# Parametrical bass clarinet mouthpiece progress

After mounths of solving mathematical puzzles, it's time for a break in the design process of the parametrical bass clainet mouthpiece. But it is wise to write down the current project progress.

## The bore

The bass clarinet mouthpiece bore appears not always to be cilindrical. It is often slightly conical. An the top of the bore is always rounded. Althought the rounded top is often slightly flattened. So the following parameters are part to the design:

- the width of the top of the bore (A)
- The widht of the bottom of the bore (B)
- the length of the bore l_bore (C)
- the height of the rouding of the bore top (D).

the curve is literally round. it follows the contours of a circle.

## The facing

The facing design is derived from several measured facing that resulted is an fourth order curve depending on the tip opening and the tip length. With the prototypes the curves appeared not to be perfect and some sanding was needed to give an acceptable result.

The chamber roof

The design of the roof excluding the transition to the bore is defined by the following parameters:

- the angle of the baffle
- the length of the baffle
- the angle of the beak inside

The design calculates the radius of a smooth curve along a circe from baffle to roof.

## The chamber cross section

The cross section of the chamber has the shape of a quadrilateral that is symmetrical in one direction and has a parallel top and bottom.

The top of the chamber corresponds with the roof or flor and the baffle of the chamber. The is always rounded.

The curve at the tip side is derived from the radius of the tip curve but then rotated with the angle of the roof at the defined z of the actual cross section.

The bottom corresponds with the window opening of the table. Then it is flat. The bottom also corresponds to the ramp side during the transition from chamber to bore. Then the bottom becomes rounded.

The sides of bass clarinet moutpieces are often flat. But since old saxophone mouthpieces often have a rounded chamber, it is also possible to defined the rounding of the sides. The rounding is defined by the angle corresponding with the segment of the circle described by the side.

For all sides the rounding can integrate seamlessly with the bore. But that depends on the type of transition selected from chamber to bore.

## Transition from chamber to bore

For most bass clarinet mouthpieces the transition from chamber to the bore is as shown in the left picture (showing to versions of the internal structure of the mouthpiece).

- The sides are flat and do not integrate to the bore
- The roof is rounded and integrates seamlessly into the bore. Which means that the curve of the top changes into the curve equal to a quarter of the bore curve. The contours of the roof follow a segment of a circle.
- The bottom is flat but becomes rounded below the end of the window and ends at a specific location on the rounded top, forming the ramp. The transition ot the barrel is rounded.

Some old saxophone mouthpieces are smoothed on all sides as shown in the right structure. The sides are also rounded and integrate seamlessly into the bore.

Result of this is an increase of the chamber volume which has noticable effect on the intonation. I get the impression that this effect is different for bas clarinets than for saxophones.

The transition from window side to the bore can have a lot of different shapes.

First the shape of the bottom of the window can be different. Often it is rectangular, but sometimes it has rounded corners or is even totally rounded, which looks very nice.

So these are the required corresponding parameters in the design:

- has rounded chamber (yes/no)
- has rounded corners (yes/no)

The last option is not in the design yet. It has to be extended with a parameter defining the radius of the corner curve.

Seen from the side the transition can have different transitions resulting in the design of the ramp. The transition can be seamless and follow a nice curve from window to the beginning of the rounded top (as shown in the top image of the figure to the right).

The transition can follow a straight line (as show in the middle image).

Both transitions can end in a specific location on the rounded top of the bore resulting in a bit squeezed transition to the bore.

## What can be done more

- I have more than hundred pages of articles about saxophone mouthpieces written by Ralph Morgan in the Saxophon Journal. There is a lot to learn, but I get the impression that a bass clarinet behaves different from a saxophone. Especially the intonation effects are different.
- There are several problems to implement the design in Openscad. Often modifications result in non manifold designs or other problems and a lot of time has to be spend on solving this.
- The first prototypes are printed in common 3D printer using PLA. It needs some work to make the prototype good enough to play. The results suffer from squeaking when the table is not smooth enough. This can be solved by sanding under water with waterproof sanding paper, also the interior is smoothed by treating it with chloroform. It is not certain that the results are representative for a well produced prototype. I hope better 3D printers will give an improvement and wonder what an experiment with CNC milling will bring.
- It would be interesting to discuss the design with designers of clarinet mouthpieces.
- Design improvements
- The tip contour is drawn along a circle arc. It should be parabolic.
- The cross section of the roof top is drawn along a circle arc. The question is if that is right.
- The facing curve is a fourth order function. It is not suitable yet, maybe it is too simple or just wrong.
- It is important to keep the internal volume of the mouthpiece within limits. A calculation of the volume is added, but it is still to simple and needs improvements.