NAFlutomat - NAF Design tool - Version 1.18
This page provides a tool for designing Native American Flutes.
It is version 1.18 (dated 10Feb2004)
of the NAFlutomat web interface written by
Ed Kort
(email edkort@comcast.net)
who has graciously allow me to post it here for general use.
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.
Lew Paxton Price
(email lewprice@softcom.net;
web page http://www.softcom.net/users/greebo/price.htm)
wrote a series of
monographs
which include the majority of equations used.
Don Forshag
and other members of the
Native
Flute Woodworking Yahoo Newsgroup
made valuable suggestions leading to this release.
The older version 1.12 of NAFlutomat is also available
here.
If you find any problems or suggestions regarding this page,
please contact me:
-- Clint Goss, March 18, 2004
Quick walkthrough:
- NAFlutomat supports tuning a flute under one set of environmental
conditions for play at another set. Enter altitude, temperature, and relative
humidity for each of these environments. Enter inside diameter and wall thickness of your flute.
- Enter flue, bird, 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 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.
Some details:
- 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 mouthpiece).
- 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".
- 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 "Playing frequency,
no holes" row and check "Tuning/Direction holes". Set the bird factor to
0.667 and adjust the TSH factor until the total bore length matches the length of your flute.
Replace the tape with the bird and again measure the tone the flute produces.
Using the TSH factor determined above, adjust the bird factor as above. 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. Nonetheless, it is simple to set them as you make each flute.
- Lew Paxton Price recommends that the ratio of bore length (plus virtual
foot extension, k1) to bore diameter squared is equal to 24. This gives a good
fundamental tone and transition to the second octave. To achieve this ratio, 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 a ratio of 24, or any other value that you enter. 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). Enter the
effective diameter in the bore diameter box to use the oval bore values. My
personal experience favors the traditional ratio of length / bore with a value
of 18. The program allows you to select either ratio.
- 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 playing
holes is used in this calculation (the thinner the wall, the small the minimum
playing hole diameter).
- 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).
- 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 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.
- 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.
Acknowledgements:
- 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 bird factors.
I thank both authors for their contributions to the art and craft of NAF
construction.
- Don Forshag and other members of the Native Flute Woodworking yahoo group
who made valuable suggestions leading to this release.
If you identify errors in the program, I can be contacted at:
edkort@comcast.net
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