Owen Jorgensen do it many times. To me, it looked like he had this
secret formula. He could do it quite quickly too. When I asked him once to
explain itto me, he just looked at me and grinned.
I think I will send him the aural instructions as they are currently but not
yet changed on my website. Note that this is not a change in the temperament
itself, just the order of the notes tuned. This order was suggested in
feedback from people who have actually learned to tune it and don't subscribe
to Pianotech.
The only changes which have ever been made are simply which intervals to
specify and how in order to create the basic idea. Originally, the A3-E4 5th
was given a specification. But that was discontinued because I felt it would
have been far more subjective and subject to error than a specification for a
3rd. It was feedback from a few users who noticed that the F3-A3 3rd usually
ended up at the same rate as the C4-E4 & G3-B3 3rds and the G3-E4 6th that
gave me the idea I could create those intervals first and have the A3-A4 5th
occur as a consequence but still end up the same. So, in that sense, it was
simply a change in order of tuning the notes, not in the temperament itself.
The EBVT has never substantially changed the way some have suggested. Even
the option that I have said exists, as it does in some other historically
documented temperaments, to alter the speed of the initial Rapidly Beating
Intervals, is not mentioned yet in my bearing plan nor on my website. First
things first.
Here is the bearing plan as I simplified it for my apprentice. I can't throw
too much at one time to him, so the specification for a 6:3 A4-A3 octave is
simplified. I also took out the Tempered Octaves idea. That will come later
for him but it also can't be done with current ETD programs, as far as I
know. Again, first things first.
Instructions for Tuning the Equal Beating Victorian Temperament (EBVT)
1. Tune A4 to A-440 pitch source or tune to a pitch you can manage.
2. Tune A3 to A4, making it sound as a pure octave except that you will want
to flatten A3 just until you would start to hear a beat occur, then stop.
3. Temper F3 from A3, a wide 3rd, estimating it to beat at 6 per second,
just slightly slower than it would be in Equal Temperament (ET). Use your
metronome set at 120 and hear 3 beats per tick.
4. Tune F4 a pure sounding octave from F3. Don't try to stretch this one,
just make it sound pure. Notice that C4 and F4 now make a pure 4th.
5. Tune Bb3(A#3) a pure 5th from F4. Notice that F3 and Bb3 make a pure
4th. Play F3-Bb3-C4-F4 all together. There should be a very still sound, no
beating.
6. Temper E4 a wide 3rd from C4, making it also beat at 6 per second, the
same as the first F3-A3 3rd. (About half the speed of the same interval in
ET.)
6. Temper G3 from E4, a wide Major 6th so that it beats exactly the same as
the F3-A3 and C4-E4 3rds. (6 beats per second). This will make the G3-C4 4th
be tempered a little more than in ET.
7.Temper B3 from G3, a wide Major 3rd so that it beats exactly the same as
the F3-A3, C4-E4 and G3-B3 3rds and the G3-E4 6th. (Exactly 6 beats per
second). Now, the F3-D4 6th will also beat rapidly but a little faster than
the previous series of Rapidly Beating Intervals (RBI). It will probably beat
at 8 beats per second.
8. Temper D4 from both G3 and A3 so that both the G3-D4 5th and the A3-D4
4th beat at exactly the same mild rate. (Each one just slightly more tempered
than in ET). If you have trouble finding the right spot, tune either
interval pure first. The other will beat strongly. Temper so that the two
have the same, lilting sound.
11. Listen to the resultant 3rd, Bb3(A#3)-D4. Temper C#4 from A3, a wide 3rd,
so that the A3-C#4 3rd beats exactly the same as the Bb3(A#3)-D43rd. This
will probably be about 9 beats per second, about the same as in ET.
12. Tune F#3 a pure 5th from C#4.
13. Tune G#3 a pure 4th from C#4.
14. Temper D#4 from both G#3 and A#3 so that both the G#3-D#4 5th and the
A#3-D#4 4th beat exactly the same as each other (slightly less tempered than
in ET or nearly pure). If you have trouble finding the right spot, tune
either interval pure first. The other will beat more noticeably. Temper so
that the two have the same, lilting sound.
15. Tune your octaves up and down by making what sound like a pure octaves
except that going up, you will want to sharpen each note just until you would
start to hear a beat occur, then stop. In the very highest part, sharpen
until the octave sounds sweet to your ear. Going down, do a mirror image of
how you went up.
***************************************************************
I, myself would like to see what the projected figures for the E3-G#3, F#-A#
and Ab3-C4 intervals would be. These often end up Equal Beating for me,
enough so that I think I may end up specifying that and have good reason to.
After thinking about this and confirming what I thought, I decided to call
Owen Jorgensen and ask him if it was legitimate. He not only said yes but
indicated that this was one of the higher refinements in temperament
construction, a step beyond the theoretically correct.
In other words, if the EBVT stands the tests of harmonic balance analysis,
even if it only meets the constraints of the Modified Meantone group of
temperaments, according to Jorgensen, that is a different but closely
parallel group of temperaments in which these imbalance issues are not
necessarily issues at all. It has precedence and is authentic, according to
Jorgensen.
So, if things do check out as I expect they will, I would have grounds upon
which to say that yes, the Moore and the Broadwood are good, mild
temperaments which make the piano have a certain, appealing character. Many
have found it to their liking, the same with the Coleman 11 and others of
his. But the EBVT belongs to a class of more highly refined temperament
tuning, the kind which can also and should be, in the opinions of both
Jorgensen and myself, be done accurately by ear, the Equal Beating
Temperaments.
Think about the position in the scale of the following intervals:
B2-D#2 Db3-F3 E3-G#4 F#3-G#3 Ab3-C4 B3-D#4 Db4-F4
I can usually get the first 5 to beat all the same, also the last 2 beat the
same but faster than the first 5. Now, to all beat exactly the same, the
first 5 intervals could never have exactly the same, numeric size. It
actually makes sense and *requires* the E3-G#3 3rd to be the largest
numerical interval, just as it was so often coming up in these analyses.
Yes, because of these very close and exacting relationships, there is little
room for error but some for options. An audible and improper imbalance can
easily be created when making a few small but cumulative errors, the same way
unintended effects can be created when trying to tune Equal Temperament.
"Sideways Well": the pit Ed Foote dug for himself to wallow in the day he
knowingly published false data for the EBVT on Pianotech.
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>
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