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My first post:

I have found an interesting harmonica here. So, I tried to know more about harmonica.

And, I have read this article , in which the author doesn't mention the physical calculation, which makes a harmonica to be played with a full-octave.

Now, I want to know about the physical calculation in diatonic harmonica. So, my question is: Is there any physical calculation which allow a harmonica can make some different sounds?.


I care about a full-octave only; such as, 8 notes: C6 - D6 - E6 - F6 - G6 - A6 - B6 - B7.


My second post:

After a short time of waiting, there is an answer for my question. In this answer, there is a function: f=(nv)/(2L). And, he said: "The frequency that is produced in any open tube depends on length".

I don't know the length what is: length of reed, or length of tube; or, both of them. Could you explain it for me, please?

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The basic model for the harmonica is an open tube as a resonator and an oscillating free reed as a driving mechanism.

The free reed could be modeled in the first (and pretty good) approximation as an oscillating cantilever beam. Which opens and closes the tube - hence the pressure and velocity variations. The frequency (or frequencies - there would be more then one peak in frequency domain) of such an opening mechanism is given by the cantilever paratemetrs such as stiffnes, mass, surface, length etc. (see the link) and intensity of the excitation mechanism: the velocity of blown air.

These frequencies are provided to the resonant open tube in which some of them are attenuated and some amplified based on tube parameters (where the length and cross section area are the most decisive parameters).

By a combination of many free reeds and resonant tubes the diatonic harmonica is given. More to that: these instruments usually posses a posibility to chose between two resonant tubes: one for the inspiration and one for the exhalation.

Note: In fact, almost all of that is valid for all reed pipsef with free reeds (e.g. for some parts of organ as well), i.e. for all the Hornbostel-Sachs class 422.3

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Each tube in the harmonica is an open tube. The frequency that is produced in any open tube depends on length, speed of sound and n, using $f=(nv)/(2L)$. The base note is where n= 1, which is the usual note you hear. If you blow a bit harder, you can hear the first harmonic, where n = 2. Here the frequency is double what was heard earlier (when n=1), and sounds an octave higher. There are more, higher harmonics that can be produced, so the answer is, yes, the physics calculations do predict higher sounds.

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