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## How to Make a Flute – The All Important Mathematical Formula

Have you ever wondered how to make a flute? I’m not talking about something cut from a straw with scissors, or pieced together with a cardboard towel tube… I mean making a flute that is a real quality, professionally tuned musical instrument. Whether you use wood, PVC (flutes made from this material sound like blowing through glass – excellent sound) or copper tubing (also sounds just as excellent) to make flutes, there is some math involved to consider, but almost all of them revolve around, and come from, the one important mathematical formula involved in how to make flute-type woodwind instruments, or even those of other types. Do you know what this mathematical formula is? Well, I’ll tell you…

If you want to know how to make a flute, you must first know two numbers. The first is the measurement of the speed of sound in inches (or centimeters, etc.) per second. In inches, that would be 13526.5, and in centimeters, that would be 34357.31—that’s the linear distance that sound travels per second, at sea level, at about 70 degrees Fahrenheit or about 21 degrees Celsius. The second number to know in flute making is how many Hertz (frequency of vibration) a given note resonates. For a short and simple example, let’s say we use the note “A”. The frequency of “A”, in Hertz, is 440. Now we take the speed of sound in inches (or centimeters) per second and divide that number by the frequency of the note, in this case 440, and we have the measured length. of the wavelength of the “A” note. That would end up being 30.74 inches, or 70.08 centimeters long.

The next step in making a flute is simple. With an open-head flute, the body of the flute should be a medium wavelength to properly play the fundamental note (the lowest possible note to play, with all the finger holes closed), in this case “A “. Due to other variable factors in flute making, such as hole diameter, wall thickness, etc., the flute will actually need to be a little shorter; depending on the thickness of the flute wall as well, this is usually about 1/3 of the diameter of the hole. Shorten the length little by little until you get the right note. How to make flute mouthpieces, or the hole for the blowing rim, is to make it half the diameter of the flute hole as wide, measuring the center point of the hole at a distance of one diameter of the hole from the inside face of the closed end.

A very convenient part of knowing how to make a flute is the fact that the math formula above is also how you would find the positions of the center points of the finger holes, based on the notes they are supposed to play. How to make flute finger holes is to start small, slowly making them larger as you “drag” them down the length of the flute towards the closed end until the correct note is reached. It’s important to find the correct hole placements along the body of the flute, but anywhere on the body at that point along the length is fine for hole placements…this allows for range of fingers and hands of different sizes.

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