NAFlutomat - Native American Flute Design Tool
This page provides a tool for designing Native American flutes.
If you are new to NAFlutomat and are not up for diving into the Quick Walkthrough or Some Details sections,
here are some suggestions for getting started:
- Set the three parameters shown in green below. They control the key of the flute you are crafting, your Inside bore diameter, and the wall thickness at the finger holes. This should get you started for a flute with no direction holes.
- Then, just click the Calculate button and look over the results. You can begin to learn this tool by changing various values and clicking Calculate to see their effect.
- Remember that mid-range flutes are in octave 4 (C4, which is fairly low for a Native American flute, up to B4, which is rather high for a Native American flute).
- Don't enter values in the yellow boxes. They will get overwritten.
- If you need to convert drill bit sizes to inches or millimeters, check out the Drill Bit Conversion Table (opens in a new window).
Standard 6-hole, Mode 1/4 NAF
by Edward Kort, with user-interface improvements by Clint Goss
This section provides the documentation for using the above NAFlutomat calculator:
- NAFlutomat supports tuning a flute under one set of
environmental conditions for play at another set. Enter temperature, and
relative humidity for each of these environments. Enter inside diameter
and wall thickness of your flute.
- Enter flue, block, and TSH parameters.
- Enter the scale temperament, either Equal temperament (concert pitch)
or Harmonic temperament.
- Enter desired playing frequencies in hertz (i.e. cycles per
second) or use the KEY of FLUTE selector to set frequencies automatically by
selecting the fundamental note. If you enter your own playing
frequencies, the scale temperament selected in 2. above will be ignored.
- Enter desired hole sizes. If you are going to modify the wall
thickness at any of the holes, enter that thickness; otherwise, enter
the same wall thickness at each hole, representing the wall thickness.
- Optionally, enter direction hole information, choosing either
the frequency or note for the flute before drilling the direction
hole(s). A good choice is 2 or 3 demi-tones below the flute fundamental.
- Press Calculate button.
- Examine results.
- Enter different hole sizes (smaller to move up the flute,
bigger to move down toward end-of-flute).
- Press Calculate again, try various hole size
schemes until you're happy with the layout.
- You now have two options to save all of the values for reuse:
- If you want to save values for your personal use (rather than
sharing with other people), you can use the Favorites (Internet
Explorer) or Bookmarks (Netscape) feature of your browser. First, press
the “Reload with parameters” button. The page will be reloaded
with a very long address. Using the Favorites/Bookmark feature, save
this page with a descriptive name. You can now start NAFlutomat with
these values by selecting this favorite/bookmark.
- If you want to save the values to send to a friend, press the
“Create URL” button. A dialog pops up, with a very long
string. Select the entire string (in Internet Explorer, it will already
be selected; in Netscape, you will need to double click it). Then copy
the string to the clipboard (in Windows, Ctrl-C; other operating systems
will have similar commands). Open a text editor (Notepad works fine in
Windows; other operating systems will have similar plain-text editors).
Paste the string into the text editor (Ctrl-V in Windows). Save this
text file; annotate it if you like. Add several URLs in the same file.
Whenever you want to use NAFlutomat with one of these saved sets, select
the entire string in the text file, copy it to the clipboard, and paste
it into the “Address” area of your favorite web browser. Hit
“Enter” to load this URL and voila, NAFlutomat will be invoked
with the saved values filled in. If you receive one of these files from
a friend, be aware that the first part of the URL (before
naflutomat.html) may be different on your computer. Look at one of your
saved URLs and change the first part of your friend's URL to match; it
should now work fine. Also, do not paste these URLs into email messages;
the line splitting “feature” of most email clients will make
the URL unusable. Instead, send the text file as an attachment.
- Boxes in which you may enter values are white. Boxes containing calculated
values are yellow. If you enter values in the yellow boxes, these values will
be ignored and overwritten with the calculated values.
- Hole numbers start with 1 at the foot of the flute (farthest from the
- You can measure the bore length to anything you want: splitting edge, back of TSH, or top of backset. But do it consistently. The difference is subsumed in the k2, calculated using the block and TSH factors you determined operationally. Please see The “TSH parameters” determine k2 below.
- When tuning the flute, use the “Tuning” columns. Be aware
that, unless the tuning and playing conditions are the same, the frequencies
in the “Tuning frequency” column will not represent standard concert-pitch
notes, as do the “Playing frequency” values. The “Tuning note”
column shows the note that is closest to concert pitch and the number of cents
the tuning note differs from this concert pitch; this provides support for standard
chromatic tuners which don't display frequencies.
The convention for designating octaves, as of version 1.37.1b, uses the
IPN notation style. In this system,
C4 is middle C on a piano, and F#4 is the lowest note on a mid-range Native American flute.
If your playing and tuning
conditions are the same, you may:
do B or C, the program will copy the playing conditions to the tuning conditions
and perform the calculations as if you had done A. Be aware that if you leave
a blank in any of the playing condition fields (or any field other than the
tuning conditions), the program will interpret the value as “0”.
- enter the same values for both sets of
- set just the playing conditions, or
- enter “NA”
(or any other string) into one or more of the tuning condition values.
- The “TSH parameters” determine k2, the virtual extension
of the bore above the TSH. The greater k2, the shorter the flute for a given
fundamental. The TSH factor reflects the TSH geometry; the block factor reflects
the shape of the block/fetish over the TSH. To determine appropriate numbers
for these factors, after assembling the flute (about an inch longer than the
calculations indicate), making/choosing the block you will use, and voicing the
flute, but before drilling any holes, do the following:
frequency for the “Tuning frequency, no holes” row; enter the bore
length in the “Total bore length” row (I know it is yellow, but the
program does not know this). Click the “Calculate TSH factor” button.
Now put the intended block on the flute and measure the tone frequency. Again,
enter this value in the same Tuning frequency box; click the “Calculate
block factor” button. All subsequent flutes, with similar TSH and block geometries,
will have quite similar TSH and block factors. If you are attempting to craft
flutes with accurately determined length/bore ratios, I recommend performing
the above procedure. If not, it doesn't really matter how you vary the two factors
to get the lengths to match; they are used in combination to determine k2. The
easiest way to do this is:
- measure the length
of the bore,
- cover the flue with a piece of tape or card stock rather than
the block, and
- measure the frequency of tone the flute produces.
it is simple to set them as you make each flute. If you are using direction
holes, you will need to reset the “Tuning/direction holes” checkbox
and the “Tuning frequency, no holes” value.
- enter 1.0 in the “TSH factor” box,
enter the frequency with your intended block in the “Tuning frequency, no
- enter the bore length in the “Total bore length”
- click the “Calculate block factor” button.
- The “Bore parameters” help you design a flute that has the
“proper” bore diameter for the specified KEY of FLUTE. By proper I mean a flute
that plays all the notes in its range with the intended tone quality, and at
the same time being responsive in note changes and overblowing. The program
supplies three methods for calculating the bore diameter. The first method uses
the classic sound chamber aspect ratio: actual bore length divided by the bore diameter; the
typical value used for this ratio is 18. Lew Paxton Price developed a different
aspect ratio. Based upon recent discussions with Lew, the ratio is implemented
in the program as the theoretical bore length divided by the bore diameter squared;
the recommended value for this ratio is 24. The third ratio yields intermediate
values; I like a value for this ratio of 16.5. To accurately achieve any of
these ratios, you will typically need to bore an oval hole. This program calculates
the ratio based upon your entered parameters; it also calculates the dimensions
of the oval bore which gives your entered ratio. It does this by setting the
bore width to the closest circular radius, in increments of 1/8″ (2 mm
if you chose metric units), allowing you to use common core box or drill bit
sizes. Optionally, you may enter the diameter of the bit you wish to use (in
the “Your router bit” column). Two of the ratios are affected by k2,
which changes with the TSH width. If you make the TSH width a fixed fraction
of the bore diameter (as I do), you may have found that you need to perform
the calculation, enter a new value for the TSH width, and recalculate (maybe
multiple times). There is now a set of widgets, in the “Design iterative
calculations” table that performs these iterations for you. It uses the
bore width that you enter in the “Your router bit” column. Enter the
effective diameter in the bore diameter box to use the oval bore values. If
you used the iteration widget, also copy the TSH width that it contains to the
“TSH parameters” table.
- There is a relationship between k2 and the highest note that can be
played on a flute. When the wavelength of a note divided by 4 is less than k2,
the energy of the note is dissipated outside of the flute (above the TSH) so
the note does not play. Lew Paxton Price calls this nodal interference. Select
the “Highest intended note” you wish your flute to play; the default
is one octave plus 3 demi-tones above the fundamental. After pressing the Calculate
button, the “Maximum k2” represents the largest value for k2 that
will allow the intended note to play. If this value is less than the “Calculated
k2”, you will be unable to play this note. Either accept this limitation,
or modify your sound mechanism. The easiest modification is to increase the
width of the TSH.
- There is also a relationship between the highest intended note and
the minimum playing hole diameters. Under the assumption that all the holes
will have similar diameters, the “Minimum playing hole diameter” represents
the smallest hole size that will allow the highest intended note to play cleanly.
This value is an approximation, and so should only be used as a guide. You probably
don't want to make holes 1 and 2 smaller than this value; the others can be
made slightly smaller. The average wall thickness at the finger holes is used
in this calculation (the thinner the wall, the small the minimum playing hole
- The frequencies set by using the KEY of FLUTE selector represent mode 1 tuning.
The mode 4 notes with hole 5 (and 4, 2, and 1) open or hole 6 (and 5, 4, 2,
and 1) open will be somewhat sharp. As is common with mode 1/4 flutes, you might
want to split the difference, make these two notes slightly flat in mode 1 and
slightly sharp in mode 4. My preference is to tune the flute as indicated, either
blowing these notes softer (and in key) in mode 4, or closing hole 2 (as well
- To make a 5-hole flute in mode 1, just set the hole diameter for hole
4 to 0.
- To determine whether this program works for you, measure one of your flutes,
getting: bore length, bore diameter, TSH parameters, hole diameters, and frequencies
for each of the fingerings. Enter these values into the program and adjust the
TSH and block factors until the total bore length matches your flute. Then compare
the hole positions on the flute to those calculated by the program. If they
match, within the errors of your measurements, the program will work for you.
I still recommend that you start, as is normal practice, with a longer flute
and smaller holes.
- I do not advocate using the very analytical approach to flute layout
represented by this program over more traditional/organic methods and tunings.
I simply offer the program as an option to those who have not yet developed
the experience to craft pleasing flutes of different keys without such aids,
who wish to explore alternate hole spacings and tunings, like to play with numbers,
or just hate to spend a lot of time making firewood because of layout errors.
- If the wall thickness at all of the tone and direction holes is the
same, just enter the thickness in the row for finger hole 6. Then click the
“Replicate Hole 6 thickness” button to copy this value for all the
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 tha tyou 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 is version 1.37.2d (dated 18Apr2011), 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
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 1.37.2e - 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: