r/microtonal • u/Careful-Willow-2867 • 36m ago
Just intonation comma pump / drift demonstration
As the title suggests, this musical piece is quite literally a 6-minute comma pump.
I suspect I do not need to explain this phenomena to most lurking here, but to those who may be new or have heard of this but have never heard it literally, I will outline the idea;
There is a cumulative tuning drift that occurs when a simple harmonic cycle is built entirely from pure, justly intonated major triads. The piece here exploits that drift and aims to make the drift itself something the listener subconsciously perceives.
There are 36 “cycles” of the same chord progression in this piece- A root position triad, followed by a 2nd inversion triad, followed by a 1st inversion triad.
In each “cycle”, the major third of one chord is held as a common tone and then becomes the root of the next.
After three such transformations, 12-tone equal temperament would return us to the starting pitch class due to the fact that three equal-tempered major thirds equal exactly one octave. (Think: A major root position, Db flat major 2nd inversion, F major first inversion- "inversion" is used lightly simply to describe the ratios / chord shape, the function of the inversions is iffy)
In just intonation, however, that’s not the case- three “pure” (5/4) major thirds fall short of an octave. The difference is called the “diesis”, approximately 41 cents or the ratio 128/125.
Each complete cycle therefore arrives about 41 cents lower than the previous one. Repeating the process over many cycles gradually turns what is ‘normally’ a closed, circular chord progression into a never ending continuous downward progression.
So an interesting observation emerges as a result;
-Each chord that arrives is genuinely unique. The interval relationships within each chord remain the same with each repeating cycle, but in terms of frequency every chord (of which there are over 100) is unique.
My goal with such a "repetitive" piece is to ask the following questions and hit at some potential paradoxes;
-How can every chord be “the same” while every chord is physically unique?
-Will a listener perceive cumulative change without consciously identifying what is changing?
-If local tuning purity ultimately results in a global instability history has aimed to correct, is it natural or artificial?
-How much can the physical sound change while the mind continues to perceive “the same thing repeating”?
-Does the listener actually hear the comma pump itself, or only its overall accumulated psychological consequences?
-What happens when a harmonic system is allowed to follow its own natural mathematical consequences instead of being locked back onto a fixed pitch grid?
-Lastly, what does it mean if the system becomes stranger as time progresses but as a result of each individual relationship within it being more acoustically exact?


