the overtone series comes from the simplest ratios, and then gets more complex with the more complex ratios. ie. 2/1 = octave
3/2 = P5
4/3 = P4
5/4 = M3
etc. the easiest way to understand this is with a string. pluck a string and it will resonate. make it half as long (with the same tension) and it will vibrate twice as fast, hence, an octave.

frequencies can go through any medium, and will go faster through an orderly matrix like crystal because of how the molecules are placed. my instinct is that some frequencies would cancel out because of feedback inside the crystal, but this is just intuition.

an example of frequencies going through something other than air is an earthquake.

There is a book you might be interested in called "Harmonograph" by Anthony Ashton, Walker publishing co. The subtitle of this book is "A Visual Guide to the Mathematics of Music". Apparently, in the 1800's they were very interested in the visual patterns that could be created by the ratios corresponding to the overtone series. They invented a device called a harmonograph to create these images on paper. Some interesting patterns emerge. Also, I highly recommend a book called "Temperament" by Stuart Isacoff, vintage books pub. This book presents an enjoyable and accessible history of our (western) tuning system and how it got that way. It goes all the way back to Pythagoras and also goes into some detail about the overtone series. About the crystals, I must admit I'm at a loss but would love to hear more about what you discover in the future. Peace!

You may know that there are several systems of categorizing instruments. In one of these, you have chordophones with strings, metallophones with metal keys, membranophones like drums, and lithophones, which are instruments made out of rocks. There is a famous ancient chinese gong set that is made out of rocks. There is also a set of stone pontoons at the Mayan city of Chichen Itza that are tuned to a lovely scale. 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.

The quartz crystal is a lithophone. It actually vibrates mechanically and has a very high Q (that 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 a 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 temperatuce 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 of 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.

You don't need air to have stuff that has 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 things is odd enough that even the planets are not going to have a perfectly harmonic overtone series. But where you see it 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 run into harmonics in quantum physics/wave mechanics and the effects of that appear even in the organization of the periodic table.

The Harmonograph book is actually in print and is a fine book and inexpensive. it's not the original book from the 1800s but the author found that old book and reprinted its diagrams with his own notes. It's not really full of insights though, but I think its a fun book. If you have a Mac and want to trade a music CD of your own music, I have a program called IntervalCalc that will display one of the types of harmonographs. I think it would be really fun to make the old mechanical harmonograph - he gives directions in the book.

Stuart Iscoff's book has a view of temperament and hearing that is promoted among certain academic circles as absolute truth, but which I find to be completely wrong, for many reasons, but including the facts about harmonic overtones I have mentioned. I don't recommend his book even though I would like to.

Theory in general about tuning is wrong. I think I will even go so far as to say that 100% of tuning theory is wrong. Yes, all of it. Stay away from theory. Most of the people who promot theory are just making up stuff based on their feelings about how the universe should follow some sort of mathematical wet dream. The absolute best thing you can do as a microtonal composer is to turn your back on all theory and start working with tunings yourself. Do not limit your self to "One True Tuning A" or "One True Tuning B" and run away fast from anyone promoting any certain class of tunings, or even disparaging any classes of tunings. There are no bad tunings. I repeat - there are no bad tunings. There is no theory that accomodates that fact, a fact that is fundamental to an understanding of pitch.

this thread is very interesting...

anyone have links to music using microtonal techniques?

----------------------------------------------------------------------------

I did find it interesting that many years ago when I generated a C major chord using sine wave generators in SoundEdit 16, the resulting waveform representation on the screen resembled a spiral...

-------------------------------------------------------

also.... I used to have a CD "Current 93 presents Harry Oldfield" which was a bunch of crystal frequencies transduced into sound. Difficult listening... makes the dogs go nutzoid!!