question about second order harmonics

[esacrewol]

I built my crack about a week ago now and I'm loving the sound (I'm coming from a schiit magni 2, this is my first experience with tubes) so I don't plan to install my speedball any time soon. Maybe towards the end of next year, just depends.  I was reading about second order harmonics and to my understanding they are only really present if a tube amp is being driven into overload. So, if that is the case, it would make sense that the crack would produce second order harmonics if i turn down the input signal enough to be able to max out the crack comfortably. Am i correct in that assumption? I mean, i'm a/b'ing it and I believe i'm hearing something, but it could very easily be placebo since i'm expecting something out of it. What do you guys think? As I'm typing this out, I now realize that perhaps overload doesn't depend on the pot position but rather the output signal strength. But I have no idea, so i'm open to hearing your thoughts!

[Paul Joppa]

Your second thought is correct - overload is at maximum power output. A single-ended tube amp has around 5%-20% at clipping, depending on the linearity of the tube and the operating point.

Below clipping, to a high degree of approximation, distortion falls linearly with output level - if it's 10% at 20volts output, it's 5% at 10v, 1% at 2v, etc. So a high sensitivity headphone will receive less distortion than one with lower sensitivity on the same amp (assuming both phones are the same impedance).

Higher order distortions fall more rapidly; third order falling as voltage squared, 4th order falling as voltage cubed, etc.

[esacrewol]

Your second thought is correct - overload is at maximum power output. A single-ended tube amp has around 5%-20% at clipping, depending on the linearity of the tube and the operating point.

Below clipping, to a high degree of approximation, distortion falls linearly with output level - if it's 10% at 20volts output, it's 5% at 10v, 1% at 2v, etc. So a high sensitivity headphone will receive less distortion than one with lower sensitivity on the same amp (assuming both phones are the same impedance).

Higher order distortions fall more rapidly; third order falling as voltage squared, 4th order falling as voltage cubed, etc.

okay that makes sense. so right now im using the hd800s which apparently has a sensitivity of roughly 103dB, which i suppose is a higher sensitivity. if i used a pair of headphones with say an 85-90dB sensitivity (with same high impedance), do you think the difference in harmonics would be noticeable at similar listening levels? or is not really worth pondering?

[Paul Joppa]

I have no useful facts about the perception of distortion, so I can't make a technical answer.

But I do have opinions and guesses, educated or not(!). I think a small amount of second harmonic distortion makes reproduced music more accessible and engaging. Too much is syrupy and muddy. The optimum amount seems to vary with the genre of music, the loudness you listen at, and your own hearing. Personally, I find that wide dynamics and spectral density (big band, classical symphonic) wants only the slightest touch, while more intimate music (jazz trios, string quartets) can handle more, and it brings the band into your living room.

The perception is largely unconscious, at least in my experience. I don't "hear" it, but if I notice my toes tapping, or I'm distracted from the book I'm reading by some bit of musical magic, that's a clue.

I suspect this is one of the reasons the HD-650 works so well with Crack - it's close to optimum for most people. But as I said, I have no basis in science for this guess.

[Paul Birkeland]

do you think the difference in harmonics would be noticeable at similar listening levels? or is not really worth pondering?

I would suspect that the overall difference in sound between the two headphones would swamp out what you're otherwise likely to hear. 

[esacrewol]

Thanks for the responses, Pauls. I guess I am hearing second order harmonics but I just can't consciously identify them. Something about the Crack is making me want to listen to music much much more than I do normally. I guess that is all thanks to those harmonics haha.

And yeah, Paul you're most definitely correct that the differences in the headphones would swamp out the differences in harmonics. I guess I was thinking in more of a "Same exact headphone in every way except with lower sensitivity" which is pretty pointless because that most likely doesn't exist.

Thanks again, Paul and Paul!

[Paul Birkeland]

When you add the Speedball, the total harmonic distortion will drop at a given listening level, so you can at least make that comparison.