agear, I’m glad you asked about harmonics in the context of music. Before I made my last post above I checked my Musical Notes chart to see how out of tune various harmonics are. Here’s the chart which shows a tempered scale, though that’s what everyone plays so those are the appropriate frequencies to consider:
http://ethanwiner.com/misc-content/notefreq.gif
This analysis is easy if you use A at 110 Hz as a starting point because you can easily do the math in your head:
2nd harmonic: 220 Hz
3rd harmonic: 330 Hz
4th harmonic: 440 Hz
5th harmonic: 550 Hz
6th harmonic: 660 Hz
7th harmonic: 770 Hz
8th harmonic: 880 Hz
9th harmonic: 990 Hz
So looking at my chart it’s clear that the 2nd, 4th, and 8th harmonics are all perfectly in tune, and thus "consonant" (versus dissonant) with an A note because they’re perfect octaves. The 3rd harmonic at 330 Hz is very close to an E, which is in the key of A major and A minor, so we’re good there too!
Next is the 5th harmonic at 550 Hz. That’s a few Hz flat of a C# which is the major note in an A major scale. So that will sound a little off if it’s loud enough to hear. But what if the music is in the key of A minor? Now that 550 Hz is way out of tune because the deciding note for minor is the C natural at 523 Hz. Fortunately, harmonics usually (though not always) decline in level as you go higher, so with normal causes of distortion the 5th harmonic is pretty soft in any competent audio gear.
And now we get to the famous 7th harmonic, or is that infamous? LOL. Here 770 Hz falls between an F# and a G, being out of tune with both. So yeah, it would be a problem if it were loud enough to hear. But again, with competent gear it will be way down by the noise floor and thus inaudible due to both its low level and masking by the rest of the music. The claim that high-order distortion components are somehow magically audible even when they’re incredibly soft is itself incredible. And as we all know, the more outrageous the claim, the more compelling must be the proof. Though at this point I’d settle for even minimal proof, as opposed to "because John Curl said so." :->)
Of course, as I have pointed out literally dozens of times in my various articles and videos, whenever you have harmonic distortion (THD) you also have similar amounts of IM distortion (IMD). And IM distortion is usually out of tune with the music, and so is much more audible and damaging than most forms of THD including the 7th harmonic. Chasing increasing small amounts of high-order THD in the presence of large quantities of IMD is like chasing unicorns.
http://ethanwiner.com/misc-content/notefreq.gif
This analysis is easy if you use A at 110 Hz as a starting point because you can easily do the math in your head:
2nd harmonic: 220 Hz
3rd harmonic: 330 Hz
4th harmonic: 440 Hz
5th harmonic: 550 Hz
6th harmonic: 660 Hz
7th harmonic: 770 Hz
8th harmonic: 880 Hz
9th harmonic: 990 Hz
So looking at my chart it’s clear that the 2nd, 4th, and 8th harmonics are all perfectly in tune, and thus "consonant" (versus dissonant) with an A note because they’re perfect octaves. The 3rd harmonic at 330 Hz is very close to an E, which is in the key of A major and A minor, so we’re good there too!
Next is the 5th harmonic at 550 Hz. That’s a few Hz flat of a C# which is the major note in an A major scale. So that will sound a little off if it’s loud enough to hear. But what if the music is in the key of A minor? Now that 550 Hz is way out of tune because the deciding note for minor is the C natural at 523 Hz. Fortunately, harmonics usually (though not always) decline in level as you go higher, so with normal causes of distortion the 5th harmonic is pretty soft in any competent audio gear.
And now we get to the famous 7th harmonic, or is that infamous? LOL. Here 770 Hz falls between an F# and a G, being out of tune with both. So yeah, it would be a problem if it were loud enough to hear. But again, with competent gear it will be way down by the noise floor and thus inaudible due to both its low level and masking by the rest of the music. The claim that high-order distortion components are somehow magically audible even when they’re incredibly soft is itself incredible. And as we all know, the more outrageous the claim, the more compelling must be the proof. Though at this point I’d settle for even minimal proof, as opposed to "because John Curl said so." :->)
Of course, as I have pointed out literally dozens of times in my various articles and videos, whenever you have harmonic distortion (THD) you also have similar amounts of IM distortion (IMD). And IM distortion is usually out of tune with the music, and so is much more audible and damaging than most forms of THD including the 7th harmonic. Chasing increasing small amounts of high-order THD in the presence of large quantities of IMD is like chasing unicorns.