Thursday, July 2, 2009

the time relationship between pitch and rhythm (and harmony and polyrhythm): Part I

Sometimes it is good to get back to basics. Sometimes it helps to pull the camera back, throw on the wide angle, and remember some of the really obvious things about musical sound-- such as:
  • A tone is a rhythm happening really, really fast.
  • A harmonic interval is a polyrhythm happening really, really fast.
But before we get to that, it pays to consider the question "What is a sound?"

Sound is, most literally, the rapid compression and rarefaction (de-compression) of air, which is perceived by tiny hairlike structures in our ears and decoded as sound by our brains. However, all sounds are not tones-- some are impulses and some are noise. A tone (with a definite pitch) results from an oscillation of impulses in a periodic manner. What is an "oscillation of impulses?" Anyone who has ever used an oscillating fan knows that an oscillation is a repeated movement back-and-forth at a constant speed. When air molecules compress and rarefy at a consistent interval in a regular pattern, an oscillation, or tone, is produced.

Because electronic music is all about creating electrical impulses that are analogous to (i.e. "electronically representative of") the air's compression and rarefaction, you can learn a lot about sound and vibration by playing around with a synthesizer. A good analog synthesizer can teach you a lot, particularly if it has multiple oscillators and an intuitive user interface. My favorite tool for this purpose is an old Moog Model D, as its knob-based interface makes sense to me.

On a synthesizer, an oscillator is a circuit designed to generate an AC voltage that swings positive, then negative at regular intervals to electronically represent air that compresses, then rarefies at regular intervals. This voltage can later be converted into actual vibrating air by a transducer, or speaker.

The Moog, like many analog synthesizers, has a few oscillators that can be set to oscillate in one of several ranges, including 5 audible ranges and one labeled "Lo." "Lo" is what is known as an LFO, or "low-frequency oscillator." This means it creates oscillations, or patterns of impulses, that if transduced into sound would be too slow for the ear to recognize as a tone. What do you get when you have a regular pattern of impulses too slow for the ear to recognize as a tone? You get a rhythm!

The slowest rate of oscillation that a human ear will recognize as a tone is approximately 20Hz, or 20 cycles per second. 20 or more impulses in one second, at regular intervals, creates a very low audible tone to most humans. Anything slower, and the typical ear will hear instead a series of successive impulses--A repetitive beat, in other words.

In synthesis, LFOs are typically used in conjunction with other circuits to create vibrato or other modulation effects (among others), and are not typically transduced into sound. However, if one has a synth like the Model D that allows patching of the LFO to the output, listening to what it sounds like can be pretty informative.

When a Model D oscillator is set to "Lo" and routed to the output, depressing a key causes a series of audible, electronically generated clicks, or impulses, that can be heard through the speaker. If keyboard control of the oscillator is turned on, then pressing a higher key causes the impulses to speed up in relation to one another. Depressing a lower key causes a slower series of impulses.

This basically creates a slow-motion movie of exactly what happens when when we use the synthesizer (or any other instrument) to create a tone, except that when we move up to a faster rate of oscillation, we get tones instead of rhythms. The faster-in-succession the impulses, the higher the pitch.

Particularly interesting is to explore the estuary between the audible and sub-sonic ranges of oscillation. For example, selecting the lowest audible range (labeled 32' on the Moog) and depressing the lowest key on the keyboard-- and then selecting "Lo" and depressing the highest key of the keyboard-- will start to give a picture of the transition between "series of impulses" and "tone." Utilizing the tuning and pitch-bend functions can start to give an even more complete picture.

In the following example, I have set the oscillator to a square-wave (which is essentially a binary "off-on" type of impulse, very good for demonstration purposes). I first depress a "low C." You will hear a series of impulses occurring at about 150 beats per minute. Then I move up in octaves, first with a C an octave higher on the keyboard, then another couple of octaves above that until I reach the top key of the keyboard. Each octave up causes the rate of clicks to double (say, from quarter notes to eighth notes, then sixteenths, etc). At this point you can almost begin to hear the impulses wanting to blur together into a tone. To go yet another octave above, we must move now to the 32' setting (signaled by a brief pause), at which point the tone becomes obvious and clear, but very low in pitch. In fact, it is so low in pitch that depending on your speakers, it may appear an octave higher than it actually is. This is because the square waveform contains a lot of harmonics and not all speakers can reproduce very low frequencies with any linearity. Finally, I go one additional octave above for good measure.

The region at which your personal ears begin to perceive tone as opposed to rhythmic pattern can be further narrowed down by utilizing the tuning function on the synth. Using the tuning adjustment and/or the pitch bend wheel, you can find the exact point at which your ear fails to hear the distinct impulses and begins to instead hear a tone.

For another example, I set the oscillator to 32' and turn the tuning and pitch bend controls all the way down. I then set the portamento ("glide") function to its maximum (slowest) setting. This allows me, by depressing the bottom and then top keys of the keyboard, to create a sweep that goes from the sub-sonic range well up into the audible band, and back down again. Notice as the rapid clicks morph into a rising tone. Pretty cool!

In Part II, we will explore harmonic relationships between tones and their relationships to polyrhythmic patterns of impulses.

No comments:

Post a Comment