FWD: Tom McGeary on unequal temperaments

Date: Fri, 29 Sep 1995 02:12:17 -0500
Sender: Harpsichords and Related Topics
Subject: Tom McGeary on unequal temperaments

Like Dr. Frosztega, I too was dismayed that Jorgensen's theory
that equal temperament was unknown in the 18th century was applied to
the discussion about Bach - esp. since most serious reviews of his books
have raised questions about his historical and evidentiary reasoning.
In a review of his most recent book (in 1992 issue of Early Keyboard
Journal), I addressed this argument at some length, which section
I've appended below.

tom mcgeary



Jorgensen's historical thesis is that "Before the twentieth century, the
system of equal temperament commonly practiced today was not possible on
pianos, harpsichords, or clavichords . . . ." (p.779)

According to Jorgensen, historical tuners could not set equal temperament
because "During the nineteenth century and before, . . . one did not count or
compare beat frequencies. In fact, one did not listen to beats at all. . . .
In the past, tuning by ear meant that one judged the relationships between the
two notes of an interval by listening to the notes melodically only. The
first note was never sustained while the second note was being played.
Therefore, no beats could be heard. (p.4) . . . In the past, tempering
techniques consisted of listening carefully to the colors or qualities of
chords in order to make aesthetic judgments for each tone. (p. xxi) . . . On
technical grounds, . . . equal temperament on pianos or harpsichords was
impossible during the nineteeth century and before." (p.6)

This astonishing argument requires careful unravelling to show its fundamental
confusions. First, the 'facts' supporting this argument are a complete
invention on Jorgensen's part. One has only to look at the original versions
of the tuning directions that Jorgensen discusses (but not as Jorgensen
reprints them !) to see that almost all tuning directions were set out
harmonically and, therefore, that tuners presumably did tune intervals
harmonically.

Several lines from Barthold Fritz's "Anweisung, wie man Claviere, Clavecins,
und Orgeln . . . in allen zwo"lf To"nen gleich rein stimmen ko"nne" (1756) -
reprinted four times and the most influential practical tuning treatise in
Germany - are worth quoting for several reasons (beyond just Fritz's clear
advocacy of equal temperament): "The most skilled tuning masters are
accustomed to give the rule: that the major thirds beat above, the fifths,
however, beat low." Fritz gives the test of the equal-tempered major third
f - a: the speed of its beating should "approximate the eights in common time."

Fritz's statements surely suggest that tuners heard beats and might even
listen for beat rates. Moreover, they cast doubt on Jorgensen's statement
that "nineteenth-century tuners believed that the beats of thirds and sixths
were too rapid to count, compare, or use for tests" (5). Surprisingly,
Jorgensen seems not to have noticed that even his own book contains many
mentions of historic tuners hearing or using beats.

Jorgensen has the ide'e fixe that without the beat rates and test intervals
known to modern tuners and without the skill to listen to beats at the upper
harmonics, "equal temperament on pianos or harpsichords was impossible during
the nineteenth century and before" (6). Jorgensen is, of course, correct that
any keyboard instrument tuned where even a single note in the temperament
octave deviates one cent from the theoretically correct value is technically
not set in equal temperament (though such accuracy may not even be desirable).
Without electronic aids and given the complex harmonics of a vibrating string,
the phenomenon of coupled motion in pairs or triplets of strings, and the
fallibility of human ears, a theoretically exact equal temperament has
probably never been achieved.

Elsewhere Jorgensen states that "equal temperament on pianos must be judged by
the ear and not by electronic analysis of the actual frequencies" (4). If
ultimately it is an aural test for equal temperament, the question that
Jorgensen does not consider is: What degree of accuracy is sufficient to
accept a practical tuning as equal temperament? Without some standard of
accuracy, one can all-too arbitrarily dismiss out of hand all historical equal
temperaments (and presumably many modern ones as well) as too inaccurate to
count as equal temperament - notwithstanding the fact that we have no
witnesses to the accuracy of eighteenth-century tuners.

Jorgensen also uses the dubious straw-man argument to prove equal temperament
was impossible in the past. He suggests the experiment of having a group of
musicians instruct a piano tuner how to set an equal temperament going through
a cycle of fifths, with the condition that all intervals and chords be played
arpeggio and staccato! Of course the results will be an acoustical cacophony.
But for Jorgensen, "the piano has been tuned 'by ear' in equal temperament
according to nineteenth-century requirements" (5).

Even if we accept, then, that eighteeth and nineteenth century tuners could
not set a theoretically precise equal temperament that would meet Jorgensen's
modern standards, what is the appropriate practical conclusion to draw?
Certainly not the rest of Jorgensen's argument: that historical tuning of
equal temperament was "so different from that of today that it no longer can
be called equal temperament" (p.3) and that tuners were deliberately trying to
achieve key coloration.

Jorgensen fails to make a crucial distinction between random deviations from
precise equal temperament and deliberate attempts to set unequal temperaments
designed to produce key coloration. To ignore the difference between what is
ideal and what we accept as a pragmatic realization of it could lead to the
argument that we have never yet heard the Goldberg Variations ( i.e., achieved
equal temperament) because in performance there are always a few wrong notes
or rhythms that Bach did not intend ( i.e., random deviations from
theoretically correct equal temperament.)

More likely: we should realize that when and where equal temperament was the
goal, for historical accuracy we should utilize our modern practical tuning
techniques to achieve the equal temperament that musicians certainly asked for
and thought they were getting.

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