Sorry if this message appears twice; I initially sent it via a flaky
connection and wasn't sure if it made it through.
If I can butt in here, I think the answer to Monty's question is
complicated, e.g. how a perfect fourth relates to frequencies in
cycles/second. That depends on the tuning system used, e.g. if you want
to play with a piano, which is tuned using a system called equal
temperament then the tones that make up a perfect fourth, regardless of
which notes (d-g,c#-f#,...) always have the same frequency ratio. But
that's not always the preferred tuning system; I understand that some
violinists with perfect pitch find it difficult playing with piano
accompaniment because equal temperament is a sort of "detuning". I.e.
equal temperament is a deviation from the natural overtone series so
that you get the same pitch relationships in all 12 keys (Bach was
apparently the primary salesman for equal temperament, via things like
the Equal Tempered Klavier, as he loved the ability to modulate to
different keys, which the standard keyboard and equal temperament
provided for). Some people (with good enough pitch to hear the
difference!) prefer the system of just intonation, which is based on the
natural overtone series (i.e. the first overtone is an octave above the
fundamental tone and has a 2/1 frequency ration with the fundamental, a
fifth above that has a 3/2 relationship with the fundamental, etc...).
In that system frequency relationships for intervals vary based on where
in the "scale" (obtained by pulling the overtones back into the first
octave above the fundamental) you are. There are a number of other
tuning systems geared to highlight various frequency relationships. I
would suspect that great shakuhachi players (like any great musician but
shakuhachi seems, at least to me, to encourage listening at a level that
not all musicians are typically encouraged to engage in) could really
hear the differences between these systems.
There are lots of good references for this stuff and I'll make a point
to post a list if others are interested. I'm sure Dan and others could
also provide good references.
-----Original Message-----
From: Monty H. Levenson
To: shakuhachi@weber.ucsd.edu
Sent: 11/21/01 9:26 AM
Subject: Interval Classification
That produces an interval of a Perfect 4th (d-g-d). Next, play
Tsu-no-meri with an atari using the same 2nd finger (producing
Tsu-no-mere to RE and back). That produces the interval of a Major
third (e-flat to g and back). Finally, play RE with an atari to CHI
(RE-CHI-RE). That produces the interval of a Major 2nd (g-a-g).
>
> > That produces an interval of a Perfect 4th (d-g-d). Next, play
> > Tsu-no-meri with an atari using the same 2nd finger (producing
> > Tsu-no-mere to RE and back). That produces the interval of a Major
> > third (e-flat to g and back). Finally, play RE with an atari to CHI
> > (RE-CHI-RE). That produces the interval of a Major 2nd (g-a-g).
>
> > Dan
>
> Hi Dan,
>
> Thanks for all your helpful contributions to the list. As a trained
> musician and teacher, would you be willing to explain how the interval
> classification used above works, i.e. "Perfect 4th", "Major 3rd", etc.
> I'd be interested to know how this system relates to the frequencies
> in cps or hz. of the notes involved.
>
> Monty
-- Karl Young kyoung@slac.stanford.edu SLAC M/S 71 PO Box 20450 Stanford, CA 94309 650-926-3380 (voice)
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