Working With the Flute Study Model - edwardkort/WWIDesigner GitHub Wiki
The Flute Study Model models the playing frequencies of transverse flutes with embouchure holes. 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 flute study model:
- Evaluating an instrument design, using tuning tables and graphs the flute model generates.
- Optimizing a flute design.
For each note, the flute 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. If available, 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. If available, 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 in the "Target" column of the tuning table.
Nominal playing frequency is the frequency that the flute produces for the note under normal playing conditions. This is the frequency that Flutini aims to capture. To predict the nominal playing frequency, the flute model assumes that you will steadily increase the air velocity as you go from the lowest note on the instrument to the highest. The blowing level parameter in the WIDesigner Options provides some control over the start and end points of this steady increase. The nominal playing frequency appears in the "Predicted" column of the tuning table.
For a flute, the minimum, maximum and playing frequencies depend on your embouchure and where you hold your mouth relative to the embouchure hole. We use three parameters in the instrument description to capture nominal information about the player's mouth position, and refine the flute model's prediction of maximum and minimum frequency: airstream length, airstream height, and beta factor.
Nominally, the airstream length is the distance from the player's lips to the far edge of the embouchure hole. However, this distance is difficult to measure, and can change from note to note. We put an estimated value in the instrument description, and adjust the value to refine the model's prediction of maximum frequency.
Airstream height is the distance between the player's lips. It, too, is difficult to measure, and subject to change. 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 put an estimated value of airstream height in the instrument description, then adjust beta to refine the model's prediction of minimum frequency.
You can use the procedure below to calibrate the flute model for a specific instrument, even while it is under construction.
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Measure frequencies for each note through the range of the instrument. Even before drilling the holes, or cutting the tube to final length, you can measure frequencies for the harmonics of the bell note. Ideally, you would measure minimum and maximum frequencies for each playable note. More likely, because minimum and maximum frequencies are so dependent on your embouchure and mouth position, you will choose to measure nominal playing frequencies for each note, especially if the instrument has its full complement of notes. Save these measured frequencies in a tuning file: minimum and maximum frequencies in the "Min Freq" and "Max Freq" columns, or playing frequencies in the "Frequency" column. You don't need to enter target frequencies for the notes.
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Measure the current dimensions of the instrument, and save them in an instrument file. Include an estimate for airstream length, airstream height, and beta.
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Select the instrument and tuning files in the WIDesigner Study panel. Select "1. Flute Calibrator" in the Optimizer branch of the Study panel.
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Run Tool-->Optimize instrument to generate a new instrument. The airstream length and beta factor of this new instrument minimize the deviation between the measured frequencies, and the predictions of the flute model. Transfer the airstream length and beta factor to your original instrument definition.