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Cheever's Thesis Half Right

Before I explain why I think Cheever is only half right, I would like to apologize to him for my derogation in a previous post. My comment about his equation being "sloppy" was not meant to impugn its accuracy in tracing the curve of the ear’s innate distortion, which it evidently does quite well up to H5 (Fig 2-10, p. 47). My comment was meant to highlight the fact that Cheever’s TAD criterion *penalizes* a zero-harmonic (i.e., distortionless) amplifier. Nonetheless, Cheever wants us to accept his criterion as an improved method of amplifier testing.

This seems at first glance a puzzling inconsistency, but when I finally realized what Cheever was up to, his equation began to make sense (but only within the context that Cheever has carved out for it). Cheever's TAD criterion starts out by performing an RMS sum of the "percent deviation per harmonic relative to the aural harmonic level." (p. 45) The deviation for each harmonic is then crunched by his TAD equation and summed. This gives the TAD or "total aural disconsonance".

There is a table on p. 47 showing the % deviation and the overall TAD scores for two different amplifiers. The deviations show both positive and negative deltas. This indicates that any deviation from a perfect fit will be downgraded by Cheever's weighting system.

On p. 43 Cheever states that a distortionless amplifier will be sonically on a par with an amplifier that fits the ear's pattern of self-distortion: "The better sounding amplifier will have either no harmonics or those that are present must strictly conform to the aural harmonic envelope." Now, if you plug the number *zero* (or near zero for calculation purposes) into Cheever's table and run the numbers you will find that the amplifier with zero harmonics has more deviation than the 45 triode amp. Cheever's "ideal" amplifier fulfills a null condition corresponding to his "ideal" weighting system!

Cheever's criterion therefore completely neglects the gray area between zero harmonics and the null condition. I submit that there is a lot of room for discovery here. What if the level of all harmonics is near zero but otherwise varies only slightly from the ideal pattern? Cheever rejects all such results as artificially produced by feedback and irremediably tainted by it (pp. 49-51).

Mfc's thesis is more robust IMO. Mfc thinks that when feedback reduces all high-order products below the level of the open-loop circuit, that particular amplifier will sound better *with* feedback than without (this is Baxandall's thesis also). Cheever rejects this thesis because feedback contributes minute high-order products not present in the open-loop amp (pp. 49-63). While the overall envelope of the spectrum may be lower in amplitude in the feedback amp, the spectrum *extends further out*. Even tiny quantities of high-order products may have an objectionable effect because they can audibly modulate the noise floor. This is Cheever's ultimate argument against feedback (pp. 10, 49-51).

On p. 54 Cheever begins his proof that the application of feedback multiplies the spectrum of harmonics to orders higher than those found in the open-loop amp. Baxandall agrees (having written the proof in the first place), but argues against Cheever when he states: "...this is of no consequence if, when thus increased, they are, say, 120dB below the fundamental." (WW, Dec '78, p. 56)

My own reply to Cheever is that, since triodes produce inherent high-frequency feedback due to Miller effect, we must assume that they too, produce high-order products due to feedback multiplication. But triodes are widely considered to be benign with respect to distortion products. That being the case, there is bound to be a point where the level of high-order products is so far down in the noise floor that they no longer matter--regardless of device.

By relying on masking to hide distortion products, Cheever is pursuing an alternate form of perfection. There is no reason to assume that his “apparent” perfection will be any more desirable than a truly distortionless amplifier. However, since his TAD criterion cannot distinguish a distortionless amplifier, it is clearly invalid as a universal form of amplifier testing protocol.




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