So, what would be the cause of the ever present _3rd order_ harmonic distortion?

Well, you can't get rid of it, but you can lower it below the ear's ability to hear it. That's all that matters!

Woofers and subwoofers driven hard tend to produce significant amounts of 3rd-order harmonic distortion (I measured 18% from one 8" woofer). Fortunately, our ears are quite insensitive to harmonic distortion at these very low frequencies.

Transistor amps got to "inaudible distortion" long, long ago. If THD is under 0.1%, nobody can hear it. Just about any solid-state amplifier will soundly beat that spec these days, usually by a couple orders of magnitude.

Tubes and transformers are great for guitars, where you want tons of distortion. But, IMO, these have no place whatsoever in Hi-Fi or any kind of accurate audio reproduction.

Like steam engines, tubes served humanity well some seventy or eighty years ago. Like steam engines, there is no good reason to continue to use tubes today - except maybe in guitar amps, where it is the specific failings of tubes and transistors and speakers that we actually want to hear.

-Gnobuddy
 
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Well-designed tube amplifiers can also have distortion levels well below 0.1 %.

Regarding the original question: all amplifying devices haved curved input-output relations, as have loudspeakers, microphones, tapes and cartridges.
 
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Well-designed tube amplifiers can also have distortion levels well below 0.1 %.
Quite so. But once THD is lowered that far, all audible "tubey" distortion is gone (remaining distortion is far below the threshold of audibility). A decent solid-state amplifier would produce equally inaudible distortion, while at the same time providing better speaker damping, costing less, generating less heat, lasting longer, weighing less, and taking up less room.

So what's the point of a 0.1% THD tube amplifier? Why spend far more for an amplifier that sounds exactly like a solid-state amplifier, except for having less ability to handle strong bass signals and providing worse speaker damping?

I just can't make any sense out of that combination. :scratch:

Tubes for use with guitars are an entirely different kettle of fish. The goal there is to deliberately create several percent THD, maybe several tens of percent, maybe even approaching 100% (sine distorted into a square, doubling the RMS value; equal power in the fundamental and the summed harmonics). Not accurate reproduction of a Hi-Fi signal, but the opposite: extremely inaccurate signal processing, which just happens to make an otherwise bland e-guitar sound good.

-Gnobuddy
 
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A full wave rectifier produces all even order harmonics but no fundamental.
For exactly that reason, years ago I built a precision full-wave rectifier using a couple of op-amps, and fed e-guitar into it. I thought it might make interesting-sounding distortion, and/or act as an octave doubler.

I remember that I was disappointed with the results. I don't remember exactly why any more - it's been a lot of years.

I have a faint memory that it sounded fairly harsh, and that might have been the reason. I don't recall if I experimented with a following low-pass filter to roll off some of the harsher upper harmonics.

-Gnobuddy
 
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A doubler that doesn’t sound so harsh requires a Gilbert cell multiplier. Unfortunately, the dynamic range isn’t wonderful - it’s only “linear” over a very small signal. Easy to over drive. So much for a guitar pickup that can put out over a volt at the initial attack.
 
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So what's the point of a 0.1% THD tube amplifier? Why spend far more for an amplifier that sounds exactly like a solid-state amplifier, except for having less ability to handle strong bass signals and providing worse speaker damping?

I just can't make any sense out of that combination. :scratch:
Why? Because you can. As in “Damn, this thing sounds good - and it uses tubes!” The 200 watters I built sound like Crown Macrotechs. The bass handling is mostly a function of the power supply. 25 dB of feedback and paralleled tubes get Z out in the fraction of an ohm range. On the same order as the speaker wire.

When I built an electric bass amp, I let the power stage be a bit less “clean”, but still employed over 20 dB of feedback. It doesn’t clip quite as nicely, and the drive to the finals isn’t quite as well balanced. The front end however, uses a current starved 12SL7 to give the soft limiting when the input is overdriven.
 
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I built a precision full-wave rectifier using a couple of op-amps, and fed e-guitar into it.
Sounds like something I would do, back in the day. I once grafted a second order state-space filter onto a full wave rectifier, where the 1st order filter in the ordinary text book circuit is. Using that signal to drive the center frequency of another bandpass filter, it gave the classic Jerry Garcia "envelope filter" sound, only with "bounce", depending on the Q and f0 of that filter following the full wave.

With a single strike at the strings, you could get it to go wow-wow-wow-wow...

Unfortunately, the dynamic range isn’t wonderful - it’s only “linear” over a very small signal.
I've always admired how Nady used compression in their wireless transmitter, then used expansion at the receiver. Kinda like Dolby on tape, but over the transmission "medium".

One would think this technique, wrapped around various circuits such as this Gilbert, would improve things a lot. At least regarding having a constant distortion profile, against input level.

Makes me wonder what a tube guitar amp would sound like with the first stage as a compressor and the dynamics put back via manipulating the push-pull power tubes operating point. I'm sure the patent for that has been long granted...control signals derived from some circuit's analysis of the amp's input, then used to effect anything else about the amp you'd like.