Fix a fundamental frequency F, and also three small prime numbers, p,q and r.  

Now imagine associating (as Euler did) a tone with frequency F * p^x * q^y * r^z to each point (x,y,z) in 3-dimensional space .  On a special plane through (0,0,0), all the points gets associated to the fundamental frequency F.  

Imagine, furthermore, a large circle in that plane centered around (0,0,0).  Imagine flying around that circle and hearing, as you pass nearby points with integer coordinates, the pitches associated to those points (the pitches fall within the range of human hearing because you confine your flight path to that special plane).

Now, no need to imagine anymore...you can just hear here how it sounds (for primes 3,5 and 7).  I'll post realizations with other primes soon.

This process, simple as it sounds (?!?), naturally engages the categories of melody, harmony and timbre, and with shifts in emphasis that simply reflect the geometry of the circle as it passes through the Euler grid.


My Travels in Euler Space

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My Travels in Euler Space

David Victor Feldman