Pythagorean Transposition


I remember my first encounter with tuning systems and micro-tonality, and the mind blowing realization equal-temperament was not the end-all of how to organize the notes of an octave. It’s been a continual area of interest for me, especially Just Intonation and naturally occurring harmonics.

For years I have also been fascinated by the traditions of esoteric mysticism and how they relate to music, but only recently have given myself the time to study them in any significant way. Henry Corbin talks about the importance in these traditions of symbols (as opposed to metaphors and allegory) as a key point of access to higher planes of consciousness and deeper understanding of the divine world and I’ve always seen music as one such symbol.

I’m certainly not alone in this. It doesn’t take more than a casual internet search of music+mysticism to find a thriving (often painfully new age) world of people interested in the subject. The idea isn’t new, but the history and development of it was not as familiar to me as I would like. I decided to research these traditions and experiment with my own ideas of how their philosophies might come to fruition in the 21st century. Logically, I started with the beginning of western music theory and Pythagorean tuning.

A primer for those not familiar: The basic premise of Pythagorean tuning is to build the chromatic scale by stacking fifths until they reach the home pitch again (C-G-D-A, etc., all the way back to C). One finds the interval of the fifth using whole number ratios, making it perfectly aligned with the natural tuning of the harmonic series.

The problem is, when using this system of perfect 5ths stacked on top of each other, the final note (cycling back to the original seven octaves higher) is not a pure octave transposition of the original. It’s about an 1/8th of a step too high (I won’t show the math here, but trust me). So, to make everything fit neatly inside an octave, important for structuring melodies, changes have to be made to the tuning, certain notes removed, and other potential adjustments that compromise the system.

What I’ve done here is ignore the need for an octave or melodies and taken the pythagorean construction of the 12 notes verbatim starting with a very low C and going up by 5ths until we reach a new C. This becomes a kind of micro-tonal modulation or, going with Corbin’s idea, a symbol of transformation. Taking these pitches in sequence we experience a musical journey through chromaticism, each step perfectly in tune with the one previous and the one after, but increasingly distant from the original tone until we reach a completely new place. It’s a musical ascension, and at the end we are similar in form, but changed in substance.

This is less of a new piece and more the beginning of an idea, one I’m still gathering my thoughts on what to do with. In the past, I have used harmonic drones as a meditation tool, a stand alone piece until itself, or a canvas for melodic improvisation. I find it incredibly beautiful as its own sonic space (even with the synthesized instruments); as an esoteric symbol, I’m finding this notion of harmonic organization central to my work.

In it’s full form, I imagine the piece/meditation to last 20-30 minutes. In this instance, I have sped up the building of the full harmony so that it lasts about 5 minutes in length. I recommend good speakers or headphones to get the full effect, especially since the drone spans seven octaves and has very low and high tones. Here’s the link:

Pythagorean Transposition

In the coming month I’m going to work on pieces and harmonic drones in various tunings, including irrational tuning (based on ratios of irrational numbers) and transcendental tuning (based on a selection of transcendental numbers). I’ll share these pieces in a separate post down the road.

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