Equal Temperament (long)

[Charles Neuman]

Note: If this is too long for you, skip to the last paragraph.

> From: John Delacour <JD@Pianomaker.co.uk>
>
> <big snip> The evidence is
> well documented by Alexander Ellis, the translator (1885) of
> Helmholtz's Sensations of Tone (Dover Books).  Equal temperament was
> by this time well established in Germany.  Helmholtz himself writes
> (1862) "Of our great composers, Mozart and Beethoven were yet at the
> beginning of the reign of equal temperament". <big snip>

John's facts are interesting. I found some more things to add.

Apparently Owen Jorgensen wasn't so extreme about ET in 1977 as he was in
1991. In _Tuning_ (1991) I think he says that ET couldn't have existed
before 1900. However, in _Tuning the HT's by Ear_ (1977) he says (p.1):

"The year 1954 is usually given as the very general turning point when the
European world of music finally and completely adopted equal temperament."

Ok, that doesn't prove he agrees with that statement, but the next
sentence does:

"From then until now, equal tempearment has enjoyed almost universal
usage."

Interesting, eh? Then he goes on:

"The purpose of this book is to restore the original sounds of the many
temperaments used before the death of Chopin in 1849."

That implies that these HT's weren't really used much after that.

Then he describes the evolution of tuning and temperament. It goes like
this:

   1) pentatonic scale
   2) diatonic scale
   3) medieval Pythogorean tuning

at this point it branches into
   4a) the restricted meantone temperaments
and
   4b) the unrestricted well temperaments
then both branches coverge on the next step:

   5) standard equal temperament
   6) rivals of equal temperament
   7) contemporary and experimental temperaments

What's the point? The point is that if you follow the branch which
includes 4a, you get a path which goes from medieval Pythagorean tuning to
meantone to ET. Isn't that what Isacoff was "accused" of stating in his
book?

Here's more elaboration by Jorgensen (p. 7):

"For music containing limited modulations using only a small number of
scale degrees, meantone temperament was practiced from the early sixteenth
century until the middle of the nineteenth century... For music demaning
complete freedom of modulation, well temperament also was practiced from
the early sixteenth century until the middle of the nineteenth century.
However, until the eighteenth century, well temperament was not as popular
as meantone temperament."

This doesn't meant that WT had nothing to do with it. But I think he's
saying that there was a line of development that went directly from
meantone to ET. I have more to read to understand it better, so maybe I
dont' have the full picture yet.


As for Jorgensen's arguments in _Tuning_ that ET couldnt' have existed
before 1900, he says that some of the tests used to prove intervals in ET
were unknown before then, and I think he also says that the sustain on the
instruments in the 19th century was not long enough to hear the beating in
the fifths and fourths well, and thirds and sixths were never used to set
a temperament.

So, does Jorgensen contradict himself? In 1977 he says that ET existed
universally after 1954. In 1991 he says that nobody could have tuned ET
before 1900. I don't think he contradicts himself, really. I think in his
later book he uses a stricter standard for ET. It's like when people say
you can't tune ET accurately using Braide White's method, and many today
aren't tuning ET when they think they are. But I don't think it's fair to
say that because of that, ET didn't exist at all until it could be tuned
to pass the RPT exams. It seems that ET existed, in concept and in an
attempt at practice, in the last part of the 19th century. But it wouldn't
have satisfied today's tougher standards for an accurate ET tuning.

Charles