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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 put together using a cardboard paper towel tube… I mean making a flute that is a real musical instrument of quality, granted by professionals. Whether you use wood, PVC (flutes made from this material sound like they’re blowing through glass – great sound) or copper pipes (are equally great) in flute making, there are has a few mathematical elements to keep in mind, but they all pretty much revolve around and stem from the one very important mathematical formula involved in making flute type wind instruments, or even those of other types. Do you know this mathematical formula? Well, I’ll tell you…

If you want to know how to make a flute, you first need to know two numbers. The first is the measurement of the speed of sound in inches (or centimeters, etc.) per second. In inches it would be 13526.5, and in centimeters it would be 34357.31 – that’s the linear distance 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 the number of Hertz (frequency of vibration) at which a particular given note resonates. For a short and simple example, let’s say we use the “A” grade. 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 then we will have the measured length of the wavelength of the “A” note. It would end up being 30.74 inches or 70.08 centimeters long.

The next step in making a flute is simple. With an open flute, the body of the flute would actually need to be half a wavelength to properly play the root note (the lowest possible note to play, with all finger holes closed ), in this case “A”. Due to other variable factors in the manufacture of the flute, such as bore diameter, wall thickness, etc., the flute will actually need to be a bit shorter – depending on the thickness of the flute wall, it is usually about 1/3 of the bore diameter. Shorten the length little by little until the correct note is reached. How to make flute mouthpieces, or the blowing edge hole, is to make it wide by half the bore diameter of the flute, measuring the center point of the hole at a distance of one bore diameter of inner face of closed end.

A very practical part of knowing how to make a flute is that the mathematical formula above is also how you would find the positions of the center points of the finger holes, depending on the notes they are to play. How to make flute finger holes is to start small, slowly enlarging them as you “crawl” them down the length of the flute towards the closed end until the correct note is reached . It is important to find the correct hole locations along the length of the flute body, but anywhere around the body at this point along the length is suitable for the hole locations…this achieves fingers and hands of different sizes.

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