I forwarded Terry Riley's question on to Steve Curtin, the fellow who wrote most of the MR-series' MIDI Tuning Standard code. This reply probably doesn't say a whole lot more than we already know, but perhaps a little!
Steven Curtin wrote:
> I'm honored to be able to help. The name of the guy who wrote MIDI Tuning > Wrench is Jim Johnson, he's on the synth-DIY mailing list. That's odd but > not unexpected that the Unisyn stuff doesn't work, since they laid off the > guy who maintains it about six months ago :(. > > Contact info for Jim Johnson: > > Jim Johnson > Metaphoric Software > ------------------- > Makers of Techno Toys > Software for Electronic Music > http://www.technotoys.com > info@technotoys.com > > You should also mention to Terry and David that I have Forth code that can > change the tuning of the MR. I used this code to test the MTS > implemetation in the MR. He could have someone build a little standalone > tuning controller based on the New Micros 68HC11 microcontroller or > something similar.
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End of TUNING Digest 1480 *************************
Thanks for all the response to my overtone/tone color question. So does it follow that ideally one takes into consideration the natural acoustic properties of a particular instrument when one is choosing a particular tuning system for an instrument? Can anyone offer a good example where the complex vibrations and shape of a particular instrument are highly integrated with the system of tuning?
> Are overtones different frequencies > produced by different aspects of whatever materials are producing the sound?
The materials vibrating a significant factor, but the most important factor is the shapes and available kinds of movements possible in that configuration. The most important thing about a string, for example, is that its diameter is only a tiny fraction of its length, that it is anchored firmly at both fret and bridge ends, and that it is made of a flexible material.
This is what allows it to vibrate at very nearly precisely-harmonic frequencies. What makes those frequencies not completely harmonic are the departures from this idealized model of a string, such as the fact that high piano strings' are so short and thick, and under such high tension, that they are no longer a close approximation to being arbitrarily flexible and infinitely longer than their diameter.
As another example, the most acoustically-significant difference between a clarinet and a saxophone is that the saxophone's bore is conical, meaning that the diameter of the tube is much narrower at the mouthpiece end than at the bell end. Except for the bell at the end of the horn (which has a lot less acoustical significance than it would initially seem), the clarinet's bore is much closer to cylindrical (i.e., nearly equal diameter throughout).
The combination of a cylindrical bore and a reed produces stronger odd-numbered harmonics than even ones, whereas, a saxophone (as well as other conical-bored instruments like the oboe, bassoon, or most brasses), have about the same prominence of even and odd harmonics.
Now in the case of wind instruments, it's very critical to understand what the "materials" are. What vibrates in a wind instrument is the air inside the tube. The walls of the instrument itself vibrate only slightly, except in a mere handful of specific cases (quadruple-forte, unstopped F.horn, for example). That is obviously completely the opposite for a stringed instrument - the soundboard is the entire means of transferring the sound generated by the strings to the air, so the soundboard imparts its vibrational qualities to the sound of the instrument.
That is NOT to say that the material a wind instrument is made of has absolutely NO effect upon its timbre, but that is a much less significant factor than its forcing means (e.g., reed, edge, lip-buzzing) and its bore geometry. No matter what material you make a flute out of, it's always going to sound more like a traditional flute than like a bassoon.
> Thanks for all the response to my overtone/tone color question. So does it > follow that ideally one takes into consideration the natural acoustic > properties of a particular instrument when one is choosing a particular tuning > system for an instrument?
The relationships between timbre and tuning are exactly the topic of Bill Sethares' recently-published (by Springer) book/demo CD, "Tuning Timbre Spectrum Scale". Interesting book.
> Can anyone offer a good example where the complex > vibrations and shape of a particular instrument are highly integrated with the > system of tuning?
It would not be difficult to imagine that a timbre like a clarinet's, having weak even harmonics, would be more "picky" about the precision of a 5:3 major sixth than of, say, a 3:2 octave. That since it has strong 5th and 3rd harmonics that could beat against each other if not tuned precisely, whereas its second harmonic could be weak enough to not be as picky about that.