Bill, Regarding what you have written, how would this bear upon the following tuning scheme? I am tuning in ET, practicing for the RPT exam, so apply everything to ET if you will. I use an F3-F4 temperament. Expanding upwards, I use thirds, fourths, fifths, then tenths and seventeenths, along with octave combos and octave fifths. Immediately out of the temperament, fifths are favored, but they are not quite perfect, fourths have some more beat than fifths. Thirds and tenths progress evenly (attempted anyway). From C7 up, I tune for the best octave sound, checking with tenths and seventeenths and octave combos. Expanding downwards, I tune by octaves first, listening at the 6:3 partial, then checking with fifths first (since the fifth 3:2 partial pitch is an octave lower than the 6:3 partial of the octave), then fourths, then thirds and sixths, tenths, and seventeenths. I generally favor the fifths to the fourths, but get a smooth thirds progression. I also use the 6:3 check, and usually have the minor third a little slower than the major sixth. From C2 down, I use the minor fourteenth (octave-minor seventh) to get a smooth progression, gradually slowing as I reach A0. Is this what you were talking about with the thirds and sixths? John Formsma Blue Mountain, MS In a message dated 12/17/99 7:03:08 AM Pacific Standard Time, Billbrpt writes: << This is where closely voiced chords are played. It is easy to make the piano sound disharmonious by concentrating on favoring 4ths, 5ths and octaves and ignoring the 3rds. Moreover, the 3rds are pretty important all the way down to F2 but lose their importance after A3. After A3, you can let them become faster as you stretch the octaves to get more of the "singing tones" out of your 10ths. >> Dear List, I always try to correct my spelling and proofread content before I send a post but I often miss a fatal error in spite of my efforts. The above statement about the importance of 3rds to the harmony of the piano's midrange should indicate A4, not A3. I meant to say that in my opinion, the exact rate of beating of the major & minor 3rds & 6ths is most important between F2 and A4. Beyond either point, they become virtually inaudible and thus lose their importance. The wider RBIs, the 10ths, 17ths and other RBIs of over an octave become more important above and below these points. Within these areas however, is where closely voiced chords are played. If tuning involves listening to Slowly Beating Intervals (SBI) only and ignores the RBIs, cumulative errors can result in some odd, disharmonious sounding chords that are adverse to the music being played. Bill Bremmer RPT Madison, Wisconsin
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