AMS Spring 2023

The Music of Mathematics – Behold the 3D Printed Microtonal Clarinet

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Microtonal music is thought of as a system which contains intervals narrower than conventional contemporary Western semitones. It generally refers to music containing tiny intervals, but the term is also used to describe tunings that differ from the 12-tone forms most of us are used to hearing.

IFThai, Burmese, Indonesian, Turkish, and African music feature such alternative tunings, and the microtonal variation of intervals are staples of spirituals, blues, and jazz. Some music theorists use the term “ultra-chromatic” to describe intervals smaller than the semitone, and the term xenharmonic has been used as well.

The resulting soundscapes are often haunting, and even discomfiting, to the ear of Westerners used to listening to 12-tone compositions. While several designers have successfully used 3D printing technology to make musical instruments, clarthose project have been mostly limited to creating replicas of existing ones, instruments which feature normal intonation. Now a group of researchers, Nicholas Bailey, Théo Cremel, and Alex South from the Science and Music Research Group, University of Glasgow, have modeled and designed a microtonal clarinet.

If you’re hearing microtonal music for the first time, you’ll experience what you might think of as wrong-sounding notes – but they’re entirely intentional. Once a listener comes to accept this, an entirely new way of hearing music opens up.

Among musicians, it’s not a new idea. But the musical application of microtones to the clarinet are only just becoming the focus of composers, and the Glasgow team say the hope their work “may spark the imaginations of composers and performers towards qualities of microtones other than pitch.”

They say microtonal versions of wind instruments have been created in the past by artists like Richard H. Stein, a composer and clarinetist who developed a quarter-tone clarinet around 1911. That instrument featured the addition of numerous tone holes and keys not found in a standard design.

The new microtonal clarinet was designed to be 3D printed using an object-oriented, acoustic model of the instrument accomplished with C++ coding. The design was done in OpenSCAD, and they say that software was set to predict the outcome of printing a replica of a ‘Denner’ clarinet.

Constructed in four quarters and split dorsally to make it easier to remove filler material and produced by a small prototyping printer at the University of Glasgow’s engineering workshop, the clarinet has a cylindrical bore and nine tone holes.

“For each of the 19 divisions of the octave,” notes the paper, “a fingering pattern is produced which most nearly matches the desired frequency under simulation.”

The Glasgow researchers, though they say the computational work involved was massive, are pleased with the results.

“It has proven relatively easy to produce a playable instrument parametrically using a 3D printer,” they wrote of the project.


Laço Tayfa – Şurmat by vavelya

Check out a recording of a 1999 solo clarinet track by Husnu Senlendirici of the Turkish folk music group, Laco Tayfa. The microtones are represented by a yellow line in the slow-down track on the path as it plays.

You might find microtonal music a tough listen, but please let us know what you think of this kind of creative use of 3D printing in the  Music of Mathematics – Behold the 3D Printed Microtonal Clarinet thread on 3DPB.com.

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