For your consideration Mr. Macura, Steve Bench made measurement on mu of several triodes vs output voltage posted by Thomas Mayer at post #16 of favourite midrange,treble tubes thread. A piece of information I find interesting that may or may not affect your setup. Have not found original article for more detail in test setup.
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Didn't say notes are harmonic said overtones of each note are harmonic and so THD just adds to these harmonics and that's why its hard to hear. It changes the timbre but so does hitting a string harder so it's hard to tell if it's your amp or the instrument.
Who said exact.
"The effects above are difficult measure with experimentally with the required precision: the effects are only a few cents, which is not much larger than the precision of ears or tuning meters when applied to a pluck string. Further, it is difficult to adjust machine heads to achieve a precision better than a couple of cents."
But probably enough to mask fractional THD amounts. And close enough to make certain 2% THD sound "good".
Sorry should have posted this first. The above is about the small detuning of these harmonics of one note.
"The string on a musical instrument is (almost) fixed at both ends, so any vibration of the string must have nodes at each end. Now that limits the possible vibrations. For instance the string with length L could have a standing wave with wavelength twice as long as the string (wavelength λ = 2L) as shown in the first sketch in the next series. This gives a node at either end and an antinode in the middle.
This is one of the modes of vibration of the string ("mode of vibration" just means style or way of vibrating). What other modes are allowed on a string fixed at both ends? Several standing waves are shown in the next sketch.
A sketch of the first four modes of vibration of an idealised* stretched string with a fixed length. The vertical axis has been exaggerated.
Let's work out the relationships among the frequencies of these modes. For a wave, the frequency is the ratio of the speed of the wave to the length of the wave: f = v/λ. Compared to the string length L, you can see that these waves have lengths 2L, L, 2L/3, L/2. We could write this as 2L/n, where n is the number of the harmonic.
The fundamental or first mode has frequency f1 = v/λ1 = v/2L,
The second harmonic has frequency f2 = v/λ2 = 2v/2L = 2f1
The third harmonic has frequency f3 = v/λ3 = 3v/2L = 3f1,
The fourth harmonic has frequency f4 = v/λ4 = 4v/2L = 4f1, and, to generalise,
The nth harmonic has frequency fn = v/λn = nv/2L = nfs "
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I'm interested myself in why second harmonic distortion in particular is "warm and musical". This is why I'm interested in the scale we normally listen to, music is not just notes
I think it would be an interesting experiment if some music played using a just temperament were recorded and then 2nd harmonic added and see how that affected the sound compared to equal temperament music
I think it would be an interesting experiment if some music played using a just temperament were recorded and then 2nd harmonic added and see how that affected the sound compared to equal temperament music
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Kudos Pavel for going beyond the call of duty! But you know your banging your head on the wall as Dan will never use ABx because it will prove his hearing is human.
I just threw Dans comments in the same pile as the rest of his I can hear an ant fart in the back of the room pile.
Continue the good fight, even if it enlightens a couple of people on there hearing abilities its probably worth it.
I'm interested myself in why second harmonic distortion in particular is "warm and musical". This is why I'm interested in the scale we normally listen to, music is not just notes
I think it would be an interesting experiment if some music played using a just temperament were recorded and then 2nd harmonic added and see how that affected the sound compared to equal temperament music
Yes would be interesting. Most instruments have 2nd harmonics, while many dont have 3rd so 3rds might stick out more. Some more info ive found. The harmonic detuning increases with higher harmonics so THD might not be masked as much? " on horns the 7th harmonic is particularly trouble some".
PC -> ODAC -> AV Marantz SR4500 -> KEF Q100, all tweaked
Win 10 Pro 1709 64 bits, very optimized to play multimedia.
J River MC 64 bits, Kernel Streaming
The best sound is Apricot. More natural, credible but not perfect. The double bass rumbles too much. Voice is credible, sweet.
The original must be Avocato. More thin sound. Double bass with less rumble. Voice more clear but less credible to me. Lifeless.
Apricot with with lower level harmonics would sound better.
Win 10 Pro 1709 64 bits, very optimized to play multimedia.
J River MC 64 bits, Kernel Streaming
The best sound is Apricot. More natural, credible but not perfect. The double bass rumbles too much. Voice is credible, sweet.
The original must be Avocato. More thin sound. Double bass with less rumble. Voice more clear but less credible to me. Lifeless.
Apricot with with lower level harmonics would sound better.
Multiple instruments playing the same notes gives body, depth, warmth (whatever you want to call it) to sound, largely due to the very small discrepancies in their tuning, I wonder whether a little 2nd harmonic has a similar effect to our perception due to the non-harmonic scale? It's just a thought, also since our pitch perception is also based to a degree on the harmonic overtones of the played notes.
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