Equal Temperament, history of, judgement of

[Richard Moody]

Re: Equal Temperament

| At 9:23 PM -0500 21/2/02, Charles Neuman wrote:
|
| >...And popular culture just takes it for granted that ET has been
| >around for more than a century and that the difference between WT and ET
| >is insignificant. But I'd like to hear from someone who has some more
| >evidence on the subject.

The article  "Temperaments"  by Mark Lindley in Grove's New has references
to ET from the 15th century.   The lutes used it then and composers since
Frescobaldi (1583-1643) have utilized ET either in compostition,
performance, or discussion since the sixteenth century. The Groves articles
are the best foundation I have seen on the topic of temperament.   There
are other works, such as an article by John Broadwood reported to have been
published in a British scientific journal ca 1811.    In 1834 the French
writer Montal describes a rudimentary attempt at ET. Also not published, at
least in English, are factory procedures of organ makers from the 1400's
on, and harpsichord makers from 1500 on and piano makers from 1800 on.  All
of these sources are waiting to be researched.  There are tuning schemes in
piano lesson books from the 1700's.  Whether these are ET or a rough form
of meantone would be an intersting debate after they were gathered and
published.

That ET should be denied is not "history". There is no history of something
that did not exist.  What I am getting at is that the study of Historical
Temperaments is just that, a study of History.  The study of History is
like the study of Science, there is a method.
Loosely called the "Historic Method" its basic premis is, "No evidence, no
history" ---- (Charles Beard.)  The evidence of ET abounds.  The effort to
deny such evidence is futile. Again, the sources for evidence of ET are
listed in the article in New Groves, "Tempermants"  by Charles Lindsay.

The refinement of ET, I believe,  was not possible until the temperament
could be checked against the beating of 3rds and 10ths. (However I would be
willing to offer an example of ET composed of only 5ths and 4ths, to a
panel for tuning evaluation.) The beast of 3rds were known but their
nature, ie - how fast or how slow was not possible until Herman Helmholtz
published his findings on the mathematical relation of partials.  But he
did not elucidate on the beat rate of 3rds.   Even in the translation by
Ellis ca 1880, the method of computing specific beat rates for specific
intervals was given but I did not find a mention of checking ET by 3rds, or
the 3rd--10th test, or that the beat rate of 3rds doubles each octave.

This standard of tempered 3rds which ET is judged today, (which only
indicates a degree (very high though) of ideal accuracy), I think dates the
practice of what I call modern ET, or shall we say  MET?    Nah........
There is hypermodern ET but that will really be denied by a predictable
few.

When evidence is given for say, Et in the 18th century,  a common criticism
against that is they lacked the knowledge to produce an ET that would pass
a modern day Guild exam.

This at face value is true.  But if that critique is applied to ET, by
rights it should be applied the other tunings practiced at that time. Those
temperaments were just as prone to error as the critics of ET claim ET was.
Even the the temps with pure 5ths.
How accurate can you tune a pure 5th according 20th century standards using
only 18th century practices?

And conceiding that ET was not as accurate then as today, still the attempt
to produce ET in the 17th century could yield a temperament that could only
be called "ET", or close enuf.  If there must be a purist stance as far as
evaluation, then the persuit of a "perfect ET" on a piano is about as
ellusive as the pursuit  of a perfect performance on a piano.  When you
find one let us know.

So the historic reality most probably is that ANY temperament tuned before
beat tables were available suffered variances we might offer corrections
for in light of today's knowledge.

Claims that ET suffers obvious variances today are hard to believe because
of the wide spread  use of electronic devices and refinement of aural
techniques that have come down since 1900's (beat tables first published).
Because tuning is a devoloped and practiced skill---some may do it better
than others.   But in the performance venues and recording studios, I would
be surprised to see tuning variences that are objectionable by experienced
tuners, or measurable by machines even. (one cent down to half a cent).
There for I would argue that tuning variances detected by second parties of
experts with or without machines might indicate the "fault of the
instrument" rather than the error of the tuner and  beg the second party to
come up with something demonstrately better.  In less than an
ur.   ---ric



| Writing in 1869 for a popular readership, Edgar Brinsmead says
| "...hence the necessity of _tempering_ the fourths and fifths which
| has given the new scale the name of equal temperament
| JD