Of Harmonics, Fundamentals, Tubes, Etc.

[kelticwizard]

Hi, I just want to get a couple of things straight here. I've seen some things which seems to indicate I might not be correct on some things I have come to assume.

A) Take a 440 Hz tone. This is Middle A. (Long ago it used to be different, but now it's agreed on).

B) 880 Hz is the first overtone of 440 Hz. It is also the second harmonic. Is this true? I have seen some reference that 880 Hz is the first harmonic, but I do not think this is the case. I am no expert on this, and I am open to correction.

C) Since even order harmonics are actually overtones, which most natural musical instruments produce in abundance, they are considered more "musical" and easier on the ear. Odd order harmonics, such as 2640 Hz, 4400 Hz, and 6160 Hz sound comparatively harsh when mixed with 880 Hz. I realized that odd order harmonics are not entirely absent from natural instruments, but that even order harmonics, (2 times the fundamental, 4 times the fundamental, etc.) predominate.

D) Tubes might produce more distortion than transistors, but the distortion they produce tends to be even order distorion-that is, for Middle A, tubes will tend to produce distortion tones of 880 Hz, 1760 Hz, 3520 Hz, etc.

Am I correct in these ideas?

[SY]

B) 880 Hz is indeed the second harmonic, by definition. It may or may not be the first overtone, depending on the nature of the nonlinearity.

C) Lots of musical instruments (most, in fact) produce high levels of odd order harmonics, often predominating. Hook up a mike to a scope, then play a note on a clarinet or sax, for example. Olson's "Music, Physics, and Engineering" would be an excellent book to consult for a range of examples.

D) It depends on the implementation of the device. And it's sort of misleading as a measure, since one amp might have a predominant second and fourth harmonic (say) at a level of 5%, with third order down at (say) 0.5% and you'd say, "Ah, the odd order stuff is not predominant!" Another amp might have 0.001% second and fourth, but 0.003% third and fifth, so you'd say, "The odd order stuff is predominant!" But the second amp is cleaner by any critereon you'd care to name.

[kelticwizard]

Okay, let's try another question. Let's take the A note two octaves below Middle A. That will be 110 Hz.

The second harmonic will be 220 Hz. The sixth harmonic will be 660 Hz, correct?

My question is: is the sixth harmonic an even order harmonic? Because 660 Hz is the second harmonic of 330 Hz, which is an odd order harmonic of the fundamental, 110 Hz. It seems to me that 660 Hz would be more closely related to an odd order harmonic than the fundamental.

Is 660 Hz an even order or an odd order harmonic?

[SY]

Even order. Don't confuse odd-even with powers-of-two.