Re: Date of EQT's acceptance

I just wanted to respond briefly to Paul Erlich's
suggestion that mean tone temperament rather than
just intonation was most probably regarded as the
"real" basis for musical tuning up through the
19th century and early 20th century.

It's my impression based on my reading of earlier
writings that most musical theorists before the 20th
century actually believed that there was a correct way for
musical tuning based on nature. In ancient times it
had been discovered that there was a certain
psychological "resonance" aroused in listeners when
sounds produced on otherwise identical strings having
length ratios 2:1 or 3:2 and compound ratios derived
from these ratios were heard. Then by the 16th
century ratios of 5 in string lengths were recognized
as being significant in musical harmony (Zarlino). Until the
17th century, when the overtones were discovered by
Galileo and Mersenne, it was believed that somehow
the numbers themselves had been assigned a mystical
importance by the Creator. After the discovery of
the overtones, it was realized that there were physically
unique properties - not always completely understood -
possessed by pairs of sounds having small integer frequency
ratios one to another. In a "Dictionary of the Arts..."
quoted from in Jorgenson which had been published in
1764, the author states that in the quarter comma
mean tone temperament, which he speaks of as the common
or vulgar temperament, there are small departures from
the true frequency ratios for the fifth, the minor
third, and the diatonic 16/15 and chromatic 25/24
semitones of 1/4 comma or in modern terms, about 5.4
cents. He states that although these departures from
the just ratios can be clearly heard, they do not
impair the quality of the music performed in this tuning
system. The UCSD music library has quite a few 19th
century musical tomes and they usually have rather
elaborate schemes of integer frequency ratios depicted
in articles on musical harmony and intonation - some
are in languages which I don't understand.

I may be being misunderstood as to what I mean by music
in just intonation. I mean music in which the notes are
produced at pitches called for by the harmonies being
sounded. A 12 per octave keyboard tuned in a "just intonation"
scheme can only produce a limited number of harmonies where
the frequencies of all the notes are in just intonation.
If one tries to play many other chords as if the keyboard
were in equal temperament, one will sound many dissonant
chords so that the result would not be very harmonious and
it certainly wouldn't be in just intonation, although there
have been people who have done just that in order to
demonstrate how terrible just intonation sounds! Such a
"demonstration" could be presented very convincingly, but
it would be deceptive.

Dave Hill, Borrego Springs, CA