Working With the Reed Study Model - edwardkort/WWIDesigner GitHub Wiki

The Reed Study Model models the playing frequencies of single and double reed woodwinds with toneholes. It can also model a limited set of lip reed instruments with or without toneholes, such as didgeridoos, cornetts and serpents. As yet, WIDesigner cannot model instruments with valves, crooks or slides, such as trumpets and trombones. At present, the reed model is still a prototype; we need more empirical data before we can be sure the model predicts the behaviour of real instruments.

This page covers these basic concepts:

• Mouthpiece Geometry
• Measuring Frequencies
• Calibrating the Reed Model

Additional tutorials discuss evaluating an instrument design, using tuning tables the reed model generates; and describe sample files used to design simple PVC didgeridoos. The reed study model provides a number of optimizers for optimizing instrument designs.

For single-reed and double-reed mouthpieces, the interior bore profile tapers down to almost nothing at the tip of the reed, so there is some uncertainty how much of this taper to specify in WIDesigner. For double reeds, we advise you use the upper bore points in the instrument geometry to describe the staple, and omit the profile of the reed itself from the description of the bore. We are still working out guidelines for single-reed mouthpieces. WIDesigner requires that mouthpiece position be set to the position of the uppermost point in the list of bore points.

For each note, the reed model works with two different frequencies:

Target frequency or expected frequency is the frequency you want the note to play at, such as A4 = 440 Hz. This number goes in the "Frequency" column, or <frequency> tag, of your tuning file.

Nominal playing frequency is the frequency that the instrument produces for the note under normal playing conditions. To calibrate the reed model, you will put measured playing frequencies in the "Frequency" column, or <frequency> tag, of a tuning file.

The reed model uses two calibration factors, referred to as alpha and beta. As yet, we do not have a connection between the mouthpiece geometry and these factors, but we do expect them to be constant for a given mouthpiece over a range of instrument geometries and playing frequencies.

You can use the procedure below to calibrate the reed model for a specific instrument, even while it is under construction. For double reeds, the calibration parameters of a reed and staple should remain the same if you move the reed and staple to a different instrument. On the other hand, the individual player may influence the calibration parameters.

1. Measure the playing frequency for each note through the range of the instrument. Even before drilling the holes, or cutting the tube to final length, you can measure the harmonics of the bell note. Save these measured frequencies in a tuning file.

2. Measure the current dimensions of the instrument, and save them in an instrument file.

3. Select the instrument and tuning files in the WIDesigner Study panel. Select "01. Reed Calibrator" in the Optimizer branch of the Study panel.

4. Run Tool-->Optimize instrument to generate a new instrument. Alpha and beta for this new instrument minimize the deviation between the measured frequencies, and the predictions of the reed model. Transfer the alpha and beta parameters to your original instrument definition.

With reed instruments, in particular, it is not unusual to have tuning data for a single mouthpiece that comes from several different instruments. For example, one double reed and staple, or one brass mouthpiece, can be tested in different tubes. The WIDesigner reed calibrator described above cannot combine measured results from different geometries. For these circumstances, we provide a spreadsheet with the example files, ReedStudy\instruments\Calibration.xlsx.

1. Open the calibration spreadsheet with Microsoft Excel or other compatible spreadsheet application.

2. For each instrument in which the mouthpiece is tested:

   Create an instrument definition and tuning definition in WIDesigner. The instrument definition gives the actual instrument geometry, with alpha and beta for the mouthpiece both set to zero. The tuning definition gives actual, measured frequencies for each note.

   Run Tool-->Supplementary Info to produce the Supplementary Information Table.

   Select the data rows of the supplementary information table, and use copy and paste (typically, Ctrl-C and Ctrl-V) to transfer the data to the Calibration spreadsheet, beginning at the second row and working downward.

   Close the supplementary information table, and continue with the next instrument.

3. The Calibration spreadsheet shows a graph of admittance vs. frequency, with a best-fit interpolation line. Some of the plotted points may be outliers, some distance away from the main trend of the data. The example below shows an outlier circled in red.

   

4. If there are obvious outliers, we suggest you find each one in the data table, and delete its frequency value, so the outlier is not included in the graph or interpolation line.

5. Read the best-fit alpha and beta values from the top of columns H and I. For single and double reed mouthpieces, the spreadsheet will show beta with a negative sign; omit the negative sign when you transfer the value to WIDesigner. For lip reeds, transfer alpha and beta with the signs given on the spreadsheet.