Can you please tell us quantitatively what is an optimal spectra of distortions according to your views?
it is the pattern that follows the ear/brains own self-generated distortion pattern. As Cheever puts it:
"The ears’ self generated harmonics mask external harmonic distortion that has the
same character. The ears’ harmonic distortion is fully studied and falls off at a rate of
approximately 10^n. I propose that external harmonics strictly adhering to this
envelope are fully “undistorted” by our ear-brain system and are thus
indistinguishable from pure tones."
So, this is in effect an exponential decay from n = 2 to n = infinity. Or in other words monotonic.
"The increase of aural harmonics follow sound pressure level increases non-linearly
and at different rates per harmonic. Therefore absolute system SPL must be
considered."
"Intermodulation distortion is masked by this same mechanism. Amplifier topologies
exist that are free from dynamic intermodulation affects, and whose residual
intermodulation is linearly related to harmonic distortions."
"The character of the noise envelope within a sound transient is important to the brains
recognition system. Noise floor pollution via low level high order I.M. products are to
be avoided."
"Olson from RCA/Victor R&D Labs continued testing the first
8 harmonics and over a broad range of sound pressure levels, reproduced here in Fig. 2-2"
"This has been redrawn for clarity in Fig 2-3. Notice that the ear creates significant levels
of the second harmonic, nearly 10% of the fundamental for sound pressure levels (SPL’s)
of 90dBA and above. Also the slope of the harmonic reduction versus input reduction
varies with the harmonic power, beginning at approximately 1:10 for the 3rd harmonic to
1:1 for the 9th harmonic."
"A reduced SPL range is shown. Even for the moderate S.P.L. of 80dBA, the 2nd
harmonic is at the equivalent of 65dBA or normal voice level, and the 3rd at 45dB. This is
still ~40dB above the mid-band threshold of hearing, yet one does not hear the
harmonics! Only a single pure tone is heard. The ear/brain appears to be able to
completely suppress the sound of a range of harmonics if they conform to this specific
pattern."
"This pattern is the aural harmonic envelope. It follows that this same mechanism
will mask harmonics arising in the sound reproduction chain if they follow this pattern. If
the harmonics do not follow this pattern, the ear brain indeed detects these as new tones.
Therefore, for all but extreme frequencies and sound pressure levels, any electronics that
generate this harmonically consonant envelope will be transparent."
"It is a mathematical expression relating the percentage of the fundamental S.P.L.
of the ears self distortion, per harmonic, relative to the sound field S.P.L.
%Fn = (1.35 *10^(dBA/22))/n^11 = Eq. 2-1 Individual Aural Harmonics
Where: %Fn= Aural Harmonic Amplitude in % of Fundamental for the nth
harmonic.
dBA = Decibels “A” weighted Sound Pressure Level resultant from the
Fundamental.
n = The harmonic number. f = nFf where f is frequency,
Ff= fundamental frequency
"The power of the exponentiation may seem high but the fit is excellent, shown
following in Fig. 2-7."
"In calculating the magnitude of an amplifiers deviation for the aural harmonic envelope I
propose that each harmonics deviation be on a relative basis (% of reading, referenced to
the level of the nth aural harmonic derived from Eq. 2-1), rather than on the absolute
percentage referenced to the fundamentals level"
Based on all my reading, this approach makes the most overall sense as it takes into account what is known about ear/brain self-generated harmonics, masking and SPL.
This two are also going in a similar direction.
http://www.gedlee.com/Papers/Distortion_AES_I.pdf
http://www.gedlee.com/Papers/Distortion_AES_II.pdf
Based on looking at tons of measurements and also theory, one can see that push/pull can never generate this kind of distortion pattern, unless the designer deliberately finds a way to inject even order distortion into the circuit to counteract the even order cancellation that is inherent in the push/pull concept. Only single ended does this pattern naturally. Whether you agree that the theory about the masking and aural harmonics by Cheever is valid or not is another question. However, Geddes found similar things. What cannot be disputed is that the ear/brain does in fact make a monotonic pattern of its own with every sound that makes it vibrate and the brain dismisses this or at least that is what is defined as "pure". Masking is well known phenonmenon. Cheever is claiming that the signal "hides" in the self-generated pattern if the device mimics the pattern. The tighter it mimics the more pure it will sound.