The Free-Reed Journal
Articles and Essays Featuring Classical Free-Reed Instruments and Performers

Alternative Tuning Systems and Free-Reeds
Editor's Note:
The following submission was sent through the "Comment" box by Kevin Hobby in November 2004. Since Mr. Hobby introduces some interesting concepts, we thought we would post his reflections as an article.

Kevin states:
I'm admittedly quite ignorant when it comes to reed tuning but have read that the partials of reed instruments can be manipulated by the contour of the bore as well as the shape and size of the tone holes, but aside from beating reeds and their instruments I'm more curious toward anyone's thoughts on the possibility of shaping heteroglottal free reeds [ed. note: heteroglottal: reed attached to a separately made reedplate](as well as the slots they set above) in nonuniform shapes rather than their standard rectangular or slightly tapered fashion. This would be done with hopes of finding "desirable" nonharmonic timbres of which scales and tuning systems could then be based on.

I was first introduced to the concept of "vibrational nonuniformity" in the context of a nonuniform string being used as a motivating example in Sturm-Liouville Theory that, while not in every textbook, it does appear in a good number on the subject. Sadly though it seems few physics departments ever mention acoustics and the applications students will make of Sturm-Liouville theory will usually be in quantum mechanics and electro dynamics since acoustics is only occasionally taught in physics departments, or mechanical engineering and sometimes in electrical engineering... depending on the interests of the particular faculty...but anyway...

I have recently thought about the inverse problem for the modes of a nonuniform string (shaping it's contour to control the partials), but doubt that a unique solution exists and think that even approximate analysis based upon simplified models is probably quite difficult. Recently though, I was comforted by Neil MaLachian and Anton Hassells creation of a truly harmonic bell tuned to the first seven partials of the harmonic series to within 2%. A feat previously considered impossible my most, including Fletcher and Rossing. Now maybe we can be more optimistic about making these darn strings less harmonic. Well actually, it's easy to make them less harmonic -- what's not so easy is to control exactly where the inharmonic partials lie.


As is well known a considerable portion of new music explores Alternative tuning systems, (ATS) and new instruments are needed for its dependable realization- both now and in the future. I'm thinking that free reeds might well be a good candidate for such instruments. In 1997 (under the direction of Patrick Ozzard Low) Alternative Tuning Projects undertook a pilot feasibility study founded by the Arts Council of England to establish a Center in the UK for new acoustic musical instruments for alternative tuning systems. One can envision 21st Century Orchestral instruments exploring wonderfully new timbres with no help from the great computer.

The world needs daring and inquisitive minds to bring this into reality. Does anyone have any thoughts on the subject? ...Has anyone here mapped out any nonuniform reed proportions? If so I would love to see them!

There is a paper by Kalotas about a very slick way of turning the nonuniform string problem into a matrix problem.. which can then be solved (the forward problem) straightforwardly. The idea would be to use this in an iteration to try and find string contours that have desirable properties... if this interests anyone I can send you the paper and we can talk about it. I've never read or even head of an effort to study nonuniform reeds and thought maybe someone could lead me in the right direction.

Kevin Hobby

Henry Doktorski makes the following observation:
I believe Kevin is correct in predicting that the tonal qualities of the free reeds will change as the proportions and/or shape of the reeds change. This principle has been well known to pipe organ builders for centuries: the shape of the pipe affects the timbre of the tone. It should be true also for the free-reeds. I do know for a fact that reed organs have a much deeper bass because their reeds are larger than accordion reeds. Unfortunately I have little mathematical background, but I can wish Kevin good luck with his experiments!

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