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.

Why should anyone care about this?

Music has always been comprised of two basic elements, pitch and rhythm. We don’t know if either came first. The human vocal chords are built for music. Our ears and brain naturally recognize patterns in rhythms in the environment, and we have created rhythms when we chipped away to make obsidian knives, flint arrowheads, and crush acorns. Both pitch and rhythm came together as we ascended to mesas in the desert, stepping on flat resonant sandstone that created melodies of different pitches in a regular rhythm. Creating a lithophone by gathering and arranging the rocks we happened to step upon was the obvious next step taken.

But no distinction is even necessary. Pitch and rhythm are made of the same substance: they are frequencies, repeating patterns of pulses, each within different ranges. We even find that when we increase the pitch high enough, we have color. Vibrations are the building blocks of physical reality. Light, matter and sound are all vibrations. Music is as real, as physical and objective as anything else we know of, or if you prefer, things that we see and touch are every bit as unreal, ephemeral and subjective as the music we hear.

Thus pitch is the basis of music. In history, there have been times and places where much thought was given to the role and use of pitch within music. Different scales and intonation techniques were explored and embraced. The standardization of 12 tone equal temperament (tET) in the 20th century was promoted to put an end to these explorations in the west. With no choices of pitches available anymore, time and effort could be freed up for other tasks. 12 equal is essentially a product of industrialization and the fetishization of value of mechanical efficiency over emotional expression. There is no doubt that 12tET is a great, versatile tuning. But it is not the definition of music itself. Since the advent of the inexpensive keyboard, preset to a mathematically perfect 12tET, world musics and traditions, already in a precarious position, have been destroyed at an accelerated rate. Ironically, western musicians interested in ethnic traditions have been part of the problem since they will seek to play together with world musicians. Unable to tune their modern keyboards and other machines, the compromise often has to come from the world musician, whose acoustic instrument is more flexible in pitch, and thus is the one that has to change to conform to western values. Since the nuances of pitch are the heart of these traditions, the heart of the traditions themselves is wrenched out in ritual sacrifice to technology, which itself is a servant of a contrived consumerist marketplace following the latest fads, whether it is teen pop heartthrobs, or fashionable tribals leashed in submission to 12 tuning as a precondition to acceptance by major labels.

But, like cameras, like guns, like the internet — the same technology and the same electronic instruments that were used, often unintentionally, as a tool of oppression and domination can also work to reverse this trend, to return freedom to music, and to the expression of humanity it transmits. The frontier of music is pitch, the future is a return to the past in a new way, with new freedoms and possibilities. There is a fire burning in the hearts of musicians and of audiences for more and the emancipation of pitch is the key.

What universities have the best programs in microtonality?

There are several universities that have a serious microtonalist or xenharmonicist on their staff who is respected, well known and active. If your primary interest is the work done by a certain specific composer or researcher then you probably have already started by looking there and don’t need much advice.

I’d only caution that a problem with the one-sided approach from studying under a single person is that you can get locked into one specific viewpoint and then you end up as a member of a specific microtonality cult. For example, advocates of a single tuning as some sort of master key to the universe of pitch. It’s easy to think this won’t happen because you can resist assimilation, but then you notice that there are many schools in which only a specific sort of music is heard: that advocated or pioneered by a particularly strong minded faculty member. This is not to disparage any particular approaches, but to caution that there is more than one approach to pitch.

So college is a good path, right?

You didn’t actually ask the question if you should go to college at all to as part of your life education, but tackling this issue must be considered as part of a complete response. If you would have to go into debt to experience college, the answer is no, it’s not worth it. Don’t go. The debt problem can be a particular issue for those trapped in the United States where some undergraduate degrees can cost more than a house, and a graduate degree can take nearly a decade to complete, leaving students entering real life and middle age at the same time.

Debt will cripple you when you graduate and you will be forced to compromise your beliefs and plans in order to pay off that debt rather than to be free and live your life. You’ll do better studying and learning free from the constraints of academia. Build instruments, write music, perform in public, release albums. No school can teach you how to do any of this and none of it costs much money to do. Only time and effort. You just do it. The advantages of a university are easier access to some books and journals (most of which are filled with old wives tales and incorrect theories), and exposure to a community of academic thinkers. Even so, for many students, college days are about drinking, carousing and being indoctrinated into propaganda, provided at a daily cost higher than visiting Disney World, or travelling through foreign countries. If drinking and carousing seem compelling attractions, you’ll be able to do more of that as a touring musician than a student anyway and it won’t put you a quarter million dollars saddled in debt. The crippling effect of schooling debt should not be taken lightly. It will leave you unable to pursue your interests and dreams when you graduate, trapped in servitude to corporate interests. Debt is not a viable path to becoming a good musician or composer.

Education is not something that you purchase at a store and which is then pumped into your head, cooked in slowly, or applied via penetrating rays. Education is a side effect of doing things, being active and engaged in your world, and of continually trying new things and thoughtfully observing the results and effects. Somewhere near you there is another musician you can jam with. In your house right now there are musical instruments you don’t even know you own. A bottle, a tin can, a pipe, a piece of scrap wood. When you feel a hankering for intellectual community, write articles and put them on your blog or website. Sometime this year there is a music conference somewhere. Attend it and present a paper and give a performance. You are not a clone, a robot, or a slave. You are a individual doing unique things and you can share those things with others if you’d like. No degree is needed for this, nor will it help.

That’s a fine rant, but surely you have some specific recommendation?

Of the various universities world wide there is one that stands out as having both a strong and diverse base of pioneering microtonal composers. It is the University of Wollongong, south of Sydney, Australia. There you will find both Greg Schiemer and Warren Burt, and in the surrounding community lives Kraig Grady whose wife is a PhD candidate at the school. There are many students seriously engaged in all flavors of microtonality there encompassing a wide variety of approaches and philosophies. I recommend it.

August 2010 Update: There was a major upset at Wollongong in 2010 with key faculty lost including Dr Schiemer. Thus the recommendation no longer applies.