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Anyone who has played in an ocar inasubcontrabassoon quintet knows one thing well.

Piccolo ocar ina inset from aliexpress.com.   Subcontrabassoon image from subcontrabassoon.com.

Ocar inists and subcontrabassoonists know quite well that they can be expected to play passages without any chords, in the familiar sense, whatsoever.

Instead, a quintet’s ocar inists often harmonize what are more properly called clusters— three adjacent notes that would be dissonant on most other instruments—while subcontrabassoonists typically play in unison or an octave apart, with no harmonic relationship to the ocarina notes.   In fact the subcontrabassoons need not even be carefully tuned.

This reads like heresy to anyone more familiar with music theory than with ocar ina or subcontrabassoon repertoire.

That the resultant mellifluence is music to human ears (lucky enough to hear it) all but proves a concept fundamental to psychoacoustics.


             What is this fundamental concept?

            How does the music described reflect it?


The instruments here are trotted out for their pitch ranges. Ocar inas produce extremely high frequencies while subcontrabassoon frequencies are so low that they are as much felt as heard.

(This puzzle is based on solid musicology and science, and a fantasized world of ocar ina –subcontrabassoon music.)

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  • 2
    $\begingroup$ This video by Vi Hart may be relevant (or, at the very least, entertaining). $\endgroup$ – Deusovi Feb 17 '17 at 2:29
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So I think you're talking about

Overtones

Because

Subcontrabassoons playing in unison or in octaves would constitute a drone - a very low pitch drone. The sound generated by musical instruments is often not a single frequency, but several frequencies lined up above it in tandem, usually at multiples of the fundamental frequency. These generally taper off in volume as they get further from the fundamental, but can still be heard as it adds to the tone quality of the sound heard.

Since the ocarinas are so high-pitched, it's definitely possible that whatever fundamental they're playing is included in the overtone series of the drone instrument. This is because the overtones of the drone will get closer together as you progress through the series. For example, 5x the fundamental is closer to 4x than 4x is to 3x. To add, 2x is an octave. To cross the difference between the fundamentals of the subcontrabassoon and ocarina, it's likely that the overtones will be so close together that almost any note the ocarina plays, including all in those tone clusters fit in the overtone series.

This ties in with signal processing via Fourier analysis, which is used to find the frequencies that make up a particular sound wave. I'm guessing here, but perhaps the relationship with particle physics has to do with wave properties of photons and so on. I should probably read more about this stuff ...

The lack of careful tuning:

When two sounds are close in frequency but not exact, a listener can hear "beats" as the peaks and valleys overlap double in amplitude or cancel completely. These occur at a frequency equal to the difference between the sounds. In the case of the subcontras, that would be their fundamental, which is very low. Like really low. So low that it could be several seconds between beats, which, while still imperfect, won't be painful to listen to.

On the ocarina clusters:

As you might expect from the opposite side of the pitch spectrum, we turn the reasoning around. Tone clusters at such high frequencies will take advantage of the larger differences between adjacent fundamentals. Although the sheer highness might be grating, the token crunch to more midrange dissonances will be absent.

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  • $\begingroup$ Im not out of ideas yet, but I do have to sleep. More in the morning. $\endgroup$ – Matt Feb 17 '17 at 4:40
  • $\begingroup$ I'm not going to be allowed a good night's rest until I get some of this out. $\endgroup$ – Matt Feb 17 '17 at 4:52
  • $\begingroup$ Thanks @humn. I'm not sure I understand which direction to go for this "more" you speak of. $\endgroup$ – Matt Feb 17 '17 at 5:05
  • $\begingroup$ Before I continue reading, are you talking about molecular vibrations and how they relate to the absorption of photons (photosynthesis)? $\endgroup$ – Matt Feb 17 '17 at 5:15
  • $\begingroup$ Photosynthesis wasn't on my mind but probably involves the same concept. Almost everything at that scale does. What's so surprising is how that concept figures into human music, especially with the lowest instruments (in a way that feeds up to the the highest instruments, in terms you've already more than touched on.). $\endgroup$ – humn Feb 17 '17 at 5:17

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