The Harmonic Sequencer
I will present a project that I am working on, namely a sequencer that mimics in terms of temporal timing the relationship between the harmonic series and the equal temperament tuning, but in reverse.
My idea was triggered by thinking about the relationship between equal temperament tuning and the harmonic series. Many composers have in modern times experimented with tunings that deviate from equal temperament tuning. From Harry Partch, over LaMonte Young and Terry Riley, the list is as long as it is illustrious and varied. However, all these tuning, just and otherwise, are always regarded as deviations from the norm of the well-tempered one which has become a sort of gold standard of tuning all around the “civilized” world, and certainly here in our Western hemisphere. Working recently on a project with music by Arnold Dreyblatt (b. NYC, 1953) who works a tuning system based on the harmonic series, it struck me that by comparison the gold standard of rhythm today is, for all intents and purposes, the metronomically exact pulse that is used as an underlying norm for so much of the music produced and performed today.
My thoughts unfurled like so — once upon a time was the harmonic series: more than just an archaic notion, it is actually a property of the physical laws governing our reality. However, the harmonic series was not a satisfactory tool for creating and playing music once composers moved beyond fairly straightforward harmonicity. So, more or less simultaneously invented in the 16th century by a Chinese and a Dutchman, the working compromise known as equal temperament tuning is such a success that almost 350 years later not many composers or musicians or people bother to spend much time dealing with the harmonic series. So, what if the metronomically correct four-to-the-floor, or whatever the time signature happens to be, is also just a modern, agreed-upon standard evolved from a proto-rhythm or proto-timing that we have forgotten about? And what if that proto-timing was also based on relationship of the frequencies in the harmonic series (which after all is a reality-based, empirically tested principle governing the behaviour of sound waves in our reality).
Naturally, I am not actually suggesting there was ever such a thing as a proto-timing. All this is merely a creative conceit. But, recalling Stockhausen’s ideas about extending pitch relationships downwards into the domain of rhythm—frequencies being numbers that one can manipulate mathematically—I started working on a sequencer based not on a metrically correct clock source, but on an irregular clock source related to the harmonic series. This involves “correcting” each pulse by the same ratio that a harmonic series pitch deviates from it’s equivalent equal temperament note. Thus octaves are always 1:1, but all other pitches deviate by certain specific ratios and hence those particular steps in such a sequencer would also deviate by the given ratio.
For the symposium, I will give a presentation of this idea, as well as a practical demonstration of the sequencer (constructed in MaxMSP). The presentation will include a brief history of tuning systems and a more in-depth exploration of the concepts and mathematics I have used. The practical demonstration would display the work done for the MaxMSP patch, as well as, of course, playing several examples of the sequencer in use.
Beyond Pythagoras 