Aural Pure 5ths Equal Temperament

[Dennis Johnson]

Jim,

If I understand your temperament correctly, you are setting something
very close to a 1/5 ditonic comma meantone, with the comma divided
regularly between four fifths and the octave. Your language does not
necessarily imply regularly tempered divisions, but if your thirds are
of equal size then these divisions of the ditonic comma would need to be
equal as well. This is something different from anything I have tried, but
I have come to respect your interests.  Actually, it would not be so far
removed from the Marpurg I temperament, which is a 1/6 comma ditonic
division, all of them being fifths. In your temperament, the telling
triads would be D Maj, B Maj, E Maj, and Eb Maj, but there can be no
argument that all other keys are improved over both the standard ET
and the traditional Pythagorean triads for two reasons. First, the fifths
are pure which implies the triads to be proportionally beating (actually,
6:4 fifths are strictly proportional but that is not worth picking over)
and second, the thirds within these triads would beat identical to, or very
similar to, beat speeds of standard ET thirds. It then becomes an aesthetic
question as to whether one prefers this color, or something else.

I eventually tired of the Marpurg I temperament because I felt that the
color of a 1/6 ditonic fifth matched with an ET third did not appeal to
me. That is why I must wonder about these keys mentioned because a 1/5
ditonic fifth would beat slightly faster than a 1/6 fifth. This
is not to say that a fifth beating 1.5 bs is too fast. To the contrary.
1/4 syntonic fifths beat even faster, and they can be glorious. The
aesthetic issue, IMO, is one of balancing beat speeds in a complimentary
way between fifths and thirds. Generally, the more noticeable a fifth is
beating, the slower I like the thirds to be, with the clever exception of
an occasional proportionally beating triad that can hide a faster
beating fifth. In my experience, when a noticeably beating fifth beats in
no rhythmic relationship to the thirds, and the thirds are beating as
fast as standard ET, you get a color much less satisfying than a traditional
Pythagorean triad with much faster thirds and a pure fifth.

Hope I did not ramble too long, but thanks for sharing this preview of
your article.


Dennis Johnson
St. Olaf College