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Meantone chains

🔗Paul G Hjelmstad <phjelmstad@msn.com>

2/28/2007 1:24:19 PM

Is this of any use?

Here's an idea I found in my notes from about 15 years ago: (10 B.T.)

Take a parallelogram (0,0), (4,4), (11, 5), (7,1) Area: 24
Take another one (0,0), (3,3), (8,4), (5,1) Area: 12

Now form chains of these parallelograms:

The first is equated with the white key ribbon: F,A,C,E,G,B,D. Each
parallelogram is based on (0,4,7), but represented also as (0,1,4)
(D4)

The second is equated with the black key ribbon Bb, Db, Eb,Gb, Ab.
Each paralleogram is based on(0,3,5) but represented also as (0,1,3)
(Inverse of D4= S3)

I have a lot of other calculations which I cannot make any sense
of now.

Int(12/7)= 1
Int(12/5)= 2
Int(24/7)= 3
Int(24/5)= 4

I wish I knew what I thought I was onto! This is long before
tuning-math.

PGH