RE:A catalog of chords [replies to Carl]

-----Original Message-----
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Date: Thu, 10 Mar 2005 20:55:56 -0800
From: Carl Lumma
Subject: Re: Re: A catalog of chords

[Carl]
E-mail requires line breaks every 76 chars.

[Yahya]
Thanks, Carl, I'll keep trying to avoid unecessary line breaks. :-)

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Date: Thu, 10 Mar 2005 21:01:55 -0800
From: Carl Lumma <ekin@lumma.org>
Subject: Re: Re: A catalog of chords

[Yahya, earlier]
May I suggest you try instead the following function -

For each chord element a_i, with i = 1, 2, 3, ... (corresponding to
your a, b, c, and allowing tetrads etc.) write a_i = Product_j p_j^k_i_j
as the unique factorisation of a_i into powers k_i_j of primes p_j,
for j = 1, 2, 3, ... .

[Carl]
You lost me. You want a product here (capital pi)?

[Yahya]
Exactly! Is there a clearer way to write it in ASCII? Eg "PI"?

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[Yahya, earlier]
My motivation for choosing this measure is simple: all chord elements
with the same PMPP can be reached from unison in the same number of
steps in each prime dimension. By which I mean, when you've found
your way to the note 9, you've already traversed the distance to the
note 3, so there is nothing more "remote" about it.

[Carl]
Hmm... isn't 9 farther along the 3 dimension than 3 itself?

[Yahya]
Sure ... I'll try again: 3 is not more remote than 9 = 3^2. So adding a
3 to any chord containing a 9 will not make a more remote chord.
However, adding a 9 to a chord containing a 3 _may_ make a more remote
chord.

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