Here’s a subset of pitches derived from a theoretically Infinite scale. The theory of this new system of intonation is based on Zeno’s Paradox, which attempts to prove the impossibility of motion between one finite point to another. The harmonic ratios of this temperament are not based in prime numbers like in just intonation, but instead based around the infinite division of the number 100 (or of any arbitrary distance between two points, which can then be quantified and divided evenly).  I believe that the “mode” of its scale is rightly Modus Ponens, (an ancient logical axiom) which states:

Its effect is of one endless stream of octaves going lower and lower

The basis of my scale is poised as a response to Plato’s Timaeus in which Socrates describes the manner in which the “world soul” was created by the Demiurge , through the creation of the intervals the octave, the fifth, and the fourth below. They believed these three intervals corresponded to the creations of the ontological categories , Being (2/1), Difference (3/2), and Sameness (9/8).

I like to imagine this could have been an alternate tuning used by a rival “mystery” school to the Pythagoreans & Platonists, one that also believed in the primacy of numbers in describing the world, but whose sonorities lead them to Monism instead of to the rationalist idealism of the Platonic school. Monism suits the use of the monochord as a “philosophical instrument” by also rendering its a priori conceptual schemas into an a posteriori sonority because it suggests (through an iterative process of division) the manner in which all differences and multiplicities are related and originate from the fundamental (the “Monad” for the monists), and thus cannot be seen as distinct from the whole. They are instead part of the 1/1’s infinite attributes and modalities of being. Where the Pythagorean wants to inscribe metaphysical weight to musical notes arising from perfect prime numbers and link them to a harmony of the spheres; my imaginary school of Parmenides (the monist philosopher of which Zeno was a follower) could just as simply use Zeno’s paradox to to create a system of notes that disprove the notion that a bridge could move between any two fixed points of a string.

The advantage of this temperament from the point of view of Parmenides is that it retains perfect octaves by a simple process: division by two. By doing this it is able to rhetorically usurp the Pythagorean schools great conceptual aspiration which also happens to be the octave, by simple and elegant means. Famously the Pythagorean comma has been a complication to the a priori perfection of Pythagorean intonation. There is normally a 23.46 cents difference in the completion of one octave when approached through the progression of a fifths. This comma interval is thus charged with a metaphorical lack, sonically it feels like a yearning for one’s ideals to be fulfilled by the senses, for the realization of a platonic form in a world of disharmony. Upon further listening it even hints at the real material possibility of formlessness & even nothingness (it should be noted that Nothing & Zero were highly contested concepts during Plato and Parmenides time). Plato famously distrusted the senses and this interval encapsulates the tonal horizon of his distrust, the world outside the walls of the well ordered polis (as described in the Republic) is full of disharmony.

As listening to a bunch of octaves can be a tad simplistic and boring musically I’ve added an additional scale consisting only of pythagorean commas as a type of counterpoint to our Monist “bass line” of 2/1. Together they paint a picture of the way in which different philosophical and conceptual differences inform and highlight one another. The sound of their differences are heightened when contrasted against one another and show us how we can use music to study philosophy with more depth and achieve an intuitive understanding of both.

I'd like to conclude by putting forward a suggestion that all tuning systems attend to metaphysical and epistemological tendencies of their creator in the production of their intervals; and that listening to them deeply, helps us hear how these philosophical tendencies conceptualize themselves in a musical language. This approach stands outside of the realm of pure reason (where philosophical themes are often siloed- especially in the west), but as a sensation which describes a taxonomy of differences and how they form a hermeneutic relationship with itself. Harmony is at once a political, metaphysical, and musical language always working in tandem on multiple aspects of the psyche. Thus the phenomenology of listening produces impressions of intonational naturalism, where the differences in a temperament (through their repetition within a milieu) produce the semblance of immutable natural law; much in the same way that a map can seem to precede the territory it maps and vice versa. This is because tunings are at this tension between the World and the Earth, and their sonorities can manage to stand in for either : or even oscillate between being both.

Home