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 _____________ On Mon, Mar 9, 2009 at 5:04 AM, Scott Jackson <scottwaynejackson at hotmail.com > wrote: > Dennis, or anyone, > Can you elaborate on "symmetry or proportionally beating triads". I don't > think that it is a phrase that I have heard used before. > Thanks, > > Scott Jackson > > > ----- Original Message ----- > *From:* Dennis Johnson <johnsond at stolaf.edu> > *To:* caut at ptg.org > *Sent:* Thursday, February 26, 2009 2:53 AM > *Subject:* Re: [CAUT] professor tuning variables (David Love) > > > Shifting particular notes by 1/2 cent either way to hone in symmetry or > proportionally beating triads are the aesthetic judgements that make me > smile on the job. > > Dennis Johnson > St. Olaf College > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090309/89e2e97e/attachment.html>
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