Started by
Giove
Member
Administrator
Yes, the phenomenon you are talking about is called disharmony and it is normally inversely proportional to the length of the strings and directly proportional to their gauge.
Member
Try reading here:
Inside the octave ...
... dialogue between A and B
A:
You assure me that it is as I say: mathematics and physics are exact sciences, not opinions.
B:
If you say so……
A:
I am saying it, but this "gadget" says it too. See? It is a high-precision digital frequency meter, also equipped with a powerful filter that can let through a wide band of even less than 1 Hz, eliminating all sounds and noises above and below the band you have chosen. Stay here, my dear, with this there is no joking, and I will prove to you that all your problems are nonsense. You saw for yourself that we tuned the A5 exactly to 440Hz and now the A4 shows exactly 220 Hz. Now you can play the two notes and you will hear a perfect unison.
B:
Well!……. I hear a certain hum, as if about twenty people were speaking in a very low voice inside the piano, and then I distinctly hear something like a beat every two seconds, don't you?
A:
How come? That's not possible! The instrument is precise! It must be that the piano is broken.
B:
The instrument is precise and the piano is excellent; it is you who has not considered one thing: the inharmonicity of the strings. You see: the ear does not perceive the unison by comparing the fundamental sound of the two notes (440Hz and 220Hz), but the fundamental sound of the A5 (440Hz) with the second partial of the A4.
A:
But the second partial of the A4 is 440Hz, so it's the same.
B:
No, since we tuned the A4 to 220 Hz, the second partial will be 440 Hz plus a tiny bit; in our case about 440.5Hz since we perceive 1 beat every 2 seconds, and 440.5 does not match 440.
A:
So what?
B:
Then we must lower the A4, so that its second partial vibrates at exactly the same frequency as the A5, which is 440 Hz.
A:
And then what frequency should I look for for the fundamental of the A4?
B:
I can't tell you that off the top of my head; it would require a mathematical calculation that is very complicated for me. I could find the solution for you by tuning by ear, but for you, who are so scientific, that wouldn't be enough.
However, we can do one thing: calibrate the frequency meter for a band ranging from 439 to 441 Hz, in order to select the second harmonic of the A4; then we lower the A4 slightly, until the frequency meter shows exactly 440 Hz, just like those of the A5.
A:
Bravo, you found the solution, now we are sure to obtain the unison
………………………………….
B:
I am sorry to tell you, but it seems to me that the fluctuation has actually increased; in fact, I even perceive more than one beat per second….. and the people from before continue to chatter inside the piano.
A:
But now there is no doubt: it's the piano that is broken.
B:
No, the piano is still good, it is you who has not taken one thing into account: inharmonicity.
A:
Still with this inharmonicity? What is it, the alibi for your incompetence as tuners?
B:
Perhaps that too, but mainly something that you like so much: something scientific. You see: strings, when they vibrate, do not only emit a first fundamental sound and a second partial, but also a third partial, and a fourth, a fifth, and so on. These partials, the higher they are, the more they drift in frequency (go read the article by G: Bettin). We have matched the second partial of the A4 with the fundamental sound of the A5, but it's not enough: now we must match the fourth partial of the A4 with the second of the A5, and again the sixth with the third, the eighth with the fourth, and so on.
Furthermore, one must consider that the third partial of the A4 and the third of the A5 give us respectively E5 and E6; while the fifth partial of A4 and the fifth of A5 give us respectively C*6 and C*7; and then again, with the sixth partial, E6 and E7, and so on. These partials progressively move away from each other in frequency, but, fortunately, they are progressively less audible.
A:
So what?
B:
Then we must lower the A4 a little bit more, to compensate for all these inconsistencies so as to merge the set of beats and obtain something like a sensation of swelling when playing the two notes harmonically, while the hum will be absorbed by the thirds (A-C*) and fifths (A-E). And here the frequency meter, no matter how sophisticated, no longer helps you: you have to use your ear.
A:
Oh, come off it!………………..
Administrator
Very cute!
