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Hi Bill and everybody
I've missed some test intervals on the EBVT so from Robert Scotts EBVT =
calculation I got those beats (hope I got it right)
D3-B3=3D6,1
E3-G#3=3D8,1
F3-A3=3D5,4bps
F3-C4=3D0bps
F3-A#3=3D0bps =20
F3-D4=3D7,3bps
F#3-C#3=3D0bps =20
F#3-B3=3D1,6bps
F#3-A#3=3D8,9bps
F#3-D#4=3D10,2bps
G3-D4=3D1,5bps
G3-C4=3D1,5bps
G3-B3=3D5,7bps
G3-E4=3D6,1bps
G#3-D#4=3D0,9
G#3-C#4=3D0bps =20
G#3-C4=3D9,9bps
G#3-F4=3D9,7bps
A3-E4=3D1,1bps
A3-D4=3D1,9bps
A3-C#4=3D9,4bps
A3-F#4=3D9.2bps
A#3-F4=3D0bps =20
A#3-D#4=3D1,3bps
A#3-D4=3D9,4bps
A#3-G4=3D12,2bps
B3-F#4=3D1,6bps
B3-E4=3D0,3bps
B3-D#4=3D10,9bps
B3-G#4=3D12,6bps
C4-G4=3D1,5bps
C4-F4=3D0bps =20
C4-E4=3D5,7bps
C4-A4=3D7,8bps
C#4-G#4=3D0bps =20
C#4-F#4=3D0bps =20
C#4-F4=3D12,6bps
C#4-A#4=3D13,2bps
D4-A4=3D1,9bps
D4-G4=3D2,8bps
D4-F#4=3D9bps
D#4-G#4=3D1,7bps
D#4-G4=3D14,2bps
E4-A4=3D2,1bps
E4-G#4=3D16,3bps
F4-A4=3D10,8bps
Is this what you mean?
Do you want to change anything?
A question
I can't understand why you after tuning A4 and A3 want to tune
E4-C4-G3-B3-D4-F4-F3
Why not take the short cut
F3-C4-E4 to see how the thirds of F3-A3 and C4-E4 beat the same, =
retune(?) and then take the rest of the whites
Please tell me:-)
Ola Andersson
Bergen Norway
----- Original Message -----=20
From: Billbrpt@AOL.COM=20
To: pianotech@ptg.org=20
Sent: Saturday, April 07, 2001 7:31 PM
Subject: Re: alternative temperaments
In a message dated 4/7/01 11:28:35 AM Central Daylight Time,=20
tunenbww@clear.lakes.com (Paul) writes:=20
I'm an aural tuner, so setting this temperament was a bit of a =
struggle. It=20
did work out. All of the checks proofed correct. I had several =
people try=20
the piano. Their reactions is another story.=20
I'm glad that you are an aural tuner because I have the ideal =
temperament for=20
you to try. It will be in the same general area as Jim Coleman's #11, =
yet=20
different enough to be quite significantly different in the overall =
effects=20
it produces when actual music is played. The difference is in the =
effects=20
that Equal Beating (EB) produces.=20
While not attempting to say anything negative about Jim Coleman's =
idea, it=20
was formed simply by meting out certain proportions for various =
intervals,=20
giving up purity at the top of the Cycle of 5ths in order to avoid =
harshness=20
at the bottom. Mine does essentially the same thing but because of =
the EB=20
effect, you can play early music with it and have it mimic the sound =
of a=20
much earlier temperament which would have uncalled for harshness in =
the=20
remote keys when trying to play music from the 19th or 20th Centuries. =
What happens is a canceling out effect in the Rapidly Beating =
Intervals=20
(RBI), e.g., 3rds, 6ths, 10ths & 17ths that make them sound much purer =
than=20
they really are. This is not an imaginary effect. It is the same =
effect=20
found in such acoustical tricks as Noise Cancellation Systems and Beat =
Eliminators. The gist of it is that when there are two sets of beats=20
occurring at the same time, they phase each other out so that they are =
not=20
perceived by the ear.=20
This gives you an advantage in that you can have a true, Cycle of 5ths =
based=20
temperament that can and does work well with virtually any kind of =
music, the=20
way only ET is believed to be able to do. There are many myths about =
ET and=20
one of them is that it is "Universally" practiced. In fact, most =
aural=20
tuners cannot really produce a true ET. There is always some error =
and that=20
error does produce an effect or "color", as it is called in the music. =
The Equal Beating Victorian Temperament (EBVT) that I designed stays =
well=20
within the bounds of deviation (or "error") in ET that most aural =
tuners=20
produce. Therefore, it produces no sound so extreme (either too pure =
or too=20
harsh) that the *contemporary* ear will reject it. I designed and=20
implemented this temperament in 1992 and have used it ever since as my =
own=20
personal replacement for ET. I have, in fact, tuned no pianos in ET =
since=20
1989. I tune all kinds of pianos, in homes, schools, churches, =
concert=20
halls, restaurants, hotels, etc. I have a very loyal and devoted =
following=20
that really likes the way I make my pianos sound.=20
Ed Foote's latest essay found in the liner notes of his new CD is =
quite=20
impressive. But I find a couple of areas of temperament research =
lacking in=20
his study that I usually find, even among the most knowledgeable =
alternative=20
temperament practitioners. There seems to be only one "Meantone", the =
most=20
extreme form, the one that makes the modern piano sound like an =
antique one=20
with virtually none of the resonance we expect to hear. There are =
whole=20
classes of temperaments that remain ignored and unexplored, the =
Modified=20
Meantones (not the same kind of temperament as a "Meantone") and the =
Quasi=20
Equal Temperaments. The EBVT is, in fact a Modified Meantone =
Temperament=20
although it also just barely satisfies the Rules for Well-Tempered =
Tuning as=20
written by Andreas Werkmeister in the 17th Century.=20
Ed mentioned in a recent post that a Gershwin piece in Db would have =
sounded=20
"better" in ET. I've seen him say the same about Chopin and Debussy. =
I=20
respectfully disagree. There is a reason that these composers chose a =
remote=20
key, the challenge is to find the exact combinations that make it =
sound=20
vibrant and singing but not harsh. ET is merely the default choice =
for those=20
who do not have the answer. It neutralizes the piano to the point =
where it=20
would make no difference at all which key is chosen to play in. I =
hardly=20
think anyone would choose ET if they really knew how much better music =
could=20
sound with a more advanced approach to tuning.=20
Below are the basic instructions for the EBVT. It cannot be tuned the =
way=20
most people are trying to attempt alternative temperaments, by =
imposing a set=20
of "Correction Figures" to a smooth curve calculation for ET using an=20
Electronic Tuning Device (ETD). If you tune the octaves the way I =
have=20
indicated in a very brief description, they will naturally be of =
different=20
sizes as you ascend and descend the scale. No smooth curve =
calculation can=20
produce this. They are known as "Tempered Octaves".=20
If you or anyone is interested in reading a background article I have =
written=20
to support my ideas called "Key Color", please request it privately. =
It is=20
too long to post on Pianotech. Also, please inquire if you need =
further=20
explanation of how to tune the octaves. It is really quite easy and =
simple=20
but not the way you have probably been taught.=20
Good luck with this and let me and/or the List know of your own =
reaction and=20
those of your customers.=20
Regards,=20
Bill Bremmer RPT=20
Madison, Wisconsin=20
EBVT Aural Tuning Instructions: Introduction=20
Below are the line by line instructions for tuning the EBVT. You will =
begin=20
by estimating just 2 intervals, a 5th which you will temper just =
slightly=20
more than you would for ET and a 3rd which you will temper about half =
as much=20
as you would for ET. Thereafter, all you will need to do is either =
tune an=20
interval perfectly pure or make it beat exactly the same as another. =
In=20
short, the temperament sequence itself provides you with the exact=20
information you need.=20
The instructions include the aural way of proving your pure 4ths and =
5ths. =20
When doing an initial first rough pass, it is not necessary to prove =
these=20
intervals so exactly. Also, the instructions have several places =
where they=20
tell you to "temporarily tune...etc". These are for people who are =
just=20
beginning to learn the temperament sequence.=20
With experience and during the fine tuning of the temperament, you may =
skip=20
the "temporary" part the same way you learn to skip elementary steps =
in=20
Algebra. You simply learn how to make 2 intervals beat exactly the =
same as=20
each other by placing the note to be tuned at point where it creates 2 =
equally beating intervals. This is also called "Meantone tuning".=20
The following is the way the 3rds played chromatically will sound from =
F3-F4.=20
Just imagine all values inverted and you have the most commonly made =
error=20
in tuning today which is known as "Reverse Well".=20
F3-A3: slow=20
F#3-A#3: fast=20
G3-B3: slow=20
Ab3-C4: quite fast=20
A3-C#4: moderate, about the same as ET=20
Bb-D4: moderate=20
B3-D#4: very fast=20
C4-E4: slow, half the speed of ET=20
C#4-F4: very fast=20
Equal Beating Victorian Temperament=20
(Equal Beating Victorianized Modified Meantone Temperament)=20
Instructions for Aural Tuning=20
(With Tempered Octaves)=20
1. Tune A4 to A-440 pitch source.=20
2. Tune A3 to A4, stretching the octave to a a 6:3 type.=20
3. Temper E4 from A3, a narrow 5th, a little more than an Equal=20
Temperament (ET) 5th but still slightly less than 1 beat per =
second.=20
This is an estimate and may be checked or adjusted later, if=20
necessary.=20
4. Listen to the 4th, E4-A4. It should beat faster than the 5th, =
A3-E4=20
but should not be faster than 2 beats per second.=20
5. Temper C4 from E4, a wide Major 3rd to beat approximately 6 beats =
per=20
second. (Half the speed of the same interval in ET.)=20
6. Temper G3 from E4, a wide Major 6th so that it beats exactly the =
same=20
as the C4-E4 3rd. (Approximately 6 beats per second).=20
7. Temper B3 from G3, a wide Major 3rd so that it beats exactly the =
same=20
as both the C4-E4 3rd and the G3-E4 6th. (Approximately 6 beats per =
second).=20
8. 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=20
in both the G3-D4 5th and the A3-D4 4th. (Faster than the same=20
interval in ET.)=20
9. Tune F3 a pure 5th from C4. To check this interval, use G#2 as =
the=20
test note and prove that the Ab2-F3 6th beats exactly the same as=20
the Ab2-C4 10th.=20
10. Tune F4 a pure 4th from C4. To check this interval, use G#3 as =
the=20
test note and prove that the 3rd Ab3-C4 beats exactly the same as =
the=20
Ab3-F4 6th.=20
11. Verify the F3-F4 octave. Using the test for a pure 5th which =
chooses=20
the lowest coincident partial of F3 & C4 and the test for the pure =
4th=20
C4-F4 will yield a properly stretched octave, usually a compromise=20
between a 4:2 & 6:3 type.=20
12. Check the speed of the 3rd, F3-A3. It should beat exactly the =
same=20
or very similarly to the 3rds G3-B3 and C4-E4. If it is too slow,=20
adjust the note, E4 slightly flatter and begin the sequence again.=20
If too fast, adjust E4 slightly sharper and restart the sequence.=20
13. Tune Bb3 a pure 5th from F4. Use the test note C#3 to prove that =
the=20
Db3-Bb3 6th beats exactly the same as the Db3-F4 10th.=20
14. Listen to the resultant 3rd, Bb3-D4. Temper C#4 so that the =
A3-C#4=20
3rd beats exactly the same as the Bb3-D4 3rd.=20
15. Tune F#3 a pure 5th from C#4. Use the test note A2 to prove that =
the=20
A2-F#3 6th beats exactly the same as the A2-C#4 10th.=20
16. Tune G#3 a pure 4th from C#4. Use the test note E3 to prove that =
the=20
E3-G#3 3rd beats exactly the same as the E3-C#4 6th. The Ab3-C4 =
3rd=20
will beat exactly the same as the F#3-A#3 3rd.=20
17. Temporarily tune D#4 a pure 5th from G#3 then notice the slight =
beat=20
between D#4 & A#3 and flatten D#4 until the G#3-D#4 5th beats =
exactly=20
the same as the A#3-D#4 4th. It will be a very slight beat, less =
than=20
the same interval in ET. The B3-D#4 3rd will beat very rapidly, at=20
least as fast as the F#3-A#3 & Ab3-C4 3rds below and similar to but =
perhaps not quite as fast as the C#4-F4 3rd above.=20
18. When expanding the octaves do so in a manner which will cause the=20
2nd inversion major triads of C, G, D, A, E, & B to have the 3rd & =
6th=20
beat exactly the same. The octave should be stretched enough so =
that=20
there is a very slight beat in the single octave (approximately 1/2 =
beat per second) and that the tempered 5th will beat slower than =
the=20
4th. When both the 4th and the 5th were pure in the temperament, =
the=20
octave will naturally be stretched a little less than an octave=20
whose 4th and 5th are tempered.=20
19. When expanding the outer octaves, try to reconcile the double =
octave=20
and the octave and a 5th (12th) so that the double octave and the =
12th=20
beat exactly the same. (A very slight beat, almost inaudible). This =
will naturally result in octaves which vary slightly in size up and =
down the keyboard. These will quite effectively be "tempered=20
octaves".=20
Bill Bremmer RPT=20
Madison, Wisconsin=20
April, 2000=20
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