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NAFlutomat - Native American Flute Design Tool

This page provides a tool for designing Native American flutes.

This is version 1.37.1a (dated 09Dec2010), with formatting and stylistic updates made by Clint Goss to version 1.37.1 of the NAFlutomat web interface written by Edward Kort (email edkort@comcast.net) 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.

Only Edward Kort (edkort@comcast.net) 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.

Pete Kosel (email ph_kosel@cwo.com; web page http://www.cwo.com/~ph_kosel/) 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 [Price 1997]). 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 flute-making books by Lew Paxton Price is described on the Oregon Flute Store site, but are available from other sources or by contacting Lew at lewprice@softcom.net. The Lew Paxton Price web site (primarily educational) is currently http://www.softcom.net/users/greebo/price.htm.

Members of the Native Flute Woodworking Yahoo Newsgroup made valuable suggestions leading to this release.

If you find any problems or suggestions regarding this page, please contact me.

Standard 6-hole, Mode 1/4 NAF

by Edward Kort, version 1.37.1a

Units of measurement


  Temperature Relative Humidity (%) Speed of Sound
Playing conditions
Tuning conditions


Sound Chamber Parameters
Inside bore diameter:
TSH Parameters
Flue depth
Cutting edge thickness 
TSH width
TSH length (N/S)
Wall Thickness at TSH
TSH factor
Bird/fetish factor
Calculated k2
Calculated k1

Design Iterative Calculations
TSH fraction
TSH width
Of bore diameter
Of bore width
Lesser of diameter or width
Bore Parameters
For specified inside bore diameter:
Ltheor/diam 2 ratio
Lactual/diam 2 ratio
Lactual/diam ratio

For Lt/d 2 ratio of:
For La/d 2 ratio of:
For La/d ratio of:

Closest standard router bit diameter Your router bit diameter
Bore width (router bit diameter)
Bore height (total bore depth)
Effective inside bore diameter

Nodal interference and
minimum hole size
Highest intended note
Maximum k2
Minimum playing hole diameter
Note to frequency


Scale temperament:

Fingering Playing frequency Tuning frequency Tuning note Hole Num. Hole diameter Wall thickness at hole Calc. dist. from end of flute Calc. dist. between holes
Total bore length:   
Finger diagram open open closed open open open 6
Finger diagram closed open closed open open open 5
Finger diagram closed closed open closed open open 4
Finger diagram closed closed closed open open open 3
Finger diagram closed closed closed closed open open 2
Finger diagram closed closed closed closed closed open 1
Finger diagram closed closed closed closed closed closed  
Flute key

Direction Holes

Check this box if your wish to have direction holes    Number of direction holes: 

Tuning frequency, no holes

Tuning note, no holes

Playing frequency,
no holes

Playing note, no holes

Diameter Wall thickness at hole(s) Calculated distance
from end of flute

Quick Walkthrough

This section provides the documentation for using the above NAFlutomat calculator:

  1. 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.
  2. Enter flue, bird, and TSH parameters.
  3. Enter the scale temperament, either Equal temperament (concert pitch) or Harmonic temperament.
  4. Enter desired playing frequencies in hertz (i.e. cycles per second) or use the key 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.
  5. 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.
  6. 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.
  7. Press “Calculate” button.
  8. Examine results.
  9. Enter different hole sizes (smaller to move up the flute, bigger to move down toward end-of-flute).
  10. Press “Calculate” again, try various hole size schemes until you're happy with the layout.
  11. You now have two options to save all of the values for reuse:
    1. 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.
    2. 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.

Some details:

  1. 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.
  2. Hole numbers start with 1 at the foot of the flute (farthest from the mouthpiece).
  3. 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. My convention for designating octaves (a minor extension of the original Flutomat) is that notes in the same octave as concert A (440 Hz) are designed with a capital letter (for example, G). An octave lower adds a “,” (for example, G,), an octave higher is lower case (for example, g), and two octaves higher adds a “,” (for example, g,). I would have liked to have done something prettier, but javascript doesn't really support formatting in text boxes. If your playing and tuning conditions are the same, you may: a) enter the same values for both sets of environment conditions, b) set just the playing conditions, or c) enter “NA” (or any other string) into one or more of the tuning condition values. If you 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”.
  4. 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 bird factor reflects the shape of the bird/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 bird you will use, and voicing the flute, but before drilling any holes, do the following: a) measure the length of the bore, b) cover the flue with a piece of tape or card stock rather than the bird, and c) measure the frequency of tone the flute produces. Enter that 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 bird on the flute and measure the tone frequency. Again, enter this value in the same Tuning frequency box; click the “Calculate bird factor” button. All subsequent flutes, with similar TSH and bird geometries, will have quite similar TSH and bird 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: a) enter 1.0 in the “TSH factor” box, b) enter the frequency with your intended bird in the “Tuning frequency, no holes” box, c) enter the bore length in the “Total bore length” row, and d) click the “Calculate bird factor” button. Nonetheless, 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.
  5. The “Bore parameters” help you design a flute that has the “proper” bore diameter for the specified key. 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 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 18″ (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.
  6. 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.
  7. 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 playing holes is used in this calculation (the thinner the wall, the small the minimum playing hole diameter).
  8. The frequencies set by using the key 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 as 3).
  9. To make a 5-hole flute in mode 1, just set the hole diameter for hole 4 to 0.
  10. 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 bird 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.
  11. 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.
  12. 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 other holes.

Revision History

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.

Version 1.37.1a - December 8, 2010

  • Extract common JavaScript code out into a separate file for use in other calculators.
  • 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.

Version 1.37

  • 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.


  1. Pete Kosel wrote the original Flutomat program, which is the basis of this interface and several of the equations used.
  2. Lew Paxton Price wrote a series of monographs which include the majority of equations used and the description on determining TSH and bird 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 NAF construction.

  3. Don Forshag and other members of the Native Flute Woodworking Yahoo Newsgroup who made valuable suggestions leading to this release.

If you identify errors in the program, I can be contacted at: edkort@comcast.net



To cite this page on Wikipedia: <ref name="Goss_2022_naflutomat_1_37_1a"> {{cite web |last=Goss |first=Clint |title=NAFlutomat - Native American Flute Design Tool |url=http://www.Flutopedia.com/naflutomat_1_37_1a.htm |date=7 June 2022 |website=Flutopedia |access-date=<YOUR RETRIEVAL DATE> }}</ref>