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In a message dated 1/14/02 10:35:17 PM Central Standard Time,
From: davidlovepianos@earthlink.net (David Love)
writes:
> Thanks Ed. This is a terrific way to visualize it. I am curious what Bill
> Bremmers EBVT looks like.
>
> David Love
>
The graph would look similar to the Best Broadwood. Nominally, the EBVT
ranges from 7 to 18 cents just as the Broadwood does. However, the piano's
Inharmonicity does play a factor. I first set a series of intervals to all
beat at 6 per second. It is and easy pulse to hear. (According to Dr. H. A.
Kellner, it is nothing short of *divine*).
Two things can happen, however. That rate can be just a little faster or
slower and the intervals that follow will still work. Also, Inharmonicity
affects what would be the deviation from ET to make the 4 pure 4ths and 5ths
which are part of the temperament.
These "correction figures" are often given in whole cents. A piano with a
"poor" scale design will most definitely yield skewed results. Even among
well scaled pianos, such as a Steinway with high Inharmonicity, a Yamaha with
moderate and a Kawai or M&H with low, for example, I can't imagine a single
set of deviations producing the same results or even the desired results.
I still encourage those who are interested in the EBVT to learn to do it
aurally. There are far more Equal Beating (EB) intervals which can be tuned
than in just the F3-F4 octave. That is the goal: the most EB possible.
Plus, the unique Tempered Octave method I use is essentially an EB way of
tuning which the smooth FAC curve will not quite match.
When I look at those graphs, the most "well proportioned" one appears to be
the Thomas Young. While it is good, sound theoretical thinking, I almost
never choose it because I have found many other little known ideas that
simply sound more appealing. I have heard the opinion of many fine
technicians and pianists who still maintain that the Thomas Young sounds
unacceptably out of tune and is thus not an option. Others who can tolerate
what it has to offer find it to be too bland and uninteresting. That is my
opinion of it.
The EBVT is in fact, from a little known or used class of Temperaments called
the *Modified* Meantones. Only Jorgensen ever wrote about these. You never
see them written about in books or articles or talked about in HT lectures.
Yet, that is where I found my magic. By its very nature, a Modified Meantone
Temperament (MMT) *breaks* Werkmeister's Rules for Well Tempered Tuning.
(See my website for these rules). It has what are known as "imbalances" which
mean 3rds which do not progress in beat speed according to his rules, that
is, in a strict alignment with the cycle of 5ths.
Yet these temperaments can produce strikingly beautiful sounds, mellow and
harmonious and Equal Beating among the white keys and electrifying brilliance
among the flat keys. There are actually 5ths which are slightly wide rather
than tempered narrow. This is a flagrant violation of Werkmeister's rules
but which actuall produce a very appealing sound.
The EBVT however, in order to move into the mild, Victorian category, just
*barely* meets Werkmeister's rules. The intervals do beat correctly
according to his rules but when they are analyzed as Interval Sizes, that is,
Cents Deviation from pure or Just Intonation, a true graph of the way I tune
the EBVT would show a little irregularity and slight imbalances.
Therein lies the *difference* between the EBVT and all others, the Coleman
11, the Best Broadwood or any other mild design. Long ago, I began to
realize in temperament study that it was often the *irregular* temperaments
which sounded best over the ones which looked or seemed to be more logically
and symmetrically constructed.
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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