Is it true that crystals have certain resonances? Is there any relationship between those resonances and the harmonic resonances of just intonation?

You may know that there are several systems of categorizing instruments. In one system, you have categories such as:

• chordophones — instruments with strings,
• metallophones — instruments with metal keys,
• membranophones — drums, and
• lithophones — which are instruments made out of rocks

Rock instruments are more common than you might think:

1. There is a famous ancient chinese gong set that is made out of rocks.
2. There is also a set of stone pontoons at the Mayan city of Chichen Itza that are tuned to a lovely scale.
3. For those who can’t get to China or the Yucatan Peninsula, one of the most exotic lithophones in the world is Leland Sprinkle’s Stalacpipe Organ. It can be found in Luray Caverns, about an hour west of Washington D.C. Its dulcet tones also hold the record of being the largest musical instrument in the world.

One cool thing about lithophones is that with these ancient instruments you can actually know for certain the actual scale used hundreds or thousands of years ago.

Lithophones are distinguished in having perhaps the most inharmonic spectra of any acoustic instrument. Bells and metallophones are also inharmonic. Actually, all acoustic instruments in the world are inharmonic because there is no such thing as an ideal string or waveguide. But some wind and string instruments in particular are close to being harmonic. Still, they are not exactly harmonic. Piano strings are so inharmonic that the scales have to be stretched simply to avoid excessive beating in the upper partials when octaves are played. The only way to hear a perfectly harmonic overtone series is to listen to a digital oscillator played without any effects or modulation.

Quartz is a rock and thus quartz crystals can be used to make lithophones. Quartz actually vibrates mechanically and has a very high Q (the resonance parameter). The pitch at which it vibrates has a little to do with the purity of the crystal or its temperature, but is almost entirely a function of the actual physical dimensions of the crystal. Now quartz has this thing called the piezoelectric effect which means that when you press on it, the pressure in the crystal matrix actually translates into the acceleration of electrons, creating a voltage potential across the crystal in one direction. This means that if you ring a quartz, there is a voltage generated at the same frequency! Also, if you put that crystal inside of an oscillator circuit that has been tuned close to the crystal’s resonant frequency, or one of the inharmonic overtones, then that circuit is going to lock to a very precise frequency and the frequency is not going to drift much over humidity and temperature changes like a spring or a tuning fork might because quartz is not very sensitive to those things. So it’s great for making a very stable oscillator. Because there is mechanical motion, technically you could hear the quartz if you could hear that high. Actually, watch crystals are usually pretty low frequency (32kHz is typical) so bats and dogs could certainly hear them if they were up close or if they were amplified.

Is resonance purely an acoustic phenomenon of sound? Or could you have resonance in a vacuum?

You don’t need air to have an overtone series. Anything that is periodic and not moving in a perfect circle will do. So the planets are in elliptical orbits and there is a bit of overtone action on them. The celestial mechanics of all the different heavenly bodies acting on one another through gravity is odd enough that even the planets are not going to have a perfectly harmonic overtone series. Where you see harmonic ratios more is in the relative periods of planets. Because of, I guess I’d call it gravitational resonance, you see some near-integer ratios there. But they are not exact and they are not really overtones of a single waveform.

You also run into harmonics in quantum physics/wave mechanics. The effects of that are visible in the organization of the periodic table of the elements.

Are microtonalists opposed to the standard Western tuning because that tuning is based on consonances and microtonalists favor dissonance?

No, not at all. It is a common misperception that microtonal music is dissonant. From this comes the idea that microtonalists are people who like music that sounds dissonant and out of tune. That’s true for a small number of experimental microtonalists. But this is not the case for most composers working in this field.

The misperception originally started because many early 20th century works labeled ‘microtonal’ featured serialist pieces written in 24 tone Equal Temperament. 24tET, which is also known as “quartertone” tuning, was chosen because it was easy to tune and play if you have two pianos and four hands (two players). You just tune two pianos to the standard 12 tone equal temperament, and tune them a quarter tone (50 cents) apart. But 24tET, despite this convenience in setting up, is a rather dissonant tuning that does not have particularly attractive resources.

A century ago, quartertones were an expedient way to try out new pitches. It is not any longer an advantage of convenience to limit oneself to trying out only one alternate tuning. With software tools like LMSO, any tuning can be auditioned, experimented and improvised with in an instant. For some composers, promising scales have even led to the development of new instruments and orchestras. This is now possible because there is no longer any risk of building an instrument that will use a new tuning and finding out afterwards that it doesn’t sound right. Instruments can be modeled in advance, and their sound with a given tuning can be auditioned before the first tree is sawn. This means the development of new instruments is no longer a crap shoot.

New scales bring new dissonances, yes. But they also bring new consonances as well. They bring new melodic and harmonic resources, and hence new means of expression, new capabilities, and new powers to communicate.

Isn’t microtonalism a belief that pitch is irrelevant and all scales are the same, no scale is better than any other, and thus common western tuning should not be favored.

Ivor Darreg, the renowned instrument builder and microtonalist said “There are no bad tunings.” It takes a while to actually get to the point where you can largely agree with this statement. I fought it for years but I think I have given in.

That is not to say that all tunings sound the same. It is not to say that one tuning is as good as any other. It is not to say that all tunings can be used for the same things. It is only to say that there are no bad tunings, no completely useless ones. Different tunings bring different resources to the table. Different tunings are indeed different and pitch is very relevant.

If there are no bad tunings, then isn’t the concept of harmony made meaningless?

No, it is the reverse! To the contrary, new harmonic resources become available. That is more of the point and purpose of this field, at least for some of us.

Consider traditional Jazz: in addition to the standard set of intervals, we introduce harmonic scales and septimal (7-based) intervals like the perfectly consonant subminor third, a frequency ratio of 7/6, also known as the flat or blues third. And in comes the harmonic seventh at 7/4, also a highly harmonic interval, far more harmonic than any of the traditional sevenths.

That’s just one advantage — more consonant intervals. You can also have more neutral or gray intervals, and more dissonant intervals, all depending on the scale. Some people become interested in the most consonant intervals only. But remember that music is not about stasis, it is about contrast. Stasis can be integrated but should not be the only element: change is also needed.