[CAUT] Attention ratio gurus

[Fred Sturm]

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On 3/13/05 9:52 PM, "Wimblees@aol.com" <Wimblees@aol.com> wrote:

> But why does it beat 6 or 7 bps? Which coincidental partials are we heari=
ng?
> =20
> Wim=20

Hi Wim,
    The =B3ratio=B2 is really quite simple. You are listening to the 12th
partial of the lower note beating against the 1st partial of the upper note=
.
(Yes, okay, it=B9s possible you could also hear the 24th partial beating
against the 2nd partial, 36th against 3rd, etc, etc =AD but probably not). Wh=
y
that beat rate? Luck of the draw, to a large extent, depending on the
inharmonicity of the piano and how it was tuned. Not an interval I would
worry about, in terms of what the beat rate is. Instead, one would use it t=
o
check consistency =AD playing a series of triple octave/fifths (=3D 12:1) and
seeing if the beat rates were similar, or progressing. Useful if 17ths are
hard to hear or the like. Personally, I find double octave/m7ths more usefu=
l
(eg, C1/A#3, C#1/B3). The beat is almost always quite obvious and easy to
focus on (for those counting, it=B9s 7:1).
    The whole ratio thing is really just a matter of going up the partial
ladder of each note step by step and counting. And when you get into the
higher numbers, it=B9s useful to know that going up an octave doubles whateve=
r
the number is. It is rare that a partial above the 8th is reliably useful.
On concert grands, even the 12th and 16th are meaningful in some instances,
but in smaller pianos the really high partials are too unpredictable unless
you know the particular model fairly intimately.
Regards,
Fred Sturm
University of New Mexico



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