I am implementing my own version of the Pete Kosel’s flutomat web page. It is a calculator that is used to find the hole placement in a whistle or flute. It works well as it is, but I want to add a couple of features to make it easier to use. Here is the short list of new features:
Use fractions or decimal numbers when calculating in inches.
Calculate using metric numbers. (as it does now)
Calculate and display the distance between holes.
Calculate and display the cutoff frequency and rate it for “goodness”.
Increment or decrement the hole sizes by 1/64" or by 0.05mm, depending on which measure system is selected.
A “printer friendly” popup button.
Support an arbitrary number of holes.
Other (future) enhancements:
Calculate by hole placement as well as hole size.
Support for tapered bores.
I am planning to host this on my own site and also making the javascript available for download. I would like to know if anyone has any suggestions for other features. Does this sound like something that anyone would want to use? Do I need a good flaming?
Sounds like a lot of work! I commend your efforts! The Flutomat calculator is wonderful, but it does need some augmentation. I, for one, will be greatful for your efforts.
The averaging of conical bores is not too difficult, but each of the playing holes in a conical bore need to input the differing ID measurements into each individual playing hole formula. I also suggest more detail on the calcuation of whistle labium embouchures. Many people are confused with conversion of the flutomat embouchure measurements. The trapezoidal window must be calculated for cubic volume, “averaged” and then “plugged into” the embouchure size. Maybe you could have a subroutine to deal with this?
A feature for adding an harmonic chamber under/below the windway would be nice too. Most whistles don’t require them, but adding high frequency harmonics is desirable.
You mentioned conical playing holes? Maybe a feature for calculating “average” diameters from truncated conical dimensions?
Each register creates shifting nodes and antinodes. Toneholes must be placed/centered between these antinodes. Maybe a secondary program to show how and where these nodes are shifting so placement of tonehole centers will not degrade the upper registers?
A section on “optional” voicings would be wonderful too. The Flutomat is used by makers of other woodwinds as well (A Flutomat program for Native American flutes is already available). This program can be modified to calculate Clarinets, Bagpipe Chanters and many Renaissance woodwinds.
FWIW, I have been using a calculator written in C++ for a while. It had some of the features that I mentioned above. I never released it because I don’t do C++ that well and it only worked under a UNIX-like operating system.
I have tried to create a version for conical bores. The way I tried to do it was to take the I.D. of the bore at the hole (all of them are different) and do the normal calculations that one would do for each hole. It did not seem to work at all. It seems like the corrections are not correct for the end or for the other holes.
Here is my formula for getting the ID on the taper when the offset from the small end is known:
val = (len / taper_len) * (taper_max - taper_min) + taper_min;
where:
val = the output
len = the location of the point to get the ID at, measured from the small end
taper_len = the total length of the taper
taper_max = the maximum diameter of the taper
taper_min = the minimum diameter of the taper
I have a simple C program to illustrate the idea. If you have an algorithm that will work for this, I would be happy to implement it. Also, I would like some help with the math of calculating a whistle. I cannot seem to figure out how to solve for hole sizes when the placement is known. The only way to do it (that I know of) is to
change the hole sizes iteratively until the locations are within a certain tolerance.
Hey Chuck. Sorry, I’m not a programmer. I do all my calculations “the hard way”, with a fancy scientific calculator and time-tested
formulae. I find that the mathematics are much more accurate than “empirical/trial and error” testing.
Are you familiar with the booklets of Lew Paxton Price? He has written several flute making booklets with simplified mathematic calculations for the amateur designer. These have become “standards” for amateur woodwind makers. Formulae for conical Playing holes and avereraging conical bores are in these inexpensive booklets, as well as many other helpful formulae. I highly recommend them. Here is a source…
Bart Hopkin’s booklets on acoustics are also a sure bet. (check your local library for these too.) I’ll cobb together some common formulae and post them too. Thomas Hastay.
I have Hopkins and Price’s books. I had trouble converting Price’s work to an actual program to use. The math was easy enough, but I could not get it “dialed in” for accuracy. Hopkins does the Benade thing, same as flutomat. This seems to be the best way. Also, it is not encumbered by copyrights, as Price’s work is. The problem is that Benade’s formulas are iterative. In other words, you repeat the calculation using a previous result. That makes it hard (for me at least) to adapt them to a tapered bore.
If anyone out there has a math background and some time, I would like to talk to you about this.
I think this is a brilliant idea! I will look forward to seeing what you come up with. Specially any improvement on conical bore calculation.
The old flutomat helped me a great deal and I would like to see some extensions to help people get started on their self-made super whistles!
For new makers I would like to also help with a little insight these tools can bring - play around with the bore settings and get a feel for how stuff changes a lot with very small adjustments. To help you with the quantum-jump in that: your math might be exact and considered, but understanding is the only bridge between what you know and what you can make real. The math and tools allow you to know … your own hand is what does the execution - attend to that or all that goes before is academic. And for those who prefer to use the hands of others for their results (the law of civilization!) .. be understanding, moderate and keep an eye on feasability (also the law of civilization - the blessing of hands ).
I suppose what I am saying is that if you can put your heart and soul into your creation along with your mind, you will succeed. If, at the end, you fail - this directs you to your next lesson. Making a good whistle is the most brilliant way I have ever found for improving my life and bringing more “thy will be done on earth as it is in heaven”. For the truly religeous this will make obvious sense, for the existentialist please consider that you are the pinacle of evolution and your hands hold the wisdom of 10 million years .. Decartes said " I think therefore I am": think with all you have and you might get close - mind, body and soul. Then the music starts , I would wish all can have good music in their lives. The key is “value-add” - i.e. what comes into your life returns to the world better, enhanced by the value of your presence here! This is the benchmark of life .. and whistle making
Is it the math or the programming? I was a professional programmer, so if you give me a definition I can most likely code it for you (though my preferred language is Java). I can talk some math though I fade out somewhere around degree level.
I can only speak to the Kosel spreadsheet and anything based on it such as Daniel Bingamon improved version as that is what I have used and modified. I believe that Flutomat is based on the same equations/methods.
The Kosel spreadsheet uses first order approximations of formulas first published some 80 years ago that do not require an iterative process, if set up in a suitable fashion.
The trick is you do not need to know anything about the position of holes below the one being calculated, just the frequency of the note below it, which you know.
Corrections to the position of the hole from closed holes above it can be added to the result and since only closed holes above the note effect it if implemented correctly this does not have to involve iteration or create circular refs in a spreadsheet.
The formula (and presumably its first order approximation) works for open or closed, cylindrical or conical instruments so it should not be too hard to have a program work for all, though some the ‘correction formulas’ are specific for conical or cylindrical.
I am also updating my web site and it will include this page. For now, it is just some basic internal structure changes that you cannot really see. And, if I forgot to mention, it does not work yet. Post me a PM if you want the (non-working) java script. When I get it working, I will make it available as a ZIP file.
No need to pm you for a copy or for you to zip the js file, if its a javascript and online it is out there for all to see (if they know how to look which if they know how to mess with it they should)
Normally, it would be, but I have placed it in a separate file to make it easier to fool around with using a remote debugger. It is not viewable with a “view source” option.
I may take a look at it and see if I can put some of this into TWCalc. Nice thing about the C language code is that the interative functions can run longer instead of a fixed set that the spreadsheet does.
How does your embouchure hole/window formula come out? There are so many variables that affect this.
The way that the formulas are currently configured is exactly what flutomat has. I have not touched that stuff at all.
Here is my list of TODOs in the order that I am planning to do them:
What I am working on now is getting the notes to display correctly in every instance.
Make the number of holes to change correctly.
Get the calculations to display correctly.
3a. Make sure the results of the calculations match flutomat as a starting point.
Make the metric/inch conversion working correctly.
I want to do a graph like TWCalc for the cutoffs. It should be fairly easy with javascript.
Make a pull-down with different scales (aka interval sets).
After that, there is lots more that could be done. I want to stop there and see where I am.
You can get the source code by browsing to http://www.whistlemaker.com/pages/calc.js . If you (or anyone else) want to make changes, email the entire file (as an attachment, preferably), with your changes and I will check your work and merge them into the one on the web site. Be sure to make notes at the beginning of the file as to what you changed along with your name and the date. That will stay in in the file permanently. If you want to email me, please use the contact form in the web site.
I have the TWCalc source code available as well. I call it “Open Source Whistlemaking”.
On the cutoff graph, I found the use of a “Cutoff Ratio”: Cutoff / Frequency a good way to determine the quality of the tonehole. The ratio is pretty good but it really needs some form of logarithmic function.
The larger parts of the calculator are now done and it should be useful as it is.
Here is what works:
The calculations yield the same results as flutomat does, far as it goes.
Metric or inch calculations.
Arbitrary number of holes.
Printing to a printer is supported.
Inch calculations support fractions as well as decimal notation for the hole sizes.
Save and load a whistle are working using a cookie.
Iterative and non-iterative Benade calculations are supported
Most changes cause the calculations to be performed automatically.
Here is what does not work:
The cutoff frequencies are not calculated correctly. I am not sure what to do about this. (help!)
The cutoff freq graph has not been started yet.
The pull-down for different scales is not implemented.
No internal support for calculating tapers is in place, except the calculation method can be changes. For example, having separate bore diameters for each hole is not supported.
I am very interested in hearing people’s feedback on this. Especially all of the stuff that is broken. If you want to make changes yourself, contact me via PM or using the contact form on the web site. You can go directly to the calculator here: http://www.whistlemaker.com/pages/flutewhistle-calculator.php.
I have updated the calculator a little bit. You can now store more than one configuration. Everyone has their own storage because it stores them all in a single cookie on your own computer. Saving and deleting both work. I have tested it a bit more and fixed some bugs. I also got it to work as a stand-alone calculator, without WWW access, but it has to be modified for that to work. I may make a zip file available if there is any interest.
Next, I really want to get the cutoff frequencies to calculate correctly and get the graph working. And after that, I want to implement different scales (such as minor or flat-7) as a pull-down menu. Should be fairly easy. (Daniel?)
After that, I would like to work on cross fingerings. What I have in mind is to put a check box next to a hole to indicate that it is closed, and then calculate the frequency, the note and the % deviation from the actual note for the cross.
I wonder what one would have to do to get the calculator to evaluate the second octave for a set of holes.
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