[emphasis added] I agree with this bit, please consider there is always an exponent to exponential decay (hence the term) and cubic works much better than quadratic. As best I can make out, Cheever, Geddes, Hiraga and so on did not have access to amps that expressed the cubic exponent as they do not seem to mention it at all. Boyk and Sussmann are correct but the conclusion "... not desirable" (wherever that came from), is incorrect. The reason is by generating only odd orders, you are working with a cubic function and so you have two advantages:
1) distortion falls off at a faster rate as the order of the harmonic is increased
2) the 3rd easily masks those higher orders- better than seen in an SET.
Now if you do some measurements you find something interesting: the odd orders in a circuit like an SET have higher amplitude than you see in the circuit is fully differential as I've pointed out before. Since in both cases, the lower orders are masking the higher orders, the higher orders are inaudible. So which is better at that point, the one with higher distortion or the one lower?? And by lower I mean well over an order of magnitude. Quite often its over two orders of magnitude.
The bit about the tape machines- the third harmonic is there regardless of the head driver, most of which are single-ended. Its a function of the tape head magnetics influenced by the bias signal (used to help keep the head linear). Feedback will create higher orders IF the feedback node is non-linear. If you look at most amps made within the last 80 years, they almost all have this problem, despite its actually being easily avoided. At any rate, all of my studio machines have single-ended record head drivers.The Ampex 351 tape electronics are entirely single-ended on the record side with no feedback, but the 3rd harmonic is still the dominant distortion product.
I agree with your assessment of recording media. The quality of the recording really has little to do with the media and everything to do with the skill of the recording engineer. Regardless, I suspect many of the recordings we both hold dear were made with analog tape.
"The reason is by generating only odd orders, you are working with a cubic function and so you have two advantages:'"
This is completely BS, Ralph and you know it. It is WELL known that odd orders are more offensive sounding (other than third), with 7th and above being particularly nasty sounding. Also, having only odd orders puts the spacing greater between harmonic peaks and there is no masking whatsoever taking place. It is well known as well that the closer to the fundamental the greater the masking (i.e. 2nd is by far the best at masking subsequent harmonics). You might be able to sell that to your uneducated customers but not to me. NO ONE considers odd order only to be a good sonic pattern (at least those who have taken the time to think about it). Even very low levels of distortion will be audible...and still have a high Gm and Cheever metric.
From Keith Howard in Stereophile:
" Patterns 3 and 4 comprise, respectively, the odd- and even-order harmonics only "
"Pattern 3 was unpleasant, adding an edge to the sound that would surely become fatiguing over extended listening. Pattern 4 wasn't as bad, but there was still something unnatural about it. "
Pattern 3, odd only harmonics was the worst sounding of the patterns Keith overlaid on his recordings. Pattern 4, even only, was not as harsh (thus confirming the even harmonics are not as detrimental as the odd ones) but still not right.
"Pattern 1 represents an ideal Hiraga pattern of declining harmonic amplitudes, albeit at high level. Pattern 2 mimics Pattern 1 but with all the harmonics (down to the self-imposed –100dB limit) at 20dB lower amplitude."
"Pattern 1 added a distinct "dirtiness" to the sound that was not unpleasant but did change the instrumental timbre and diminish the sound's sense of fidelity—there was something clouding the sound. Pattern 2 was much better, with the closest sound to the undistorted reference"
Pattern 1 would be a SET with either quite high distortion or being pushed close to clipping (of course as Cheever demonstrated, the SPL level could be high enough to offset the audibility) and Pattern 2, the closest to the reference (an unadulterated recording) is a better SET or one kept well within it's limits.
Note also what Keith has to say about the Gedlee metric Gm: "GedLee metric values between 1 and 3 are supposed to correspond with subjective ratings of "barely perceptible but not annoying," with values of less than 1 indicating that the distortion is imperceptible. On this basis, none of these distortion patterns should be audible, despite their high harmonic amplitudes, but note that Pattern 3 has easily the highest Gm value, despite having a significantly lower THD than Pattern 1."
And wouldn't you know it, Pattern 3, odd orders only, was easily the worst Gm...Geddes had a quite good correlation between sound quality responses and his metric in the limited data set he generated for his papers.
Now, obviously, these levels of odd order are much higher than what your amps are making but it doesn't change the fact that these are OFFENSIVE sounding patterns and yours probably don't fall off exponentially...very few amps can make that claim in the real world. This means you still have odd harmonics, without their partnering higher even one before, that are audible and demonstrably poor sounding.
"Now if you do some measurements you find something interesting: the odd orders in a circuit like an SET have higher amplitude than you see in the circuit is fully differential as I've pointed out before. "
This is completely irrelevant...it doesn't matter if the SET has higher odd orders as long as there are even higher even orders coming before it. That is what both Geddes and Cheever's metrics conclude as well. Even D.E.L Shorter's inadequate metric tells a similar story. It is the relationship that matters and the pattern. What matters is that with push/pull and differential circuits you cancel out the even harmonics and this has sonically detrimental consequences. What also matters is that feedback creates higher order harmonics as it reduces the masking of beneficial, basically sonically benign, low order harmonics. What Boyk and Sussmann confirmed is that a signal modulated noise floor, as posited by Norman Crowhearst, shows up in simulation and so even if you add tons of feedback and push all of the harmonics down into the "noise"...it is not really noise and does damage to our perception still.
No one is debating that too much distortion (even 2nd order) will damage sound quality. Good SETs, run in their limits, will produce more or less the right pattern at levels, as Keith Howard put it "closest sound to the undistorted reference".