NAFlutomat - Native American Flute Design Tool
This page provides a tool for designing Native American flutes. The basic strategy is to provide inputs such as the key of the flute, the bore diameter, wall thickness, finger hole size, and many other parmeters you will be using, and this tool suggests design parameters such as the length of the sound chamber and the location of the finger holes.
Note that this tool attempts to predict the best bore length, finger hole locations, and other output parameters using a set of rather complex equations. While these equations provide can provide a “reasonable” first approximation for these parameters, they should be considered a starting point. It is typically possible to construct a well-tuned flute by using the results of this tool and then careful tuning of the flute (see the Basic-Six, Basic-Five, and Bob Grealish tuning methods). However, the “rather complex equations” used in this tool do not account for pertubations in the size and shape of the flute, the special considerations and limitations on finger hole position or size, or (in particular) the sound that you are trying to achieve.
In short: You may find this tool a useful starting point.
Also, please consider other (less “equation-based”) approaches to flute design on the Finger Hole Placement page.
Preserving Your Results
If you wish to print the results of the designs you create using this software, you might consider some techniques to elimitate printing the documentation. Here are some suggestions on how to do this, from various sources and suggestions I have received from folks at the
Flute Woodworking Yahoo Newsgroup.
Please realize that these suggestions are highly dependent of your particular computer setup:
- On Windows 7, you can use the Snipping Tool. Start ⇒ Search Programs and Files ⇒ “Snipping Tool” … and the draw a box around the area of the screen you wish to save. You end up with a JPEG image that you can edit, enlarge, save, print, etcetera.
- You can print to PDF and choose the page numbers you wish to print.
- On Windows, use the Print Screen key (possibly while holding down the Ctrl key) to capture your screen into the copy/paste buffer, and then paste the image into a drawing program.
- Many browsers offer the option to print a selected portion of a web page. Select the portion of the page you wish to print, bring up the print menu from the top pulldown menu options, and then choose “Selection”
for what you wish to print.
- On Macintosh systems, there is a Grab application that performs a similar job to the Windows Snipping Tool.
This table shows the fixed ratios used for the various harmonic temperaments and the bias from “ET” (equal temperament):
This is version 1.38b (dated August 31, 2014), with formatting and stylistic updates made by Clint Goss to
version 1.37.2 of the NAFlutomat web interface written by
who has graciously allow me to post it here for general use.
If you would like to use the previous version (the “pure” version 1.37.1 dated 19Sep2008 without formatting and stylistic updates)
it is available on the NAFlutomat 1.37.1 page. Other previous versions are available as listed in the Revision History below.
Only Edward Kort
should be contacted with questions concerning the operation of NAFlutomat.
Feel free to contact Clint Goss
regarding any other issues or suggestions about this page.
wrote the original Flutomat program, which is the basis of
this interface and several of the equations used.
The majority of equations used in NAFlutomat are based on a series
of flute theory books (or monographs) written by Lew Paxton Price
([Price 1991] and
He has written flute design software of his own,
but bears no responsibility for any aspect of this NAFlutomat software.
Accordingly, Lew Paxton Price should not be contacted regarding NAFlutomat.
The complete series of small flutemaking books by Lew Paxton Price
is described on the
Oregon Flute Store site,
but are available from other sources or by contacting Lew at
The Lew Paxton Price web site (primarily educational) is currently
http://www.lewpaxtonprice.us/ (the new site for the older
Members of the
Flute Woodworking Yahoo Newsgroup
made valuable suggestions leading to this release.
If you find any problems or suggestions regarding this page,
please contact me.
Version 1.38b — August 31, 2014
- Expand from two choices of temperament to four.
- Display the ratios of the temperaments dynamically on the interface (for other than equal temperament).
Version 1.38a — August 30, 2014
- Set background colors of the finger hole diameter fields for those finger holes that are within the range implied by the
“Highest intended note” and the “Key of Flute selections”. The background colors of the corresponding hole diameter fields are set based on how they compare with the
“Minimum Playing Hole Diameter” calculation. Pink for less than the calculated “Minimum playing hole diameter” size, and a deeper red for less than 90% of the calculated Minimum playing hole diameter size.
- The interface is expanded so that the actual form-buttons can be used within the documentation.
- Fix minor bugs and typos.
Version 1.38 — August 27, 2014
- Integration with the new Guided NAFlutomat interface — a step-by-step approach to setting the primary inputs for this tool. Guided NAFlutomat provides a sequence of pages, each of which sets one or a few inputs. Each page has extensive documentation on the inputs on that page, and also provides default values based on previous inputs.
- Move the selection of Scale Temperament to a separate section and table.
- Explicitly show inches vs. centimeters, °F vs.°C, and feet/sec vs. meters/sec on the interface to reinforce the units that have been selected. Change the label dynamically when the radio buttons are changed. However, automatic conversion of the input values is not done.
- New introductory text which sets the scene for how NAFlutomat fits into the scheme of flute-design approaches and tools.
- Add a note on the lack of conversion of input values when changing between Imperial and Metric.
Version 1.37.2e — January 4, 2013
- Reorganize the sections on this page for better readability.
- Highlight the most important and most basic parameters for getting started with this tool in soothing green.
- Add “Getting Started” documentation at the beginning.
- Reorganize the Direction Holes section for more comprehensibility.
Version 1.37.2d — April 18, 2011
- Modification only to the documentation … addition of note about measurement of the bore length (new third item in the “Some Details” section).
- Set math expressions (such as k2) in a different font style for ease of reading.
Version 1.37.2c — January 31, 2011
- Repair broken calculation of the direction holes, which were off by an octave.
Thanks to Jeremy Howell for reporting this problem.
Version 1.37.2b — December 9, 2010
- Change the interface to use the IPN notation style of, for example, “F#2” rather than “F,,#”.
- Upgrade to use standard MIDI note numbers (previously used MIDI numbers off by one octave).
- This incorporates Ed Kort's bug fix that became official with a version change from 1.37.1 to 1.37.2.
Version 1.37.1a — December 9, 2010
- A bug found during yesterday's development caused a hang of the code if an ultra-low flute key was selected.
This bug was fixed by patches to the findBoreParameters() routine from Ed Kort.
No version number change in the base code - it's still 1.37.1 in the base code and 1.37.1a in this web version.
- This version is available on the NAFlutomat 1.37.1a page.
Version 1.37.1a — December 8, 2010
- Formatting and style changes (including the relocation of this revision history) to match the style of other Flutopedia pages.
Version 1.37.1 — September 19, 2008
- Minor bug fix to version 37: Fixed reloading of URL parameters when the L/d ratio was saved.
- This version is available on the NAFlutomat 1.37.1 page.
- Adds a new aspect ratio.
- Metric calculations have been fixed.
- Added a note-frequency converter.
- Changes from version 1.34:
- Added iterative calculations for bore parameters, TSH factor, and Bird factor.
- Changed direction hole frequency to reference tuning rather than playing frequency.
- Added wall thickness replication button.
- Pete Kosel wrote the original Flutomat program, which is the basis of
this interface and several of the equations used.
- Lew Paxton Price wrote a series of monographs which include the
majority of equations used and the description on determining TSH and
block factors. The aspect ratio (bore length / bore diameter ^ 2) is
calculated according to personal discussions with Lew and differs from
that presented in his books. I thank Lew for these discussions.
I thank both Pete Kosel and Lew Paxton Price for their contributions to the art and craft of Native American flute
- Don Forshag and other members of the
Flute Woodworking Yahoo Newsgroup who made valuable suggestions leading to this release.
If you identify errors in the program, I can be contacted at: