One of the most basic formulas....

- math -

Shekkon!
(Mohawk language; greeting)

Okay, today let's discuss what needs to be done in order to figure out how to decide the length of woodwind instruments, and where to place the holes.... now, this here formula can also be applied to other instruments besides woodwinds, such as the chromatic drum set we will be making in future posts, so keep that well in mind.

I'll try to make this as simple and illustrative (even if a mite wordy) to understand with as much ease as possible. Here we go....

Basically, we need to remember that sound travels in waves - the difference from one wave to another is a result of it's frequency - for instance, let's imagine a rain barrel, full of water.... if we give it a couple of gentle, rocking nudges, we can see that waves, or ripples, appear on the surface. These waves, due to the gentle push on the barrel's body, are somewhat large, a little smooth, and a bit slow, moving from the barrel's rim towards the center and back again.

Now, after the waves subside, and all is calm at the surface, if we then take a rock and sharply whack it against the barrel's body, we then see something different - the waves, or ripples, are much smaller, speedier, and more numerous.

This is an example of FREQUENCY - how frequently are the waves passing through a given space in a given time?

In the above analogous illustration, the ripples and waves representing sound, the larger, softer, slower (and fewer), lower frequency waves would be a low, bass sound. The smaller, sharper, speedier (and more numerous), higher frequency ripples would be a higher tone.

So, in order to find our woodwind instrument's length - let's make this a basic flute - we need to know what note we would like to base this on. We need to know the FUNDAMENTAL NOTE.... this is the note played with all holes closed, the lowest note that this flute can play. Once we decide on a note, we need to know it's frequency.

Let's say we want to make this an A flute - A will be the fundamental note. The frequency of A (measured in "Hertz", which is the root-word in terms I'm sure you've heard of, such as 'megahertz' and 'gigahertz' and so on), is 440 hertz.

Now, we need a referrence frame from which to do our deductive math - we need to know the speed of sound.

Now, at sea level, at about 70-73 degrees F or so, the speed of sound, in inches, is 13526.5 inches per second. Within this distance, the note A makes 440 ripples through the air - this is A's frequency.

Now, we need to find out the WAVELENGTH of A - the distance between the tops, or crests, of each ripple, or wave, within said distance. If we want to find out how far it is from one wavecrest to another, we can understand that since, within the space of 13526.5 inches, there are 440 of these waves, we can know that a wavelength is 1/440th of 13526.5 - in other words, we DIVIDE the distance by the frequency.

Now, 13526.5 divided by 440 equals 30.742 - or, 30 and about 3/4 inches.

Now we know that the wavelength of A is roughly 30 & 3/4", so we can make our flute to that length, right? Wrong.

An open ended flute's body, is actually HALF the length of it's fundamental note's wavelength.... so, that means that our A flute needs to be roughly about 15 & 3/8" long.

Let's also assume for now, that the *inside* diameter of this particular flute's barrel, or body, is 3/4" wide. There are important reasons for this, but we'll discuss that later. In the meantime, if you want to try making one out of 3/4" PVC pipe, grab some now, and follow along - but don't cut it to any precise length yet.... maybe start it at about 20" long first - why?

Well, in order to properly tune this flute, we should first make the sounding mechanism. This first flute will be a transverse (sideblown) flute. Plug up one end of the pipe with cork, wood, or a PVC end piece, and now you will measure your flute body's length from the face of the plug on the flute's interior, to the open end. THIS is the flute length dimension you will be using in your math to find it's length, and where to put the holes.

There is a certain mathematical way to find what size to make the embouchure (the hole you blow into), and where to put it. Once we do that, and it makes a sound, then we can cut our flute to length, and check it's tuning as we do.

We will go over this in the next post. See y'all next post! ^_^

Nia:wen!
(Mohawk language; Thank you)

- math –