The Harmonic series, for the clarinet

Mr. Friedland, I am a novice clarinet player.  You have made reference to “harmonic fingerings” for the clarinet.  Could you explain what harmonic fingerings are and when they are used?  A couple of examples would b great!  Thank you.
In order to understand what a harmonic fingering is, you must first understand that the clarinet was and is still a cylindrical pipe which has a series of fundamental pitches which overblow, which for your purposes mean that when you open a certain key, you get notes which are twelve notes above the initial note, and are called unto themselves harmonic fingerings. For instance, when you pay the lowest note on the clarinet and then open the “so-called” reigster key the same fingering goes up twelve notes(rather than an octave which are the overlown notes of a saxophone or a flute.
The primary(or first, or lowest) notes of the clarinet go from low E to throat Bb. Each of these pitches
has a particular number of vibrations per second, or frequency. By applying pressure
to the reed, we can make it vibrate a various multiples of that frequency. These other,higher frequencies are called harmonics. When the fundamental frequency is doubled,the pitch rises one octave to its second harmonic. This is what happens when you press the octave key on a saxophone, oboe or bassoon. The clarinet’s physical structure causes it not to sound octaves or other even-numbered harmonics, so its pitch rises
in much longer, less even leaps.Because the clarinet does not overblow octaves and other even-numbered harmonics,
its high note fingerings can seem confusing at first. Below are the fundamental notes from which the highest fingerings are derived. Practice moving between the different registersto help develop your embouchure & fingers.
Chalemeau register – This is the bottom register, where the instrument’s natural sound is
heard. This pitch is called the fundamental. This register is named for the folk instrument
that later became the clarinet.
Clarion register – Press your left thumb on the register key and go up a 12th to the notes
with the clear sound that gave the clarinet its name. This is the third harmonic,or three times the frequency of the fundamental pitch.
Altissimo register – Vent the “E” tone hole by sliding or removing your left index finger.
For pitches “D” and above, put your right pinkie on the pinkie Eb key. This is the fifth
harmonic or five times the fundamental frequency. To move up from C# to G, remove
your left ring finger from the “C” tone hole. This is the seventh harmonic, or seven timesthe fundamental frequency.
I hope this will help a little. Certainly when you improve and develop your embouchure, you will be able to first understand the clarinet and that it actually overblows as do all instruments.
Don’t be confused, as it will become clearer and clearer.
Best wishes, Sherman

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