Klarinet Archive - Posting 000362.txt from 2004/11
From: Adam Michlin <amichlin@-----.com>
Subj: Re: [kl] RE: pitch standard
Date: Tue, 9 Nov 2004 11:50:03 -0500
There is a wonderful book written by Stuart Isacoff called:
"Temperament: The Idea That Solved Music's Riddle" - Pg. 15-16:
"Play the well-known scale do-re-mi-fa-sol-la-ti do: The top and bottom
dos, if isolated from the rest, merge effortlessly as though one were a
continuation of the other. The same effect results when any two res, mis or
fas are sounded simultaneously. In each of these cases the higher tone (an
octave above the lower one) is vibrating twice as fast. Or play play do and
sol (the fifth note of the scale that begins on do) together. In this case,
the higher tone is vibrating three times for every two vibrations of the
lower one one, and the ear perceives a joyful agreement between the two.
For centuries these auditory experiences served as corroboration of
immutable natural law-affirmed by theological as well as musical authority.
But as music evolved a palette of complex harmonies and intricate textures,
and instruments with fixed pitches (like lutes and keyboards) came into
prominence, something unexpected happened: The unchangeable harmonic
formulas seemed to falter. As it turns out, the strings of a piano, or of
its earlier incarnation the harpsichord, may be tuned so that any of the of
the cherished ratios can be rendered perfectly throughout the range of the
instrument. A do can be put in tune with every other do, for example; a re
in tune with every other re. Each of these tones on the keyboard can be set
to vibrate exactly twice as a fast as the like-named partner below it.
However, the musical tones that will produce those perfect 2:1
relationships across the keyboard are different from the ones needed to
create perfect 3:2 relationships. So making all the octaves (the distance
from do to do) "pure" guarantees that all the fifths (the distance from do
to sol, or re to la) can't be. Remarkably, these (and other) long-revered
musical proportions refuse to keep company. When multiplied their various
progeny threaten to collide abrasively, as if there were a curvature in
musical space."
The long way of saying you can establish a temperament using a circle of
pure fifths, but it isn't going to work well. The book goes into much more
detail. Highly recommended, perhaps the best book on music, history and
science I have ever read. Extremely well written.
Please note that I don't think Keith was referring to a temperament. A
temperament is only required with fixed pitch instruments or semi-fixed
pitch instruments (a real grey area we clarinetists live in) to compensate
for the above problem (as well as a few other problems). Singers, for
example, have the ability to sing any pitch in any context (sometimes to
very hazardous ends, I might add!) so the problem doesn't really exist in a
pure choral environment (leaving aside keyboard accompaniment).
I have played with a few singers I wish could be tempered, though.
-Adam
PS: It really starts to get interesting when you stack pure major and minor
thirds and compare the resulting pitches with those derived from pure
octaves and fifths.
At 06:40 AM 11/9/2004 -0800, Ormondtoby Montoya wrote:
>Keith wrote:
>
> > We can tune octaves, fifths and triads easily
> > by absence of beats.
>
>If you establish a complete 'circle of fifths' this way, then haven't
>you established the entire temperament already, and thus you don't have
>any freedom to adjust anything else?
>
>Or do you mean simply to establish one fifth and then build other
>intervals from there?
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