Perfect fifths

Dennis Johnson johnsond@stolaf.edu
Tue, 04 Feb 1997 16:02:50 -0600 (CST)


The only advantage that this temperament may have over conventional equal=
=20
(IMO) is the porportional, or nearly porportionally beating triads.=20
Actually, by definition, porportionally beating thirds within a triad=20
require a 6:4 fifth, as opposed to a 3:2 fifth, which should be slightly wi=
der.
The disadvantage this temperament has over equal is that the thirds are=20
faster and the octave has a very noticable roll to it, though not as bad=20
as some might expect. This is for the same reason that a 1/4 syntonic=20
fifth beats much slower than a 1/4 syntonic third. I suppose we could=20
call it a Pythagorean Octave.

It was no coincidence that Pythagorean tuning and its=20
transposed versions on keyboards, declined in favor with the advent of=20
polyphony. Likewise, equal temperament gained favor on pianos at a time=20
when tonality was being questioned and its boundries were breaking down.

I second Jim=D5s last comment, and am much more interested in what a=20
particular temperament has to offer to the music, than to how=20
interesting it may look on paper. I am the last one to discourage=20
experimentation with temperament because this is the best way to=20
learn, but with so many more musically (historical, tonal, etc..)=20
appropriate options which have yet to be explored in so many places, this=
=20
one just doesn=D5t it for me.


If you want a more interesting version of equal, with porportionally=20
beating triads, and with a clean octave, try the Marpurg I (that is the=20
letter I, not the number, as many have presumed). This temperament=20
alternates two pure fifths and two tempered fifths, and the thirds are=20
all equal.=20



Dennis Johnson
St. Olaf College





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