Re: [tuning-math] Glumma
- From: Gene W Smith <genewardsmith@xxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxx
- Date: Fri, 12 Jul 2002 14:36:45 -0700
On Fri, 12 Jul 2002 12:07:28 -0700 Carl Lumma <carl@xxxxxxxxx> writes:
> >glumma [1, 36/35, 8/7, 6/5, 5/4, 48/35, 10/7, 3/2, 5/3, 12/7, 7/4,
> >96/49]
>
> Rock! What pattern of scale degrees produces the chords?
The six complete tetrads in cubic lattice notation form a 2x3 rectangle:
[0 -1 0] [0 0 0]
[-1 -1 0] [-1 0 0]
[-2 -1 0] [-2 0 0]
The rule is that the chord [a b c] is major (otonal) if a+b+c is even,
and minor if it is odd. A major chord has
root 3^((-a+b+c)/2) 5^((a-b+c)/2) 7^(a+b-c)/2), and a minor chord root
3^((-a+b+c-1)/2) 5^((a-b+c+1)/2) 7^((a+b-c+1)/2).
This means that [0 0 0] and [-1 0 0] are the major and minor tonic
tetrads, and [-1 -1 0] and [-2 -1 0] are the major and
minor tetrads on 8/7. [0 -1 0] is the minor tetrad with root 5/3, and [-2
0 0] the major tetrad with root 48/35.
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