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RE: NPD 36 (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

3/25/1997 1:43:11 PM
From: PAULE

I e-mailed to find out more about this system.
I got the following response:

>The NPD 36 system is reforming to the proportion number: 4, 5, 6, 7, 8.
>Intervals h(n) are generators change amplitude these proportion
>frequency.

I'm not sure what that means, but it sounds like a 7-limit system is the
intent. 36-equal is in fact consistent through the 7-limit, but not the
9-limit. The accuracy of 36-equal within the 7-limit is actually slightly
greater than that of 22-equal (though 22-equal is consistent through the
11-limit).

>The intervals round has 36 sounds and based on the interval 19
>microtons.
>Therefor C major-0 key have intervals:0, 2, 4, 6, 8, 10, 12, 14, 15, 17,
>19, 21, 23, 25,
> 27, 29, 31, 33, 34, (36).

which, we may recall, Tomasz has named

>C, Q, Z, D, K, R, E, L, F, M, T, G, N, U, A, O, V, B, W, c.

So the scale is generated by an interval of 633 cents, which represents 10/7
in this system, starting on F or 15. Since three consecutive 633-cent
intervals mod the octave give a 700-cent interval, 19 notes from the cycle
of 633-cent intervals are needed to obtain a traditional diatonic scale (7
notes plus 6*2 intermediate notes).

There are seven 4:5:6:7 chords in this scale, and seven 1/7:1/6:1/5:1/4
chords as well. All six consonant triads of the diatonic scale have been
"septimalized," in other words, consonant tetrads that are built on these
triads exist in the scale.

Here is a little progression using Tomasz's letter names, M indicates a
4:5:6:7 chord (4 is the root), and m indicates a 1/7:1/6:1/5:1/4 chord (1/6
is the root)

CM Om TM Em QM Vm GM CM

00-02-04-04-02-04-06-00

12-14-12-12-14-16-14-12

21-21-19-21-23-23-21-21

29-29-31-33-31-31-33-29


This is a clever system and definitely seems worth exploring by microtonal
composers. It seems unlikely, though, that one could maintain a sense of
"key" unless the diatonic notes are treated as the main notes and the other
notes used only for "septimalization" or for passing tones or chords.

Thanks to Tomasz Liese for his original contribution, and please reply if he
disagrees or has additional comments.


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