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

Ever wondered how to make a flute? I’m not talking about something cut from a drinking straw with scissors, or put together using a cardboard paper towel tube… I mean make a flute that’s a genuine quality, professionally tuned musical instrument. Whether you use wood, PVC (flutes made from this material sound like blowing through glass – an excellent sound), or copper pipe (also sounds just as excellent) in flute making, there are a few mathematical things to keep in mind, but they all pretty much revolve around, and stem from, the one all-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 first need to know two numbers. The first one 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 – this is how far in linear distance sound travels per second, at sea level, at about 70 degrees Fahrenheit, or at about 21 degrees Celsius. The second number to know in flute making is how many Hertz (frequency of vibration) that a particular given note resonates at. For a brief 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 note’s frequency, in this case 440, and we will then have the measured length of the wavelength of the note “A”. This would end up to be 30.74 inches, or 70.08 centimeters long.

The next step in how to make a flute is simple. With an open ended flute, the body of the flute would actually need to be one half-wavelength long to play the fundamental note (the lowest note possible to play, with all finger holes closed) properly, in this case “A”. Due to other variable factors in flute making such as bore diameter, wall thickness and etc., the flute will actually need to be a tiny bit shorter – depending upon the thickness of the flute wall factoring in as well, this is generally about 1/3 of the bore diameter. Shorten the length little by little until the correct note is achieved. How to make flute embouchures, or the blowing edge hole, is to make it half of the flute’s bore diameter wide, measuring the center point of the hole to be a bore diameter’s distance from the inner face of the closed end.

A very convenient part about knowing how to make a flute is in the fact that the above mathematical formula is also how you would find the positions for the finger holes’ center points, according to the notes they are to play. How to make flute finger holes is to start small, slowly making them bigger as you “creep” them up the length of the flute towards the closed end until the right note is achieved. Finding the correct hole placements along the length of the flute’s body is important, but anywhere around the body at that point along the length is fine for hole placements… this allows for the reach of different sized fingers and hands.

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