I’m currently Working on a 7-limit scale to complement the original pitches I started working on for the piece. This is constructed as a harmonic space1 in two dimensions, five and seven, and can has the following relations:

  7/5 7/4 35/32  
32/25 8/5 1/1 5/4 25/16
  64/35 8/7 40/21  

In notation:

image notation of scale

Since one of my main interests here is to find interesting beating patterns, this particular pitch set provides a few pairs that gives nice patterns. One of these, $\frac{32}{25}$ against $\frac{5}{4}$, has a simple rhythmic pattern, given the fundamental is 200Hz, of $\frac{1}{6}$ as is given by:

$\frac{1}{200(\frac{32}{25} - \frac{5}{4})}$


1 Tenney (2008) On ’Crystal Growth’ in Harmonic Space (1993 - 1998)., Contemporary Music Review.

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