Ah, thank you for that clarification Dennis. I wasn't sure if you were referring to tuning in equal or wohl-temperament; now it makes sense to me. Yes, i believe that proportional or equal beating intervals are very useful for smoothing out and making a temperament sound more consonant. I think that aural tuners are responding to such consonance even when tuning their own quasi-equal temperament. Scott Jackson ----- Original Message ----- From: Dennis Johnson To: caut at ptg.org Sent: Tuesday, March 10, 2009 12:30 AM Subject: Re: [CAUT] professor tuning variables Hi Scott- A proportionally beating triad is a triad in which 2 or more of the contained intervals are beating at speeds proportional to each other. For example, inside a pure fifth the root position minor triad (m3 and M3) should both beat at exactly the same speeds. To be technical, there can be an inharmonic difference between this 6:4 fifth and usual 3:2 fifth most commonly used for testing the purity, but that is a decision for the tuner. My use of the word symmetry in this case refers to the relationship between sharp and flat keys. For example, in a theoretically perfect Thomas Young temperament the circle has symmetry because corresponding sharp and flat keys are exactly the size across the circle. FA=GB, BbD=BF#, EbG=AC#,AbC=EG#, DbF=BD#, and GbBb=F#A#. This particular temperament, and theoretical variations of it, are discussed in detail in Jorgensen's big red Tuning book. Hope that helps, Dennis Johnson ____________ -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090310/56a5daef/attachment-0001.html>
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