Reed Instrument Example: Didgeridoos - edwardkort/WWIDesigner GitHub Wiki

Introduction

To WIDesigner, a didgeridoo (or didjeridu) is a lip reed instrument with no toneholes. WIDesigner can help with tuning the fundamental pitch and overtones in a didgeridoo design. The overtones are sometimes referred to as "trumpet" notes.

Sample Files

The WIDesigner reed study sample files include a tuning file and two sample instruments. Didgeridoo-D2-D3-tuning.xml describes a fundamental note tuned to D2, and first overtone, or first trumpet, tuned to D3.

Didgeridoo-2stage-D2-D3.xml describes an instrument made of two sections of cylindrical pipe: the first section has an inside diameter of 1.312", and the second section an inside diameter of 2.125". The length of the sections are adjusted to give a fundamental near D2 and a first trumpet near D3. With a narrower second section, the two harmonics cannot be tuned to an octave apart (or less).

Didgeridoo-3stage-D2-D3.xml describes an instrument made of three sections of cylindrical pipe, with inside diameters of 1.312", 2" and 3" and a stepped bore between sections. The length of the sections are adjusted to give a fundamental at D2 and a first trumpet at D3, with close to equal section lengths.

The bore point optimizers of the reed study leave the top two bore points unchanged. To allow for this, the two instruments include a redundant bore point 1" from the end of the instrument; the bore point optimizers will adjust any bore points below this 1" marker.

Constraint Files

The sample constraint files include two sets of constraints for designing instruments made of cylindrical pipe with a stepped bore between sections.

DidgeridooConstraints-2stage.xml uses the bore position optimizer to tune a bore with five bore points. The top two bore points are left unchanged. The first constraint limits the absolute position of the bottom bore point. The second constraint limits the position of the third bore point (the end of the first section of the bore) relative to the distance between points 2 and 5, to between 0.01 and 0.99; in essence, the bore point can be anywhere between points 2 and 5. The final constraint limits the position of the fourth bore point to be just past the third bore point: 0.00 to 0.01 of the distance from point 3 to point 5; this produces the sudden step in the bore diameter between the two sections.

DidgeridooConstraints-3stage.xml uses the bore position optimizer to tune a bore with seven bore points. The top two bore points are left unchanged. The first constraint limits the absolute position of the bottom bore point. The second constraint limits the position of the third bore point (the end of the first section of the bore) relative to the distance between points 2 and 7, to between 0.31 and 0.33; in essence, this point must be about one third of the way up the bore. The third constraint limits the position of the fourth bore point to be just past the third bore point: 0.00 to 0.01 of the distance from point 3 to point 7; this produces the sudden step in the bore diameter between the first two sections. The fourth constraint limits the position of the fifth bore point (the end of the first section of the bore) relative to the distance between points 4 and 7, to between 0.48 and 0.51; in essence, this point must be about half way between points 4 and 7, or about one third of the total bore. The final constraint limits the position of the sixth bore point to be just past the fifth bore point: 0.00 to 0.01 of the distance from point 5 to point 7; this produces the sudden step in the bore diameter between the final two sections.

Our sample tuning file for didgeridoos has only two notes: the fundamental and first trumpet. If the optimization has more than two degrees of freedom, we may have an infinite number of optimal instrument geometries; WIDesigner will find only one geometry, not necessarily the most useful one. To avoid this, the sample constraint files have only one or two significant degrees of freedom. For the 2-stage constraints, the significant degrees are the total bore length and the length of the first section. For the 3-stage constraints, the only significant degree of freedom is the total bore length; each stage of the bore is constrained to be about 1/3 of this total length, with slight variations permitted to perfect the tuning of the two notes. For some 3-stage instruments, with different bore diameters, it may be necessary to relax one of the relative position constraints, so the bore sections are not necessarily equal, to get the two notes in perfect tune.