Metatron Press MPCD-106R3 (2000)
“A resonant rosary of non-metric pulses and uncommon harmonies.” Nine frequencies of sine tones (120, 121, 123, 127, 132, 140, 150, 164, 185) no pair of which have the same difference as any other pair, arranged according to gray code, with the tones’ first appearances in ascending order, each possible combination of tones appearing exactly once.
In simpler terms: This piece is built from the phenomenon of beat frequencies. When we hear two pitches that are, say, one cycle per second apart, we not only hear the pitches, but hear a distinct pulsing, once per second.
I selected the pitches in this piece, starting from 120 cycles per second, so that the difference in pitch between any two notes would not be the same as the difference between any other two notes. For example, the first two pitches are 120 and 121 cycles per second, respectively, one cycle per second apart. When you hear them, you hear one pulse per second. No other pair of pitches are one cycle per second apart. The nine pitches make 36 different pairs, with 36 different frequencies of pulses between them.
The recording puts together all the possible different combinations of these nine tones. I used an ordering known as Gray Code (yes, also the name of an ensemble I’m in, which was named for the ordering method), which arranges the combinations of tone so that, in going from one to the next, only one tone needs to be added or removed.
There are 512 possible combinations of the nine tones (including the silent one in which none are heard). The piece is 1024 (2 times 512) seconds long. We hear each combination for one second. In the second between combinations, one tone fades in or fades out.
This is what happens in the first fifteen seconds:
- The first tone (120) fades in.
- The first tone plays at full volume.
- The second tone (121) fades in. We start to hear a pulse.
- The first and second tones (120 and 121) play together at full volume. We hear the difference pulse between them, once within the second.
- The first tone fades out. The pulse dissipates.
- The second tone plays alone at full volume. We hear no pulse.
- The third tone (123) fades in. We start to hear another pulse.
- The second and third tones (121 and 123) play together at full volume. We hear the difference pulse between them. Since 123-121=2, we hear two pulses during that second.
- The first tone (120) fades back in. While the 2 beat per second pulse from the previous second continues, we start to hear the difference pulses between the first and second and between the first and third tones.
- The three tones play together at full volume. We hear three pulses: 0ne (121-120), two (123-121), and three (123-120) pulses per second.
- The second tone (121) fades out. The pulses from the difference between it and the other two tones dissipate.
- The first (120) and third (123) tones play at full volume. We hear only the difference pulse between them, at three beats per second.
- The first tone fades out again. The pulse dissipates.
- The third tone plays alone. We hear just the one pitch, with no pulse.
This admittedly goes by rather quickly. But knowing what’s going on mathematically may give you a better sense of what you’re hearing. (Or not.)
This piece came about in a goofily practical sense. On my first visit to California, I visited a large computer store and encountered three-inch CD-Rs for the first time. Intrigued, I bought a box of them and wondered what sort of piece I might create specifically for that medium.
Three-inch CDs can contain up to 21 munites of audio. That comes to 1260 seconds, which is just over 2 to the 11th power, or 1024 seconds. Since I was working with powers of two and Gray Code in my other composing at the time, it struck me to use that fact in the composing. That suggested that I needed to arrange ten different sounds (plus silence) in a form that would clearly indicate the changes. Using Gray Code, and the way that things change within it, meant that I would use one sound fewer so that I could use the intervening seconds to make the changes. Once I started thinking about beat frequencies, the piece quickly came together.
I find this piece, purely abstract (or viewed another way, purely concrete) as it is, to be one of my most comforting to hear. Whatever else in the world may be falling apart, the simple march of physics and arithmetic moves inexorably on. I asked my more theologically adept friend, Tom Bickley, if I was right in hearing this as a religious piece. He said, “Yes, in the purest sense.”
By the way, I recommend listening to the piece on a system with good bass response, since the pitches are all quite deep, in the octave two below Middle C. I also recommend listening to it at a relatively high volume, but different people respond to the pulsing differently. You would probably do best to start at a lower volume and turn it up gradually to a level that you find more appropriate.