Optimizing a Whistle or Flute Design - edwardkort/WWIDesigner GitHub Wiki
Introduction
This tutorial illustrates how to use WIDesigner to optimize the design of a whistle or transverse flute. How you optimize the design depends on where you are in the construction process. The process can begin once you know the geometry of the whistle's window and windway, or the flute's embouchure hole.
- Planning the Toneholes, after the head and bore of the instrument are more-or-less complete, before you drill any toneholes. Leave the bore a bit long, to allow for fine-tuning. At this point, the instrument plays just the fundamental note, somewhat flat of the final design pitch. By overblowing, you can generally play at least three overtones above that.
- Fine-Tuning the Model, for an instrument that has toneholes that are still substantially smaller than the final size.
- Fine-Tuning the Instrument, when the holes are close to their final size.
- Planning a New Instrument, when you want to include changes to the bore taper while a flute or whistle is still on the drawing board.
If your design has a tuning slide, we suggest you make all tuning measurements with the slide in the same position, in the middle of its range.
Planning the Toneholes
1. The Instrument Model
Use WIDesigner to record the current dimensions of the whistle or flute in an instrument file. Fill in the mouthpiece dimensions, including a rough guess at the window height or airstream length and airstream height. Set the beta factor to 0.4. In the table of bore points, enter the top and bottom of the bore, and any points where the taper of the bore changes. You can leave the hole table empty, or enter rough guesses for position and diameter of the holes you plan to drill.
2. Calibrate the Model
Measure the minimum and maximum frequency of the fundamental and next three overtones according to these instructions for whistle or flute and record them in a tuning file. You can create your file from the sample file WhistleStudy\tunings\BellNoteTuning-0hole.xml or FluteStudy\tunings\BellNoteTuning-0hole.xml if your instrument's hole table is empty, or WhistleStudy\tunings\BellNoteTuning-6hole.xml or FluteStudy\tunings\BellNoteTuning-6hole.xml if your instrument's hole table has 6 holes. You don't need to enter target frequencies in this tuning file.
Use the procedure for whistle to get recommended values for window height and beta. Use the procedure for flute to get recommended values for airstream length and beta.
3a. Optimize the Design with Default Constraints
If you haven't already done so, enter rough guesses for the diameter and position of the holes, in the hole table of your instrument definition.
Choose a tuning file with target frequencies for the notes of your whistle. You can use one of the WIDesigner sample files, or create your own. Select this tuning file in the Tuning branch of the Study panel.
Set a blowing level in the Edit-->Options... dialog.
Select "4. Hole Size+Spacing Optimizer" in the Optimizer branch of the Study panel, and run Tool-->Optimize instrument to generate a new instrument definition with recommended hole sizes and positions, and a recommended bore length.
Use the WIDesigner tools to evaluate the new instrument definition.
- If the tuning is satisfactory, save the instrument in a file, as the first draft of your instrument design.
- If some notes aren't quite right, you can manually adjust hole sizes and positions to see the effect on tuning.
- If the tuning isn't satisfactory, or some hole sizes or spacings are larger or smaller than you want, you can re-run the optimization with customized constraints, as described in the next section.
- If you want to use specific hole sizes, enter them in the instrument definition, and re-run the optimization using "3. Hole Spacing Optimizer" to find optimal positions for these holes.
- If you want the holes in specific positions, enter these positions in the instrument definition, and re-run the optimization using "2. Hole Size Optimizer" to find optimal sizes for these holes.
3b. Optimize the Design with Custom Constraints
Select your instrument definition in the Instrument branch of the Study panel, and "4. Hole Size+Spacing Optimizer" in the Optimizer branch. Run File-->Create default constraints to create a new constraints definition. Adjust the constraints according to your preferences. If you want to save the constraints in a file, use File-->Save-as Constraints.
For a large-hole flute with 6 holes, WIDesigner includes a sample constraints file FluteStudyModel\HoleObjectiveFunction\LargeHoleSize_Spacing_6holes.xml. Select your instrument definition in the Instrument branch of the Study panel, and use File-->Open constraints to open this file.
Select your customized constraints in the Optimizer branch of the Study panel, and run Tool-->Optimize instrument to generate a new instrument definition.
Fine Tuning the Model
When you have an instrument design you are satisfied with, you can drill the holes, and perhaps trim the bore closer to its final length. Drill the holes under-sized at first, to allow for fine-tuning. Once you have holes drilled, you can re-measure the tuning and re-calibrate the model. If the re-calibration produces new values for window height or beta, you may want to re-optimize the hole sizes with the new values.
1. Re-Calibrate the Model
Measure frequencies of the whistle or flute again, this time for all of the notes, and record them in a tuning file.
For a whistle, use the procedure here to get new values for window height and beta. For a flute, use the procedure here to get new values for airstream length and beta.
2a. Re-Optimize Hole Sizes with Default Constraints
With your draft instrument design and target tuning file selected in the Study panel, select "2. Hole Size Optimizer" in the Optimizer branch, and run Tool-->Optimize instrument to generate a new instrument definition.
2b. Re-Optimize Hole Sizes with Custom Constraints
Select your instrument definition in the Instrument branch of the Study panel, and "2. Hole Size Optimizer" in the Optimizer branch. Run File-->Create default constraints to create a new hole-size constraints definition. Adjust the constraints according to your preferences. If you want to save the constraints in a file, use File-->Save-as Constraints.
For a large-hole flute with 6 holes, WIDesigner includes a sample constraints file FluteStudyModel\HoleSizeObjectiveFunction\LargeHoleSize_6holes.xml. Select your instrument definition in the Instrument branch of the Study panel, and use File-->Open constraints to open this file.
Once a tonehole is drilled, you can make it larger, but you can't generally make it smaller. With custom constraints, you can enter the existing diameter of each hole as the lower bound for the hole size.
Select your customized constraints in the Optimizer branch of the Study panel, and run Tool-->Optimize instrument to generate a new instrument definition.
3. Adjusting the Stopper Position
For a flute with an adjustable stopper at the top of the bore, you can use WIDesigner to see whether adjusting the stopper position might improve the tuning. Selecting "6. Stopper Position Optimizer" will vary the distance from the topmost bore point to the upper end of the embouchure hole to optimize the tuning.
Fine-Tuning the Instrument
We recommend that you always make the final tuning adjustments--trimming the bore to its final length and drilling the holes to their final size--based on what you measure on the actual whistle.
Planning a New Instrument
If your construction process allows you to make different bore tapers, the whistle study model and flute study model can optimize a variety of bore profiles.
For the simple taper optimizer, create three entries in the instrument's list of bore points. The first entry supplies the position and diameter at the head of the bore. The second entry supplies the bore diameter where the two tapered sections meet. Selecting "5. Taper Optimizer" in the Optimizer branch will keep these two diameters constant, and vary the diameter at the end of the bore, and the position of the second bore point, to optimize the tuning.
Selecting 5.1 Hole and Taper Optimizer" will keep the first two diameters constant, and vary the following to optimize the tuning:
- Bore length and diameter at the end of the bore
- Position of the second bore point
- Position and diameter of each tonehole
To vary the bore geometry of the headjoint more generally, add bore points to the bore point table for the points you want the taper to change. Give a name to at least the bore point at the bottom of the head-joint, a name that contains "Head". Use the upper bore diameter optimizers in the whistle study model, the headjoint optimizers in the flute study model, or the upper bore spacing optimizers in either study model, to vary the diameter or position of all bore points above the bore point with "Head" in its name.
To vary the bore geometry of the instrument body below the headjoint, add bore points to the bore point table for the points you want the taper to change. Give a name to at least the bore point at the top of the body, a name that contains "Body". Use the lower bore diameter optimizers to vary the diameter of all bore points below the bore point with "Body" in its name.