Two simple questions

in effect there were three questions...

The counting of harmonics or the way in which they are formed does not depend on the country one is in.

When we produce a sound (a generic one like C1), we do not produce a sound at a single frequency, but an agglomeration of sounds that resonate together with the fundamental sound (which in this case is C1). These sounds are called concatenated harmonics, which follow a particular sequence.

Starting from c1 (fundamental), we have the first harmonic c2; for the third harmonic, a perfect 5th is added (resulting in G), then a perfect 4th is added (C), and one continues by adding a major 3rd, a minor 3rd, another minor 3rd, other major 2nds, and a minor 2nd .....

Physically, this happens due to the infinite modes of vibration of the string. To each configuration corresponds a certain frequency and therefore a certain sound. As one moves forward with the harmonics, they always have higher frequencies (more and more nodes will be formed).

The explanation is a bit crude, but I didn't quite understand what you are interested in knowing.

DrJellyfish wrote:

1. how do you count harmonics? let me explain: by first harmonic do you mean the fundamental (see Wikipedia)?

2. is the first C on the piano C0 or C1? (it seems to me that it changes depending on the country)

P.S. but where do you post this kind of stuff?

The fundamental sound is the fundamental sound that corresponds to the first harmonic; in the second, there is the octave. If we are talking about harmonics, then we must consider everything within the theory of harmonics, and the first is no exception just because it is the fundamental.

The first C is C1 because C0 is not contemplated; this is because if we call them C1, C0, then going down to B, Bb, and A, how should I call them? B-1, Bb-1, A-1? Within the keyboard... C0 exists in MIDI language where there is even a C-1 due to issues related to hidden functions. For example, by making a C-1 instruction play, one hears a pre-made and sampled chord.

eh re-reading it better I misinterpreted the question. sorry...

the series of natural harmonics does not complete precisely as Sisyphus used to say... that is, those that you add are not major thirds or minor thirds, they are precise frequencies that do not belong to the equal tempered system

Thank you all, the doubts I had were precisely these:

if I have C1 as the fundamental, should I call C2 the first or second harmonic (as per Wikipedia)?

And also from Wikipedia, it turns out that in some countries the first A of the piano is indeed A-1...

DrJellyfish wrote:

Thanks to everyone, the doubts I had were precisely these:

if I have C1 as the fundamental, should I call C2 the first or second harmonic (as per Wikipedia)?

And also from Wikipedia, it turns out that in some countries the first A of the piano is indeed A-1...

True theory dictates that the first harmonic is the fundamental sound; it is a matter of physics; harmonics are generated by the nodes that are created when a string vibrates: no node -> fundamental sound (first harmonic), with one node the string divides in two, so we find the second harmonic (string length = 1/n with n=2, therefore the frequency of the second harmonic is the frequency of the first, i.e., the fundamental, multiplied by n). In common language when speaking, people tend to call the first harmonic what would actually be the second because they use the term fundamental sound, which however in the theory of harmonics is the first. In short, it has become a usage when talking about harmonics, but if one wants to be precise, it is wrong to call the sound generated by 1/n with n=2 the first harmonic. It is precisely the value of n that decides which harmonic it is.

As for C0, I think Wikipedia made a blunder. I don't recall ever seeing any tuning fork that was different from A4 = 440Hz, but I don't know, I don't rule out that in other countries there is A3 = 440Hz. Even all electronic tuners report A4 at 440 Hz. I believe this too might be a usage in other countries, but I wouldn't know. It has happened to me to see A3 = 440 Hz in MIDI uses, as I also wrote to you before.

thallo wrote:

the series of natural harmonics does not complete precisely as Sisyphus used to say... that is, those that you add are not major thirds or minor thirds, they are precise frequencies that do not belong to the equal tempered system

Exactly so much so that some harmonic sounds are sharper or flatter by a certain number of cents compared to the equal tempered system. Among other things, we are always talking about a theoretical framework, because in practice things go very differently due to inharmonicity. Inharmonicity, as we have said many times, is precisely that delta of deviation of the real curve from that of the theoretical harmonics; in fact, if one wants to be precise, the one of the theoretical harmonics (seen in a lin/log graph, i.e., semilogarithmic) would be a straight line, while the real one in the same reference system is a curve. In essence (always at a theoretical level), we can think that the vibrating string forms nodes that follow the geometric series 1/n. The sonic result that we are able to hear is nothing other than the summation of 1/n attenuated by a certain factor that increases step by step, because the further you go with the harmonics, the weaker the harmonics themselves become. If we set aside the discussion on dynamics and reason only on the frequency factor, then the formula loses the attenuation factor and what must be reasoned about are only the elements of the geometric series 1/n for each step n.

This means that we have to look at what happens at the moment when the string reduces its length from 1 to 1/2 - 1/3 - 1/4 - 1/5 -...- 1/n.

Since frequency is inversely proportional to length, it means that if l(n) = 1/n, then the frequency f = f(f) * n.

Let's make an example... If a C1 string is 200 cm long and its frequency for the fundamental (which is equal to the first harmonic!) is 32.70 Hz, then its second harmonic is generated by the node that divides the string into l/2 = 100 cm and the frequency of the section l/2 is f = 32.70 * 2 = 65.4 Hz which is equivalent to C2. Its third harmonic is for l/3 = 66.66 cm so f = 32.70 * 3 = 98.10Hz which is equivalent to G2 + 2 cents (100 cents are a semitone, so 2 cents are 1/50 of a semitone, and if we take the preceding semitone, i.e., F# at 92.50 Hz, and find the difference, we get 5.5Hz which divided by 50 gives exactly the 0.11 Hz excess) since G2 for the tempered scale should be 98 Hz. Proceeding for n=4, n=5, etc. etc., all the theoretical frequencies of the other harmonics are obtained, and if you go further you will see that many deviate even significantly by positive values (sharper) or negative values (flatter) from the frequencies calculated based on the equal tempered system. In the real case, however, the harmonics become increasingly imprecise but also less audible (fortunately) due to the attenuation factor we spoke of earlier, because it is a system where energy is not conserved; it is partially dissipated by internal dissipative elastic forces, and partly the string is attenuated by the air. (Principle of action and reaction: the string compresses the air which responds with an equal and opposite force). Setting aside the attenuation of internal forces, the energy at each step of n must divide, and thus at each division the energy at a certain instant

dt is divided by n, which is why at a generic instant we will "hear" the subsequent harmonics becoming progressively weaker.

LEGEND:

n = step

l(n) = length of the string at step n

f(f) = Frequency of the fundamental which consists of the first harmonic

... wow!

Anyway, I also lean towards A4 at 440.

Regarding pitch, there are fundamentally 2 systems:

- scientific notation (literal.. A B C .. A of the tuning fork: A4)

- franco-belgian system (syllabic.. La Si Do .. A of the tuning fork: La3)

i which have a difference of 1 octave as they start from two different reference points (http://it.wikipedia.org/wiki/Notazione_dell%27altezza).

Therefore, to be precise, if the note is indicated with a letter, the first system should be used; if the syllable is used, the second. Then, you find everything.

Thanks Zedef, I didn't know this thing.