NOTE: The tones in this piece are low enough that most laptop speakers won't produce them. Please use headphones or larger speakers. After an initial pause, the piece has continuous sound.
For Alvin Lucier (2016)
for sine waves
I came up with the general concept for this piece in 2009 and finally solidified it in 2016. After performing some of Alvin Lucier’s music in 2009, I became fascinated by the idea that tones both above and below another tone could produce the exact same rate of beating (because the rate is determined by the difference of the tones’ frequencies). Additionally, when two tones are close enough to each other, it can even be difficult to discern which one is above or below the other.
In a very simple sense, beating ends up sounding like a wobble or sometimes like vibrato. Some of Lucier’s music focuses on creating beats and the various acoustic/physical phenomena that result. Perhaps the most famous example of this is his series called Still and Moving Lines of Silence in Families of Hyperbolas.
In my piece For Alvin Lucier, a single sine wave is continuously played while the other sine waves fade in and out. These additional sine waves alternate at frequencies above and below the initial, central sine wave. The frequencies above and below are always the same distance from the central tone, so they create the exact same beating rate.
As the sine waves alternate, their frequency differences from the central tone follow the Fibonacci sequence. They expand from one to thirteen hertz, at which point the lower and upper frequencies swap positions in the speakers and follow the pattern backwards.
This recorded version does this process once, frequencies expanding and contracting around the central sine wave, but an installation version would continuously perform this expansion and contraction indefinitely. In this stereo version, the center pitch is panned to the center and the two other sine waves only come out of one or the other speaker. In a live or installation version, there are three speakers (one for each sine wave).
Thanks to Alvin Lucier for all of his beautiful music. This piece is humbly dedicated to him.