I find it, as a side bar, interesting that the one thing we think of as
being so perfect and without flaw is mathematics. If mathematics was so
flawless why is one of the most basic of concepts, that of pie, in itself an
imperfect number having no resolution this side of infinity? So it is no
wonder (in my opinion) that in an effort to justify tonality, an imperfect
relationship in practice, with yet another imperfect concept should yield an
imperfect result?
----- Original Message -----
From: "William Brohinsky" <[email protected]>
To: "Lute List" <[email protected]>
Sent: Saturday, September 26, 2009 10:43 AM
Subject: [LUTE] Re: lute music, ET, etc
It has long been my opinion that temperament is only necessary and
workable on fixed-pitch instruments of limited resources.
Specifically, it is a great work-around for a specific problem. For
the rest of us, it is not a temperament that will be important to us
(except where a specific composer adhered to a specific temperament,
rather than some other system.)
On instruments, like and especially the lute, where the performer's
fingers are on the strings and corrections can be made on-the-fly,
nothing that fits the definition of temperament is really necessary.
Instead, there are adjustments that need to be made for the specific
requirements of the instrument. In the case of the lute, the
requirements involve things like different string
mass/diameter/tension, and nut-grooves vs. saddle triangle shape
(i.e., the height of the string and distance from the saddle as
determined by the triangle-shaped bit where the string part through
the saddle meets the string part over the saddle.)
Organs respond well to temperaments, within each rank, and require
some kind of resolution between different ranks, which may have
pitches perceived differently because of harmonic content.
Harpsichords do well, since the density difference between lowest and
highest notes is not greatly different and string lengths even of the
highest notes and tensions lead to string-behavior throughout the
compass.
Pianos respond badly to any kind of one-octave temperament-fits-all
because the densities and tensions and string lengths cause the upper
strings to act more and more like bars than strings. This is affected
even more by the length of the piano's harp (most stark between
spinets and 12-foot concert grands.) And it is influenced more subtly,
but no less significantly, by the piano's scale-design and
implementation.
So there's no surprise that the purely mathematical solution
(immediately available to anyone who has risen in technical acumen to
understand the 12th root of 2) to ET12 is not applicable in the real
world. The surprise may be that it can be made to work at all, even if
the "it" that is being made to work is but a shadow of the
mathematical solution!
I find the most satisfying surprise in the discussion of tunings and
temperaments is how Dowland's tuning, which is described in his
nephew's book of lessons, makes his music sound better than any other
system I've tried, even under these poorly-trained (and aging)
fingers. Holborne doesn't sound so good to me in Dowland's tuning.
Unlike Mr. Turovsky, I don't believe in the aphorism that good music
doesn't rely on a specific tuning system or temperament. I believe
that good composers take into account their available materials
without conscious effort and produce music which uses them all to best
advantage. After all, much of late 19th C and early 20th C analysis of
renaissance music concluded that it was drab, purposeless and aimless,
which seems to me to have been predicated on their using the
temperament-of-the-day instead of any kind of just intonation. Compare
a cylinder recording of an orchestra like Toscannini's, which can be
corrected to reproduce all of the sound that was there at the
recording, and compare that to the same piece played by one of today's
symphonies: the difference in the sound and attractiveness of the
music is incredible.
I'm saying, here, that temperament/tuning doesn't make bad music
interesting, but it can make "GOOD" music more interesting, when
properly applied. Which I think says what Roman wanted to say about
Harrison.
Anyway, from a performance->listener point of view, the ability of
untrained folk to not hear bad intonation should be well-known by now.
And the ability of critical people to be, or claim to be, highly
sensitive to "out of tune" is also well-known. What isn't well-known
is a universal rule for how accurate a tuning (or temperament) has to
be in order to please everyone. So it is unlikely that math alone is
going to be a solution-source for musicians.
ray
To get on or off this list see list information at
http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
__________ Information from ESET NOD32 Antivirus, version of virus
signature database 4459 (20090926) __________
The message was checked by ESET NOD32 Antivirus.
http://www.eset.com
__________ Information from ESET NOD32 Antivirus, version of virus signature
database 4459 (20090926) __________
The message was checked by ESET NOD32 Antivirus.
http://www.eset.com
