If you understand why the flute makes the sound it does, it may be useful in your performance. I think it is still important to learn the speed of breath and harmonics by your feelings, but here I would like to explain the theory behind it.
Unlike the saxophone, the flute does not have a reed that converts breath into vibration. So, in the case of the flute, it is called an air reed. In short, the breath alone creates the vibration.
The air vibrates through a phenomenon called the “Karman vortex,” which means that when you place an obstacle in the fluid, vortices alternately form behind it. I can’t explain it well with just text, so I’ll draw the following illustration.
Think of the arrow as the fluid and the yellow circle as the obstacle. When the speed of the fluid exceeds a certain speed, a Kalman vortex is created behind the obstacle. The higher the speed of the fluid, the finer the Kalman vortex will be, and makes the faster oscillation.
Now let’s consider this in the case of the flute.
When you play the flute, you blow against the edge of the lip plate. Think of this breath as fluid. And when you play the flute, you blow half of the breath in and the other half out. In other words, the edge of the lip plate is an obstacle to the fluid, so a Kalman vortex is created behind it, causing the air inside to vibrate. The vibration of the air is a change in pressure, which is transmitted to the inside of the pipe and resonates to produce sound. (For details, see below.)
Earlier, I mentioned that the faster the speed of the fluid, the faster the vibration of the Kalman vortex. In other words, the faster the speed of the breath, the faster the vibration, and the higher the frequency of the sound. So, the higher the pitch, the faster you need to breathe.
Resonance of Open Tube
Sound is a vibration of air, but the human ear cannot understand it if it vibrates just a little. Therefore, it is necessary to make the vibration strong to some extent. The tube plays this role.
In the case of the flute, the mouth piece and the tip of the foot tube are open, so it can be regarded as an open tube. In this open tube, only the sound of a specific frequency can be resonated and converted into a strong vibration. The sound of these resonant frequencies is what we hear.
So how is this frequency determined? It is determined by the length of the tube. This is also difficult to explain, so I will draw diagrams.
The sound vibrations are reflected at the end of the tube. (Strange as it may seem, it reflects even when the tube is open.) There is a frequency at which these traveling waves and reflected waves overlap and strengthen each other. These are the specific frequencies shown in the diagram above. Waves at these frequencies are called standing waves because they appear as if they are stationary and vibrating there. In the case of an open tube, since it is a free-end reflection, it resonates when 1/2 of the wavelength of the sound wave is exactly the length of the tube. This is the fundamental vibration.
Sounds with frequencies two, three, or four times higher than this fundamental vibration also resonate. This is what is called harmonics.
However, this only allows the sound to be played at a specific frequency (pitch), so there are many holes in the body of the tube, and by pressing and releasing them with fingers, the length of the tube can be adjusted to produce various pitches.
Returning to the air reed for a moment here, although the resonant sound can be adjusted with the fingers, the breath is not simply a matter of vibrating the air. By creating a Kalman vortex vibration that is close to the frequency of the resonant sound, the sound will be easier to produce. So you need to be aware of not only your fingers, but also the speed of your breath depending on the pitch. For low notes, slow down the breath speed, and for high notes, speed up the breath speed.
The more you create vibrations close to the frequency you want to produce by your breath, the easier it will be for you to produce the sound.
In the case of the flute, all the notes in the first octave (lower notes) are played with the fundamental vibration, but all the notes above the second octave are played with harmonics. If you use the same fingering but increase the speed of your breath, you’ll get a higher sound.
I think this harmonic practice is important for the flute, and I would like to explain the logic behind it as well. I will explain this assuming that you hold the low D note.
The low D is a fingering with only the pinky finger of the right hand separated, so only the sound hole at the very tip is an open tube. In this case, the distance between the mouth piece and the tone hole is half the wavelength of the resonant sound (although there are complicated calculations involved). This is the fundamental vibration of the D.
If you keep this fingering and increase the speed of your breath, you will be able to get an octave higher D. The reason for this is that vibrations twice as high as the fundamental vibrations will resonate better in the tube. When the number of vibrations (frequency) is doubled, the pitch goes up an octave.
Using the same fingering and increasing the speed of the breath further, a note three times the fundamental vibration will resonate. This is not a D note, but a medium A. The reason for this is that the triple harmonic is 1.5 times the frequency of the middle D note. When the frequency is 1.5 times higher, the pitch is a perfect fifth, so five degrees higher than D is A.
If you increase the speed of your breath, you will get a high D, which is a quadruple vibration. This is twice as high as the middle D note, so it is an octave higher and becomes a high D.
This is where it starts to get difficult, but if you increase the speed of your breath, you will get a high F#. This is a 5-fold vibration. This is 1.25 times higher than the high D which is 4 times higher than the low D. When the frequency is increased by 1.25 times, the major third note is produced.
There are some that are 6 times, but I’ll leave it at that. You can see from this that you can get quite a variety of sounds with just harmonics. But it’s hard to go back and forth between these sounds with just harmonics. (That’s why it’s great for basic practice.) For this reason, the sound hole in the belly of the standing wave is opened for the middle and high notes so that harmonics can be easily produced.
This is an example of the middle D note. When you play the middle D note, you release the index finger of your left hand (the uppermost sound hole), right? This position is half the wavelength of the low D. If you open this hole, sound reflections will be generated here as well, making it easier to create standing waves of double vibration.
The same is true for the harmonics of other pitches, and opening the sound hole in the belly of the standing wave makes it easier to produce harmonics. When it comes to the higher notes in the upper register, there are many fingers that are held down every other note, right? That’s because of the quadruple or quintuple vibration, and there are many standing wave bellies, so we open up various holes.
I’ve written a long and complicated story, but what I wanted to say was…
It’s important to practice Harmonics!
If you can learn to control pitch (overtones) not only with your fingers but also with the speed of your breath, you will be able to move from low notes to high notes with ease.