using beats to tune

[Richard Moody]

|And if it's true that tuners
| didn't use beats to tune a piano prior to 1917,  what did they listen to?

Actually the concept of beats has been around for a long time.  As to how
long, who and where, that would be the topic for a thesis.  For the best
grounding in tuning history, New Groves, the article "temperament" by Mark
Lindley is the most definitive I have found.
    But as far as tuning by beats to get ET,  I am interested when they
first listened to 3rds and 10ths for the tests and proofs.  It does seem
that the exact knowledge of this did not appear until after 1900 when beat
tables were first published.  That the beats of 3rds doubled each octave
and the beats of the 10ths equaled the beats of the root 3rd.   (C3--E3 is
the same rate as C3--E4).   The best source for the development of beat
tables is Jorgenson in "Big Red" so far as I have found.

    It is often quoted that Aristoxenes in ancient Greece proposed ET.
This was in response to the comma of Pythagoras.  Since that comma was the
result of the ratio of 3/2 (the 5th) multiplied twelve times (3/2^12) and
compared to 2^7, as the ratio of the two values to indicate its distance
beyond the pure octave, it is apparent that Aristoxones proposed that a
value slightly smaller than 3/2 multiplied 12 times would come out to be a
2/1 octave.   It is also presumed that they, (Greeks) knew that a 3rd from
four 5ths would be sharp from the pure 3rd of 5/4, (the comma of Didymus)
and therefore Aristoxones' value for a 3rd would be greater than 5/4 but
less than the so called Pyghagorean 3rd. (81/64)  This is all explained in
Braid White, "Tuning and Allied Arts".
        But no one knew the exact nature until Helmholtz demonstrated that
beats of intervals result from the arithmetical difference of their
coincident partials.   It is interesting to note in the book "Sensation of
Tone" the translation of Helmholtz by Ellis, no mention is made of actual
beat rates, no beat rate table is given even though the computation of
beats is suggested.
    So from the idea of ET of Aristoxenes in response to the Pythagoreans
in Ancient Greece to attempts in 17th and 18th century Europe as mentioned
in New Groves,  ET as a concept has been around for a long time.  The
attempts of ET are less documented but that may be because they have not
been translated into English.  There is a reference to an article by John
Broadwood in 1812 in a scientific journal, and from a translation of Montal
(1830) (by Clark on this list) that give methods of tuning ET.  There are
the writing of Hipkins about tuning for Chopin from which one might
conclude he tuned ET.
    In the consideration of how ET was tuned don't forget that
inharmonicity was not understood to be a factor until the late 1930's at
the earliest.  While this was more of a problem for the tuning machines, it
still shed light on nuances of ET such as stretching and explainations of
"flaws of scaling".
    One of the exciting aspects of ET to me is that methods are still being
researched, tested and refined.  I think there are issues to be considered
that will enable us to tune a little better and a little more consistant
than our teachers at least from the aural side.   Hoever, one aspect of
this tradition that I still tip my hat to is stability.  But we must
realize that with piano design according to scientific principles and
modern machines of analysis, instruments with a better capicity for ET are
being produced.  In that sense we may yet hear even a better ET in the
future.  ---ric


----- Original Message -----
From: <Tvak@AOL.COM>
To: <pianotech@ptg.org>
Sent: Thursday, November 15, 2001 7:40 AM
Subject: using beats to tune


| Did I misinterpret something that was posted recently in the discussion
| regarding temperaments?  I was surprised to learn that ET did not really
| exist prior to 1917.  Now, the part I'm unclear on: I believe that it was
| stated that this treatise, published in 1917, was the first to utilize
the
| concept of listening to beats in order to tune a temperament.
|
| First of all, is the above information correct?  And if it's true that
tuners
| didn't use beats to tune a piano prior to 1917,  what did they listen to?
I
| can't imagine.  (I must have misunderstood the information posted.)
| Certainly, tuning unisons could not be done without eliminating beats.
| Perhaps tuners didn't use coincidental partials to tune prior to 1917?
|
| Straighten me out!
|
| Tom Sivak