I’ve been wondering a lot about why a flute is the shape it is. Why does it have the diameter it does and why are the holes the size they are? What effect would changing these parameters have on the pitch of the flute? Would they also affect the timbre? I’ve done some research on this and have put together some interesting facts.
Changing the diameter of a flute doesn’t really affect its pitch, although a wider flute will be better suited to low registers and a narrow flute to high registers. The diameter of the modern flute is a compromise to be able to play well over many registers. The dominant effect on pitch is the position of the tone holes along the tube.
When you blow into a flute, you create a sound wave that vibrates down the tube until it finds a hole to escape from. The length of the tube is the length between the hole you blow into and the hole the air escapes from. By changing this length you change the pitch of the note. When you cover a hole with your finger, you are increasing the length of the tube and lowering the pitch (thinking in one octave only). This is shown in the diagram below.
The flute is constructed so that each hole is in the correct place to give a particular tube length that corresponds to a particular pitch. But say you wanted to make a flute yourself – what are the most important things to consider? The position of the holes is certainly very important, but what about other parameters – the size of the holes, the diameter of the tube? These things will also impact on the quality of sound.
How does the diameter of a flute affect its pitch?
Changing the diameter of a flute will not affect its pitch. The pitch is determined only by the tube length, not by the diameter. But the diameter of flutes is a set number that we don’t vary, so there must be a reason why this is the case. The diameter is 3/4″ and this is standard amongst flute makers.
The reason the diameter of the flute is important is that it affects the timbre across different pitch ranges. If you were to make the diameter of the flute smaller, you would worsen the quality of the sound on the lower octaves and if you were to make it wider, you would worsen the sound for the higher octaves. It may be that you could make a flute with a better sound across the lower notes by increasing the diameter, but the quality of the high notes would suffer and vice versa.
This is because if you make the diameter smaller, you block out some of the lower overtones. A wider diameter will therefore allow for increased richness in the lower register, but will lose some of the higher harmonics, as a wider tube equates to more losses in the higher frequency sound waves.
The diameter will also affect the response of the instrument. If you have a larger diameter of tube, you have a larger area to fill with air. This naturally slows down the instrument’s response. Different players may have different preferences for diameter size. An example of this is the alto flute, which is available with different diameters so that players can try them out and see which works for them. The timbre will vary a small amount and some may be more suited than others to higher or lower register playing.
How does the size and position of the tone holes in a flute affect its pitch?
The position of tone holes in relation to pitch is a simple thing to understand so I won’t say too much on it. Basically, the length of the tube between the point where you blow into the flute and the hole sets the pitch. Lengthening the tube makes the note lower and shortening it makes the note higher. You can overblow to get higher harmonics using the same fingering.
The size of the tone holes of different instrument will vary dependent on the pitch range of an instrument. A lower-pitched instrument will have larger tone holes and a higher-pitched instrument will have smaller tone holes. This is not just due to the fact that the instrument size is larger, so the holes are made bigger, but has actual scientific meaning.
The first thing is that a larger tone hole will give a louder sound. Usually if the instrument is lower in pitch, the sound is quieter to the listener and so if the size of the hole is increased, the sound can be louder. There has to be a limit on the hole size if the instrument is open-holed because the player has to be able to cover the holes easily with their fingers.
The other important part is related to the wavelength. The pitch of a note is determined by its wavelength. The lower the note, the longer the wavelength – the reverse of frequency where the higher the note, the higher the frequency. The size of the hole affects a wave’s ability to escape through it and the size of the wave has an impact on this.
For a note with a small wavelength (a high pitch), the wave will be small and can easily escape through a small tone hole. This means more sound will get out through the hole. For a lower pitch, with a longer wavelength, it will be more difficult for the sound to escape. This leads to lower notes needing larger tone holes.
This is not always possible. If you think of a flute, to get the octave above the fundamental, you overblow the notes. This means you are using the same size of hole for pitches an octave apart. But with a flute, the low notes are always harder to sound loudly and require the player to push more air through the instrument. This is a result of the tone holes being the same size for both octaves and a compromise has to be made on size such that the low notes sound, while the high notes are still controllable.
To sum this up, if the only thing you are considering is the pitch that will come out of the instrument, all you need to care about is the position of the holes. If you care about the timbre, you have to think a lot more carefully. The diameter of the flute and the hole size have to be carefully optimised to allow the player to get a decent sound over the full range of the instrument.