Skip to content

pitch == rhythm

Duality is concept that was crucial — and somewhat magical — in my training as an economist.  I first encountered it when I learned linear programming, and then in my microeconomic theory classes, with the duality at the heart of the theory of optimizing behavior by both individuals and firms.

So now I’m kicking myself for not noticing the fundamental duality of pitch and rhythm, well-explained and demonstrated by Dan Tepfer.  What a wonderful observation!

I had noted before that in English we say a pitch is “higher” than another, when what is actually different is that the “higher” pitch is a frequency that fluctuates faster.  And the speed of the sound wave fluctuations is, of course, a rhythm.  We hear this in familiar settings: when something repeats a sound at a high frequency, we hear a pitch (e.g, a plane propeller).  But Tepfer focuses our attention on intervals and chords, created by polyrhythms.  For example, the familiar three-against-two rhythm generates a perfect fifth.

Makes me wonder: the current explanation for how “consonant” an interval is — with the fifth being the optimum optimorum if you don’t count the octave — is the simplicity of the frequency ratio, 3:2 in the case of a fifth. Is that why the three-against-two rhythm is the most common polyrhythm that is non-integral?  Or is it just because it’s easier to play than, say, six-against-five, which generates a minor third?

The duality between pitch and rhythm also shows up in how we talk about tuning.  When two strings are tuned slightly differently, we hear “beats” as they go in and out of phase.

Post a Comment

Your email is never published nor shared. Required fields are marked *