Another question regarding Well Temperament

A440A@AOL.COM A440A@AOL.COM
Tue, 22 Aug 2000 20:37:16 EDT


 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.   



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