Octave Equivalence - Bohlen Pierce

>
> >
> > It seems to me that 2/1, 3/1, 4/1, 5/1 etc should exhibit a
> continuous, perhaps exponential, decrease of equivalence, rather than
> 2/1 being 100% equivalent, and all others 0% equivilent.
> >
> > Dante
>
> Gee... that's interesting Dante... but, the 12th serving as the
> "octave" doesn't seem to be doing the same thing as the "walloping"
> 2/1. I don't think it's "accustomization" either.

I heard one theory that since the inner ear is arranged as a spiral,
the hairs at 2x frequency are adjacent ACROSS the spiral (rather than
side to side). This somehow would supprt a physical reason for octave
equivalency, but no other. The same place I read this said that
octave equivalency has also been tested and detected in animals (dogs,
though I don't know how).

> Paul??
>

Yeah... Paul??

Bob Valentine

> __________ ____ __ _ _
> Joseph Pehrson
>

>I heard one theory that since the inner ear is arranged as a spiral,
>the hairs at 2x frequency are adjacent ACROSS the spiral (rather than
>side to side). This somehow would supprt a physical reason for octave
>equivalency, but no other. The same place I read this said that
>octave equivalency has also been tested and detected in animals (dogs,
>though I don't know how).

Spiral models of music perception have been proposed many times because
the spiral mathematically combines logarithmic and linear scales (same
distance along the spiral can be correlated with linear freq differences
while radial distances can be correlated with equal freq ratios: so we can
draw a spiral so that twice, four times, eight times, the distance on the
spiral line up on the same radius of the spiral.) It's sometimes proposed
as a multidimesional scaling of pitch ("invariants in sound" - Johns, Hahn)
and sometimes speculatively as an actual physical reality. In the latter
case, though, I think we're talking about the arrangements of neurons, not
of the cochlea. In actuality, I don't think anyone has the slightest clue
about the arrangements of individual neurons, and I don't find the spiral
to be a particularly useful mathematical abstraction.

jason