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

Introduction

The Whistle Study Model models the playing frequencies of whistles and other keyless fipple flutes. In keeping with the discussion at Tuning Winds, it predicts a minimum and maximum playing frequency for each note along with a nominal playing frequency.

This page covers two basic concepts:

Additional tutorials describe the use of the whistle study model:

Measuring Frequencies

For each note, the whistle model works with four different frequencies. This section discusses what differentiates them, and how to measure them.

Maximum frequency is the frequency of the highest steady pitch that you can play for the note before it breaks into the next register. This number goes in the "Max Freq" column, or <frequencyMax> tag, of your tuning file.

Minimum frequency, in the second register and higher, is the frequency of the lowest steady pitch that you can play before it drops down into a lower register. In the lowest register, "minimum frequency" is not well defined: generally speaking, it would be the lowest steady pitch that sounds like a musical note rather than wind noise. This number goes in the "Min Freq" column, or <frequencyMin> tag, of your tuning file.

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, and appears in the "Target" column of the tuning table.

Nominal playing frequency is the frequency that the whistle actually produces for the note under normal playing conditions. This is the frequency that Flutini aims to capture. To predict the nominal playing frequency, the whistle model assumes that you will steadily increase the air velocity in the windway as you go from the lowest note on the instrument to the highest. When you measure playing frequencies, do not try to blow notes in tune (at their target frequency); aim for the regular increase of air velocity going up the scale that you might use when playing a tune, and measure the frequencies the whistle actually produces. The blowing level parameter in the WIDesigner Options provides some control over the start and end points of this steady increase. WIDesigner's prediction of nominal playing frequency appears in the "Predicted" column of the tuning table.

Calibrating the Whistle Model

The objective of instrument optimization is to get the playing frequency of all notes to match the target frequency as much as possible. The objective of calibration, on the other hand, is to get WIDesigner's prediction of the playing frequency to match the measured playing frequency as much as possible.

We refine the whistle model's frequency predictions with two parameters in the instrument description: window height and beta factor.

Nominally, window height is the thickness of the whistle head at the window. However, this thickness is rarely uniform around the perimeter of the window, so a precise measurement is difficult. We adjust the value to refine the model's prediction of maximum frequency.

Beta factor is a dimensionless value, the "jet spatial amplification coefficient" in the work of Patricio de la Cuadra, and Roman Auvray (Bibliography), used in modelling the instrument's loop gain. For most instruments, 0.4 is a useful starting point for beta. We adjust beta to refine the model's prediction of minimum frequency.

You can use the procedure below to calibrate the whistle model for a specific instrument, even while it is under construction. Even before drilling the holes, or cutting the tube to final length, you can measure frequencies for the harmonics of the bell note.

  1. Measure frequencies for each note through the range of the instrument, and save the measurements in a tuning file. You have two choices of what to measure:

    • Measure minimum and maximum frequencies for each note, and put the values in the "Min Freq" and "Max Freq" columns of the tuning file. In this case, you can leave the target frequency in the Frequency column or leave the Frequency column blank.

    • Measure actual playing frequencies, and put the values in the "Frequency" column. In this case, do not use the tuning file for optimization; use it only for calibrating the model. Again, do not try to blow notes in tune; aim for the regular increase of air velocity going up the scale that you might use when playing a tune.

  2. Measure the current dimensions of the instrument, and save them in an instrument file. Include an estimate for window height and beta.

  3. Select the instrument and tuning files in the WIDesigner Study panel. Select "1. Whistle Calibrator" in the Optimizer branch of the Study panel.

  4. Run Tool-->Optimize instrument to generate a new instrument. The window height and beta factor of this new instrument minimize the deviation between the measured frequencies, and the predictions of the whistle model. Transfer the window height and beta factor to your original instrument definition.