Douglas writes:
<< In the number of proportional beat
triads, well temperament is superior to equal temperament and also most of
the meantone temperaments. This gives well temperament a certain rhythmic
harmoniousness."
I was with him up until the last two sentences, then came "proportional beat
triads" and "rhythmic harmoniousness."
Anyone want to try and educate me on proportional beat triads and rhythmic
harmoniousness? >>
Greetings,
The "proportional" refers to triadic sharing of multiples. Which means
that you will have a major third that is beating exactly half as fast as the
minor third, so that C-E-G will have two rates of beating, (C-E and E-G)
which are syncronized. This produces a stronger pulsing effect while also
contributing to clarity. The more common denominators that exist in the
triad, the more resonance is produced by the interaction of the intervals.
Proportionality can also extend to the interaction of the fifths and
thirds, usually among the intermediate keys. This is so because thirds and
fifths are in acoustical opposition and in a well temperament, the keys with
the most highly tempered thirds have the purest fifths,( an important
consideration for Chopin!), and the keys with the purest thirds have the most
highly tempered fifths. This produces a very strong contrast in the remote
keys, since there is a very "active" sound to the harmony, yet the melodic
line can make use of pure intervals. This is a reason that keys such as F#,
B or Ab were considered "expressive" keys, the harmony was quite emotionally
affective.
In the keys found in the middle of the circle of fifths, there is a less
dramatic difference in the tempering, allowing certain "alignments" of the
intervals to produce triads with a lot of the beating working together.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.
This PTG archive page provided courtesy of Moy Piano Service, LLC