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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