Re: What is music ... = spirals ?

Subject: Re: What is music ... = spirals ?
From: Kevin Austin (
Date: Sun Nov 20 2005 - 19:43:29 EST

This is one of the bases of western music theory, and seems to have
evolved at a time when range was restricted to the human voice.

Find a piano. In the bottom octave of the piano you will play the
note pattern D E F E F E D. In the very top octave of the piano you
will play Eb F Gb F Gb F Eb. Play them together. Do you hear them as
being pitch class equivalents?

One response is: "No, I hear minor ninths miles apart." Another
response is: "Wow! They sound like octaves!". A third response is:
"Er, the notes are too far apart for me to judge them as a unit."
(beyond the critical bandwidth).



At 18:10 -0500 2005/11/20, Michael Gogins wrote:
>Pitch is a linear space, pitch-class is a quotient of that linear
>space and thus a circle. That is, pitch without respect to octave is
>a circle.
>-----Original Message-----
>From: Kenneth Newby <>
>Sent: Nov 20, 2005 4:36 PM
>Subject: Re: What is music ... = spirals
>Hmmm... I wonder if we're conflating objective features with subjective 
>(perceptual) here? Color and pitch are both percepts and both have a 
>"circular" nature: the circular nature of perceived color and the 
>circular nature of octave equivalence. Both color and pitch can be 
>represented as frequencies but neither of these frequency 
>representations imply circularity.

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