AW.: RE: Re: compact lattices

I've largely stayed out of the discussions on compact lattices (e.g.
maximizing n-ads with a given number of tones, in both rational and tempered
tone spaces), mostly because this was an active interest for me 10 or 15
years ago, but I would like to add one point.

When I look at and listen to pitches on a lattice, I seek paths that are
musically useful to me. This will mean first locating paths that are
familiar to me, and then the more exotic ones. For example, I found the
Hanson/Wilson lattices (dominated by 6/5s) to be interesting but not
immediately useful, both because they were short on chains of perfect fifths
and they lacked the variety of something like an eikosany. In other words,
not conventional enough for old music and not exotic enough for something
new. Similarly, I find most of the twelve tone lattices posted on the list
to fall between these attractive extremes, and frequently wish for some
indication of the musical utility the lattice maker has found or imagined in
the construction.

Inventing a set of pitches is, in and of itself, not an act of great
virtuosity or art. Finding paths among the pitches, on the other hand, is
where music making really starts.

Daniel Wolf
Frankfurt am Main

At 08:15 9/30/99 EDT, you wrote:
>From: DWolf77309@cs.com
>
>I've largely stayed out of the discussions on compact lattices (e.g.
>maximizing n-ads with a given number of tones, in both rational and tempered
>tone spaces), mostly because this was an active interest for me 10 or 15
>years ago, but I would like to add one point.
>
>When I look at and listen to pitches on a lattice, I seek paths that are
>musically useful to me. This will mean first locating paths that are
>familiar to me, and then the more exotic ones. For example, I found the
>Hanson/Wilson lattices (dominated by 6/5s) to be interesting but not
>immediately useful, both because they were short on chains of perfect fifths
>and they lacked the variety of something like an eikosany. In other words,
>not conventional enough for old music and not exotic enough for something
>new. Similarly, I find most of the twelve tone lattices posted on the list
>to fall between these attractive extremes, and frequently wish for some
>indication of the musical utility the lattice maker has found or imagined in
>the construction.
>
>Inventing a set of pitches is, in and of itself, not an act of great
>virtuosity or art. Finding paths among the pitches, on the other hand, is
>where music making really starts.
>
>Daniel Wolf
>Frankfurt am Main
>
>
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Dr. Wolf,

You hit it right on the head. This is precisely the issue in 'seyir' in the
maqam tradition. For the musical habitat provided by a given maqam
there seems to be uncountably many 'admissible' paths the musician can
choose from, together with an infinite set of 'in-admissible' paths.
Finding magical admissible paths might be one way of characterizing the
essence of maqam music.

Respectfully,
Dr. Can Akkoc
Alabama School of Mathematics and Science
1255 Dauphin Street
Mobile, AL 36604
USA

Phone: (334) 441-2126
Fax: (334) 441-3290
Web: http://199.20.31.100/GIFT/