Historical Temperaments

Ed Remler writes:

>Prior to the publication by Mersenne of the correct frequency ratios
>for ET in 1636 it would have been practically impossible to tune in ET.
>Subsequent to that time it spread through continental Europe. the
history >of the use of beats to tune in ET is
>unknown to me, but exact rules for ET tuning are relatively unimportant.

I must respectfully disagree. ET is an exact placement of the pitches,
and getting there accurately enough to distinguish ones tuning from the late
well-temperaments requires aural measurements that must be exact. As the
temperament wars of the early 1800's raged, ( Stanhope, Farey, see Jorgensen,
"Tuning" pg 295), nothing was said about these techniques.
Beats were used for the many equal beating temperaments, true, but that
is setting intervals directly, not using the beats caused by test notes (for
the maj3rd/min3rd fifth test, or the maj3rd/sixth test for fourths). Without
the use of these tests, I will defy anybody to tune an acceptable ET on a
piano, and there will be darn few that can do it on a harpsichord. A
clavichord has so much "bebung" variability, I would hesitate to draw any
conclusions from what the players said about their tuning at all.
Montal gives a set of instructions for tuning a temperament that,
according to Bill Garlick, results in a very good to excellent ET. These
were published in 1836, which to my knowledge is the earliest date assigned
a written bearing plan that actually worked. We do see that Hipkins
documented the Broadwood tuners use of non-equal temperament ca.1848

Also:
> von Helmholtz (p.321 of
>Dover Edition) quotes Marpurg who quotes Kirnberger, a pupil of J.S.
>Bach, that he required all major Thirds to be sharpened, and this can
>only mean sharpened with respect to MT which is 14 cents flatter the ET.
>This is important not only to show Bach's preferences, but to indicate
>how clavier tuners probably tuned in ET as a practical matter at that
>time (pre 1750).
Requiring that "all thirds be tuned sharp" is not saying that they are
all tuned equally sharp. Sharpening a third slightly from pure lets the
tuner know two things, how tempered the interval is, and on which side of
pure. It makes for easier tuning, but there is considerable difficulty in
getting them all the same. There is little evidence that Bach wanted all
keys identical.

> There is no doubt that all the great masters of the classical period
>considered ET to be the ideal.

There is considerable doubt. Especially among those that tune
professionally. The distinctions between irregular and regular circulating
temperaments must be appreciated. This is important, because the
greatest keyboard works composed so far seem to have come from the period in
which the tuning underwent its most rapid changes. Can any list of composers
compare with those that worked between 1700 and 1850? This whole era was
concerned with tonality, the plausibility of an atonal tuning being popular
is (IMHO) thin.

> I am also happy to stand with them in disagreeing with the remark often
>made here and elsewhere that ET is some sort of a 'compromise' system of
>tuning. ET is certainly not and should not be considered in the same
>league as MT which is a compromise. ET was a great discovery-both
>aesthetic and scientific-and without it, Western music could not have
>achieved its unique glory.

Hmmm. I tune equal temperaments for a living. I think I know the
relationships in a 12TET backwards and forwards on at least a hundred
different pianos, ( yes, the aural sizes of the thirds are different on
different sizes of instruments, 9' pianos beat faster than spinets). I
consider ET to be a compromise, because there is something lacking. That
something is the pure interval.
There is something physiologically important about being subjected to
pure intervals, and the dissonance of the tempered intervals is useful in
providing a context for this appreciation. With 12TET, there is no textural
difference, and the context must come from without.
ET is a great developement, but the unique glory of Western Music was
formed before it was firmly in place. I personally see ET as more of an
entropic, dead-end detour, than a realized ideal of musical perfection.
As to the temperaments used by the past? In 1780, a piano performance
would have been followed by a discussion on the tuning, comparing the beauty
of certain keys with the resulting damage elsewhere. We need to hear the
music played in more than just the ubiquitous ET of today, and then, just
like the theorists of old, we need to debate how the music sounds best.

Regards,
Ed Foote
Precision Piano Works
Nashville, Tn. .

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