NAFlutomat - Native American Flute Design Tool

Getting Started

If you are new to NAFlutomat, I suggest beginning with the Guided Version of NAFlutomat. It was developed in August 2014 as a kinder, gentler approach to this sometimes-daunting design tool for flute-crafting. The guided version is composed of a series of eight steps, each on their own page, that helps you set the most important inputs to this NAFlutomat tool. Each step provides descriptions and explanations of the inputs on that page.

Then, if you 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.
• After setting the three parameters shown in green, click the button and look over the results show in the yellow boxes. You can begin to learn this tool by changing various values in the white boxes and clicking to see how they effect the results in the yellow boxes.
• 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 when you click the button.
• 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.

Version 1.38b — August 31, 2014

Units of Measurement

Environment

Parameters

Pitch Standard

Temperament

Calculation

Fingering	Playing Frequency (Hz)	Tuning Frequency (Hz)	Tuning Note	Hole Number	Hole diameter	Wall thickness at hole	Calculated dist. from end of flute	Calculated dist. between holes
Total bore length:							in
				6	in	in	in	in in in in in
				5	in	in	in
				4	in	in	in
				3	in	in	in
				2	in	in	in
				1	in	in	in
				see Finger Hole Size for hole diameter colors (opens in a new window)
KEY of FLUTE:	G#5  G5  F#5  F5  E5  D#5  D5  C#5  C5  B4  A#4  A4  G#4  G4  F#4  F4  E4  D#4  D4  C#4  C4  B3  A#3  A3  G#3  G3  F#3  F3  E3  D#3  D3  C#3  C3  B2  A#2  A2  G#2  G2  F#2  F2  E2  D#2  D2

Direction Holes

Check this box if your wish to have direction holes:      Number of direction holes:  1 2 3 4
 

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, block, and TSH parameters.
3. Select a Pitch Standard. The default is A4 = 440Hz.
4. Choose a Scale Temperament. This should be Equal temperament if you are designing a concert-tuned flute.
5. Enter your 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 above will be ignored.
6. Enter your desired finger 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.
7. 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.
8. Press the button.
9. Examine the results.
   The “Calculated dist. from end of flute” column provides the calculated distance from the center of the finger hole to the foot end of the flute.
   The “Calculated dist. between holes” column indicates how much stretch is required between adjacent playing fingers.
10. Adjust the finger hole sizes: make them smaller to move them up the flute, larger to move down toward foot end.
11. Press again, try various finger hole size schemes until you're happy with the layout.
12. 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 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 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. The Notepad application works fine in Windows; other operating systems 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.htm) 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. 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.
4. 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:
   1. enter the same values for both sets of environment conditions,
   2. set just the playing conditions, or
   3. 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”.
5. 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:
   1. measure the length of the bore,
   2. cover the flue with a piece of tape or card stock rather than the block, and
   3. 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 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 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:
   1. enter 1.0 in the “TSH factor” box,
   2. enter the frequency with your intended block in the “Tuning Frequency, no holes” box,
   3. enter the bore length in the “Total bore length” row, and
   4. click the 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.
6. 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.
7. 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 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.
8. 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 finger 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 smaller the minimum playing hole diameter).
9. The background color of the finger hole diameter fields is set 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. See the Finger Hole Size and Nodal Interference pages for a description (they open in a new window).
10. The frequencies set by using the KEY of FLUTE selector represent mode 1 tuning. The mode 4 notes and will be somewhat sharp. As is common with mode 1/4 flutes, you might want to split the difference, make the mode 1 notes and slightly flat and make the mode 4 notes and slightly sharp. 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).
11. To make a 5-hole flute in mode 1, just set the hole diameter for hole 4 to 0.
12. 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.
13. 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.
14. If the wall thickness at all of the finger holes and direction holes is the same, just enter the thickness in the row for finger hole 6. Then click the button to copy this value for all the other holes.