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Secrets of the Flute

More About Flute Theory


People have sometimes asked what parts of the two "Secrets" books was known before they were written and what parts were my original work.   At least one disgruntled physicist has claimed that my work was not original, and another has claimed that my work was incorrect.

When I became interested in flutes, the following was available.
1.   It was known that the speed of sound in air can be determined by the temperature of the air (the altitude is not the determining factor although it does influence the temperature).
2.   The Bernoulli principle was known (airflow can cause a vacuum in a flute).
3.   It was probably understood that the vacuum/pressure principle made the sound of the flute - but this was certainly not published very widely or adequately explained.
4.   There was a vague idea about the relationship of the flute length and the speed of sound but the false lengths that I call K1 and K2 were not known - with exception of one author who had discovered one of them but did not know what it was.
5.   Nodes were known to exist and understood to a limited degree.
6.   The energy relationship with frequency was known.

There were numerous incorrect theories about the functioning of the flute such as the idea that there was "drift" air from the head to the foot (this is true for instruments like the tuba or the bugle - horns - but not the flute type instruments) or that there was straight flow of air in the flute as opposed to curved airflow caused by a vortex.

Before I began to explore the nature of the flute, I was told by practically everyone that what I was attempting to do was impossible.   Frankly, I was not certain that the answers could be found - but as I found the first answer, which was the existence and nature of the false length found at the flute foot, I realized that whatever I found, it would be an improvement over what little had been found before.

In my experiments and subsequent calculations, I was able to determine, among other things,
(1)   that a vortex formed at the foot during the "inhalation" portion of the flute cycle,
(2)   that this vortex could be converted to a false length for the flute sound chamber,
(3)   that this vortex caused the air in the flute to take a circular or spiral path,
(4)   that the spiral path affected the theoretical length of the flute for certain calculations,
(5)   that a similar phenomenon occurred at the flute embouchure and could be calculated according to the type of flute,
(6)   that the correct theoretical length for the flute bore could be determined from the foregoing information and the air temperature,
(7)   that the ratio of theoretical bore length to the bore cross-sectional area determined in part the transitions from one octave to another,
(8)   that the effect of the playing holes could be calculated by an equation which considered them to be parallel paths (other flute bores),
(9)   that the correct placements of the playing holes could thus be determined and the flute could be tailored to one's individual hand,
(10)   that both the straight bore flutes and the tapered bore flutes could be designed from the above,
(11)   the existence of a phenomenon I call nodal interference, its nature, and how to avoid it,
(12)   that energy (frequency) affects playing hole size,
(13)   the correct minimum and maximum for hole sizes for any particular flute,
(14)   the correct equations for correct tuning or direction hole placements,
(15)   the size and placements for holes in a barrel with a closed foot,
(16)   the correct way to use backsetting in a flute,
(17)   why and how the tapered head works (18)   the existence and role of "hobo" air in the flute (19)   and how to use the hobo air to affect.

From the various equations that came from the above, it was possible to create a flute design program for a computer.   This program has been used by many flutemakers as has proven to be a correct and valuable tool.   Although today the knowledge incorporated in the flute design program appears to be relatively obvious and simple, intensive effort was required to discover the exact equations to describe it.   About twenty years was required to discover the information found in Secrets of the Flute and another five years to fully explore and discover the information found in More Secrets of the Flute.   Another two years was needed to develop the design program for my own use, and four more years was required to fully develop the program into one that is user-friendly for the average craftsman.

The flute design program is accurate to within a thousandth of an inch, which is more accuracy than can be managed with most of today's woodworking tools.   When I use the program, I make the flute blank as best I can and measure it with a micrometer.   Then I enter the measurements back into the original design.   The resulting answers for the hole sizes and placements are used for the finished flute.

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