Review of AFMM concert by Paul Griffiths

Hello - I'm having difficulty keeping up with all of the
interesting relevant discussion on the tuning list. I
plan to contribute to other discussions soon as time permits.
I was struck by the tone of Paul Griffiths' NY Times review
of the AFMM Concert at Columbia University - exemplified by
explanatory comments to the public such as: "...Also, the norm
for Western music has long been 12-step equal temperament,
with anything else being regarded as irregular, eccentric or
plain wrong..."

Such a tone of writing shows that the author is laboring
under some serious misconceptions, which, however, to him
probably seem "just common sense - obviously true". Some
response is required.

As Clif Ashcraft indicated in Tuning 202 1st message,
singing in the just diatonic scale as well as other non
12 EQT musical practices by non fringe musicians is
done and enjoyed in the present.

12 EQT provides an illusion of universality and
because of its convenience of use on keyboard instruments
of limited design and undoubtedly because of the
commercial advantages it afforded those in the 19th
century musical instrument trade, it has been accepted
unquestioningly by many present day experts. There is now
much beautiful choral music in more appealing intonation than
12 EQT readily available in CD recordings. Hopefully this is
helping to lead to a deeper understanding of the fact that
12 EQT has SERIOUS drawbacks.

Now, in addition, recordings in piano in mean
tone temperament and just intonation
are becoming available, and it is possible that these
will help to awaken some more musicians to the existence of
something which isn't well represented by the 12 EQT
approximations, which really don't sound as good to
a great many people as the compositions do in
mean tone temperament or just intonation. One musician
who heard side by side performances of the same score
music in EQT and mean tone temperament remarked that he
was very surprised to hear such a difference, that he
had been taught that the EQT compromises were so slight
that they were of no practical musical significance. He
then said to me that he simply couldn't understand how
EQT ever could have been adopted.

Anyway, I'm sending excerpts from the following paper
published in the Journal of the Acoustical Society of
America in July 1943 which serve as evidence that
all along many serious musical thinkers have
spoken out regarding 12 EQT's defects and the
detriment to music wrought by acceptance of its
deceptively simple and UNIVERSAL, but actually very
constrictive scheme for music composition and performance.

Excerpts from the paper: Mean-Tone Temperament:
The Classical System of Instrumental Tuning
by William Braid White, The School of Pianoforte Technology,
Chicago, Illinois
published in the Journal of the Acoustical Society of America
July, 1943 Volume 15 Number 1

Preliminary Section

For now more than a century, musical instruments of the keyed or
valved types, of which the intonation is wholly or partially beyond
the performer�s control, have been tuned in what is called the
�Equal Temperament,� whereby the octave is divided into twelve
equal semitones, whose frequency ratio is therefore 1:(2**1/12) =
1:1.0594631...

Equal temperament is a compromise adopted for practical reasons,
and particularly because the keyboard pattern of musical
instruments had already, by the end of the seventeenth century,
become settled in its present form. So long as this keyboard
pattern shall be retained, equal temperament is likely to prevail
for the tuning of keyboard instruments. Since, moreover, these
instruments have come, in practical fact, to dominate the art of
music, they have also gradually but irresistibly imposed equal
temperament upon that art as a whole, especially in the field of
composition; so that the system has come to be taken for granted,
and its defects completely ignored by the generality of
musicians, while the great world outside professional circles
remains almost entirely ignorant that any tuning problem calling
for compromise or defect even exists.

Now, equal temperament gives to the musician complete freedom of
modulation (transfer from tonality to tonality) throughout all
the combinations possible within a twelve-semitone octave. It
treats all such combinations in the same way; and it
standardizes, as well as vastly simplifies, both the construction
and the playing of keyboard instruments.

These advantages, however, are gained only at the cost of serious
defects. Equal temperament allows one and only one interval, the
octave, to be tuned exactly. Every other interval is necessarily
more or less distorted (made too wide or too narrow). Some of the
facts are shown below in Table I.

TABLE I. Distortions of some musical intervals by equal
temperament.
Name of Interval Exact (untempered) Kind of Amount of
frequency ratio Distortion Distortion
in cents*

Perfect fifth 2:3 Narrowed 2
Perfect fourth 3:4 Widened 2
Major third 4:5 Widened 14
Minor third 5:6 Narrowed 16
Major sixth 3:5 Widened 16
Minor sixth 5:8 Narrowed 14
Harmonic minor
seventh 4:7 Widened 31
Major seventh 8:15 Widened 12
Minor seventh 5:9 Narrowed 18

* The �cent� is an artificial interval representing .01 equal
tempered semitone. Its frequency ratio is, therefore,
1:2**(1/1200) = 1:1.0005778 nearly. The cent is defined in the
A.S.A. Standard Acoustical Terminology - Z24..6.12, 1936.

The distortions shown above are peculiar to equal temperament, and
of course they COLOR AND PSYCHOLOGICALLY INFLUENCE THE EFFECTS OF
ALL MUSIC PERFORMED ACCORDING TO ITS REQUIREMENTS. Naturally,
then, it comes about that when music, written originally in days
when another and very different system of intonation was
prevalent, and thus essentially determined by that system as to
its chordal and general harmonic pattern, is performed, as
necessarily happens today, on equally tempered keyboard
instruments, it does not sound and cannot in fact sound as its
composers expected it to sound and as it sounded to their
listeners.

This other system, the immediate predecessor of equal temperament,
held the field for some three hundred years, up to the opening of
the nineteenth century, before it was superseded
completely.

(until the latter half of the 19th century
in the United States -- Ellis translating Helmholtz
gives 1846 and 1854 respectively as the dates of adoption of
equal temperament in the trade for pianos and organs
in England respectively - D. Hill.)

For it, our present system of musical intonation was
worked out, with its foundation of key signatures and relations.
It prevailed during the whole of the great formative or classical
period of our western music; nor can there be any doubt that its
psychological influences, as well as the conditions it imposed
upon every kind of musical composition, were markedly different
from that which we have come in these days so completely to accept
and take for granted.

For these reasons, if for no others, it seems worth while once
more to set forth an exposition of this classical system of
intonation, the famous �Mean-Tone� temperament, and to give
likewise some simple and practical directions whereby it may be
tuned upon pianofortes and organs. The intonational and therefore
the psychological differences of musical effect thus revealed are
well worth the attention and study of all who are interested in
musical science. The remainder of this paper is devoted to this
object.

Conclusion of Paper

...The equal temperament telescopes the discrepancies and thus
evades the difficulties, although at the cost of other defects.

Nevertheless, as everyone will testify who has made the trial,
the mean-tone tuning is better fitted for the performance of
music that was written when it stood as the prevailing system
of tuning; and that of course comprises the music of the whole
classical age, from Tallis and Byrd to Mozart and Beethoven.
It is certain that equal temperament does not represent the
last, even if it certainly comprises the latest, word that may
be said on the subject of musical intonation. AS THE ART OF
MUSIC CONTINUES ITS DEVELOPMENT, THE QUESTIONS THAT EQUAL
TEMPERAMENT LEAVES UNANSWERED WILL PERSISTENTLY PRESS FOR
ATTENTION. Meanwhile the present paper, by directing
attention once more to the system that for so long held the
field and that formed the foundation of the most splendid
achievements in musical composition yet brought into being,
may do something to uncover a fascinating and fruitful
region of research and discovery.

I believe that the relevant parts of Dr. White's paper
ought to be required reading in any music course which covers
the topic of musical intonation and temperament. They're well
worth reading by anyone with access to a university
library.

Dave Hill La Mesa, CA

> I believe that the relevant parts of Dr. White's paper
> ought to be required reading in any music course which covers
> the topic of musical intonation and temperament. They're well
> worth reading by anyone with access to a university
> library.
>
> Dave Hill La Mesa, CA

How about required reading for any music major? I'd be in favor of that!