Virgil's naturaL beats

[Richard Moody]

----- Original Message -----
From: Jon Page <jonpage@mediaone.net>
To: <pianotech@ptg.org>
Sent: Sunday, February 11, 2001 7:07 AM
Subject: Re: Virgil's naturaL beats


>
> > I have heard the HT people say that when there are proportional beatings
> > in a temperament chord, the beatings counteract one another.

When I was instructed on tuning, one check was that a major triad would
cancel the slow roll of the fifth.

Jon Page


    I always noticed in a triad you don't hear the beats of the 3rds so much.
Some of the older tuning instructions do give triads as tests.  I just saw
triads in Braid White's 1909 book, "Piano Construction" but he didn't say much
about them.
    It is like the beats cancel each other out somewhat.  This is especially
noticable on my synthesizer, and I guess then on organs. So I am wondering since
the difference of two close frequencies produces a beat, then wouldn't the
difference of two beat rates (also fequencies) produce a slower beat equal to
the difference?  How do 3 coincident frequencies in a triad interact?   If you
take C-E G In root position you have the 3/2 of C-G (.88), 5/4 of C-E (10.38),
and 6/5 of E-G 17.79 bps).  The aritimetical difference between the major 3rd
and minor 3rd is     7.41.    If the .88 rate of the 5th is considered then that
takes it down to 6.53 bps.   Hmmm that is exactly the beat rate of E--G# 3rd
below middle C.

BUT when I listen to the synth (Roland Juno 60) the beat rate of the triad
sounds like it is the same as the C--E below m C  which is 5.19, much slower
than
the E--G# 3rd.  Interesting therate sounds as the 3rd an octave down.
Also I can hear the 5th beating through it.  Of course these are very long
sustained notes where the piano notes are evanescent.  When you press C-E you
hear the 10.38 but when you press the G with that it slows down.  Or if you
press E-G you hear the
fast minor 3rd but when you add the C it slows down to the 5.2  bps.
Interesting.   As they say on the internet, FWIW   for whatever it's
worth.   ---ric