FLUTRESO.TXT -- How to use the program FLUTRES2.BAS

FLUTRES2.BAS is a program in BASIC that will run in QBASIC or QuickBasic.
It calculates the expected sounding frequencies for each note on a 
Boehm flute, given the geometrical parameters that characterize the design.

The program is saved in text form so that it may be printed out
using a word processor such as Microsoft Word.
Change the font to a condensed font such as Abadi condensed light 
so that each line appears in its entirety without word wrap. 

The geometrical parameters of the particular flute to be
analyzed are to be entered into lines 520-700.
All dimensions are in millimeters. Each line is for a
particular hole, as labeled in the remark on that line. The
four pieces of data are, respectively: the position of the
center of the hole (measured from the center of the A hole
which is the reference, positive values increase going down
the tube), the value of H for the hole, and the cavity
parameters a and b for the hole.  These last three values may
be calculated using FLUTEKEY.EXE. Line 550 is for an
additional C# hole that occurs on some flutes. If it is
absent, enter a position intermediate between those in 540
and 560, an extremely large value for H, like 1 times 10 to
the 5th, (1E5 in BASIC) which effectively says the susceptance is zero,
and zeros for each of its cavity parameters. If the flute has a C
foot, line 690 should specify the position of the end of the
flute tube, the value of H should be 5.8 (the end correction
for a tube 19 mm in diameter) and zero cavity parameters.
Line 700 should then have the same position value, an
extremely large H, and zeros for the cavity parameters. For a
B foot, line 690 is constructed like that for any other hole,
while line 700 should carry the end position, the value of
5.8 for H, and zero cavity parameters.

Initially, set the value for WD in line 40 to zero. This is
the headjoint withdrawal, which needs to be set to tune A4 to
440 Hz. We will explain this after describing how to run the
program.

Run the program. Choose (2) Manual Note Choice. You will
be asked if you want to review parameters.  Answer "Y". A
listing of the data you entered will be presented.
Check it for errors, omissions, and if OK proceed.  You will
be asked for a note choice. Specify the note you want
to look at, using the standard notation like A4 for the
tuning A.  If you want an accidental, always specify the
sharp, for example, D#5, not E-flat5.  You will be presented
by a diagram showing the fingering the program used, the name
of the note, the frequency for an A 440 equal-tempered scale,
the wavelength in the tube, the column excess, i. e. how much
longer the air column was than would be required to make this
note exactly in tune, and the deviation in cents for the
sounded note.

The first time you do this, ask for A4 and note the column
excess. Go back into the program and enter the negative of
this value for the value of WD in line 6, which amounts to pulling out the
headjoint that much. Running the program again should give an
A4 that has zero cents deviation. If not, adjust WD until
this is the case.

In manual mode you may ask for any notes in the flute range
to get the deviations. This is convenient if you are working
on a particular hole to make an adjustment, and want to see
how a particular geometric change affects the notes which
involve that hole.  Similarly, "TRILLS -MANUAL" will give
results regarding the use of the trill keys. 

By choosing "PRINT OUT ENTIRE SCALE" you will get a printout
showing the parameters used, the column excess and cents
deviation for each note of the scale, the upper note and
frequency interval for trills using the trill keys, and a
graphical presentation of the deviations.

Lines 3010 to 3510 establishes the fingering used for each
note, as labeled in the remarks associated with some lines.
A closed key is represented by 1, an open key by 0.  You can
change the fingering by altering these lines. Line 3300 gives 
the fingering for a conventional E. For a split E the 10th number 
should be changed to 1, that is line 3300 would read 
1,1,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0. After making this change, 
run the manual program and look at E6 to check the fingering. 
Or one might wish to see the effect of playing F# with the middle finger
instead of the third, in which case line 3320 should be altered.

It is convenient to keep a separate copy of lines 500 to 700 so that they 
may be substituted in programs for different flutes.