60 vs 45

Paul & All,

While I agree that equilateral triangles work better than squares for
modeling triads, I still feel much better with right angles in 3D
(7-Limit). For one thing, while both triangles and squares tile a plane,
tetrahedrons aren't space-filling like cubes. For another, one of my
favorite 12-tone piano-mappable tunings doesn't work with 60 degree angles...

1/1 21/20 35/32 6/5 5/4 21/16 7/5 3/2 8/5 105/64 7/4 15/8

With squares, this looks like two rectangular prisms, one on top of the
other. With tetrahedrons, you wind up with a problem...

5/4-------15/8
/ \ . /
/ . \ /
/ \ /
1/1-------3/2

..The dots (7/4 and 21/16) are a 3/2 apart, but are not represented by the
same length or direction as the other 3/2's in the diagram. What to do?

Carl


SMTPOriginator: tuning@eartha.mills.edu
From: Paul Hahn
Subject: Re: 60 vs 45
PostedDate: 29-01-98 18:30:34
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