🚀 go-pugleaf

In article <8515@charon.cwi.nl> dik@cwi.nl (Dik T. Winter) writes:

>The frequency of A' at 440 is currently indeed standard, but for older music
>you would like to have a lower pitch.

It is a myth that absolute pitch has been getting gradually higher since the
baroque. See Arthur Mendel's comprehensive look at absolute pitch in Acta
Musicologica. At least in the baroque pitch references were local at best,
and though there were the different pitches for choir and instruments in
many areas (usually referred to, even by English-speakers, as chorton and
kammerton - there's also so-called tief-kammerton in some areas), there
was no ONE chorton or ONE kammerton. Each varied by as much as a major third
one way or the other from place to place.

>Further, the relative frequencies as given above are first used by Bach in
>his 'Wohltemperiertes Klavier'.

First of all, it is another myth that Bach used equal temperament. While we
don't have any direct evidence exactly what tuning system he used, his son
Emanuel said in a letter to Kirnberger specifically that J.S. Bach did NOT
use equal temperament. It is likely that he preferred one of the many so-
called "good" or "well" temperaments in which all keys are playable, but
the more common keys are somewhat more consonant. After all, it is the
"well" tempered, not "equal" tempered klavier.

Secondly, equal temperament had been recognized long before Bach's day. The
theoretical possibility of it had been alluded to by Aristoxeneus, and
by at least the 17th century, several people had written about it. It isn't
that equal temperament was unknown until the 18th century, just that compo-
sers made a deliberate decision to use something else. In particular, they
don't seem to have liked the relatively out-of-tune thirds (in relation to
pure 5/4 and 6/5 thirds).

> An older list of relative frequencies is:
>	C   D   E   F   G   A   B   C
>	24  27  30  32  36  40  45  48

This is called a "just" tuning system because the frequency ratios are
represented by relatively small numbers. I suppose one could make a case
for it being "older" than equal temperament in the sense that we have
evidence for just tuning systems going back to Sumeria, but many other
tuning systems were more widely used in European music: mean-tone
temperaments, "good" temperaments, "circular" temperaments, and equal
temperament were apparently more popular, though at different times.

This is not to say that I have anything against just intonation, quite
the contrary. I use just intonation in my own composition. Sythesizers
and computers allow one to adopt just intonation without having to build
my own instruments. I'm even a member of the Just Intonation Network (email
me for more information about the JIN).

Bill Alves