Another Golden Ear Myth Bites the Dust

Another Golden Ear Myth relates to so-called euphonic distortion;

One expression of the idea that I found on the web is:

"Low Total Harmonic Distortion measurements are reassuring to a degree, but most people find odd harmonic artifacts much more objectionable than even harmonic ones (tube amplifier lovers seem to actually like a bit of even harmonic intrusion to give a euphoric rather than clinical insight into their recordings). I'm just saying that of two pieces of kit with similar THD measurements, the one with the higher odd harmonic components is likely to sound less musical unless the designer has managed to get the overall THD to a spectacularly low level."

In fact all Harmonic Distortion of any order is a consequence of nonlinear amplitude response or curvature of the transfer function. Any transfer function that is curved will produce IM distortion if passing any signal that is composed of more than one tone, which is of critical importance for high fidelity since all natural music is composed of multiple concurrent tones. IM distortion is generally aharmonic, that is anything but harmonically related to the signal being amplified, and generally perceived by even those with the foggiest notion of high fidelity to be highly adverse to listening pleasure.

To summarize, any audio component that has any amount of harmonic distortion of high or low orders produces as much if not more IM distortion which sounds ugly. So the statement "most people find odd harmonic artifacts much more objectionable than even harmonic ones " is totally false because in fact they find all harmonic artifacts to be objectionable because those artifacts can't help but also generate IM.

Most tubed amplifiers that have acceptable sound are being operated at such low power levels that they really don't have much nonlinear distortion at all. The most commonly audible characteristics of tubed amplifiers trace back to their low damping factor.

The only way to have the HD profile be a greater factor than the IM is to listen to pure test tones. As soon as you start listening to music, the IM will overwhelm the harmonic distortion.

Let's say that you have an amp that has only a second order nonlinearity that is as large as possible.

If you put in 1KHz, you will get out a 2 KHz tone half the amplitude of the input wave, plus a DC signal that is also half the amplitude of the input, but since your speakers and ears dont' respond to DC, it will be inaudible.

If you put in a 1 KHz tone and a 1.5 KHz tone that are together the same amplitude, you will make each half the maximum amplitude so they don't clip when you sum them.

Due to the same nonlinearity you will get a 500 Hz tone, a 2 KHz tone, a 2500 Hz. tone and a 3 KHz tone. Right off you get about four times as many audible distortion-related spurious responses. The 500 and 2500 Hz tones are about half the size of each input wave, and the 2 KHz and 3 KHz tones are about half as large as them. So, the spurious responses from the IM are all audible and when added together have a about double the percentage as the one audible tone from the harmonic distortion.

Thus the IM will overwhelm the harmonic distortion. Furthermore the harmonic distortion is likely to be masked by the natural harmonic structure of musical sounds, while the IM distortion as you can see, is about half tones that are not harmonically related to the source, and won't have anything to mask them in the music. They will blare in your ear!

In the days when tubes were all we had, we put our most productive efforts into producing tubed amps with low nonlinear distortion and high damping factors. This tended to make tubed amplifiers more complex, heavier, and more expensive but in the case of such legendary brands as McIntosh good audible performance was obtained that way.

(1) THD and IM are not forms of distortion. The forms of distortion are linear and nonlinear distortion. Not seeing IM or THD on that short list, they must be absent for a reason and the reason is that they are irrelevant to a discussion of forms of distortion. I say so, Geddes says so, Linkwitz says so, a ton of other recognized authorities you may not have heard of say so, by gosh it could even be true! ;-)

(2) Well then, what are THD and IM if they are not forms of distortion? They are means for characterizing or quantifying or measuring distortion. They are means, not the ends. Are cubic centimeters a form of automobile engine displacement? No! Cubic centimeters are a means for characterizing or quantifying or measuring engine displacement.

(3) THD and IM are means for measuring nonlinear distortion, so what is nonlinear distortion? Nonlinear distortion is a something whose fundamental cause is things that take in one tone and put out more than one tone, where the additional new tone(s) have a more-or-less consistent correlation with the input. This contrasts with noise and interfering signals where that correlation is random. This contrasts with frequency response and phase distortion where the same tones that go in, come out but with their relative timings and/or sizes changed.

(4) Can you estimate IM given THD or vice-versa? Yes you can. The procedure is that you estimate the underlying form of nonlinear distortion from either THD or IM measurements or better yet from a FFT analysis, and then simulate the other measurement based on what you find out about the distortion mechanism at hand. This would be more popular except for the fact that are about an infinite combinations of number of tones, tone frequencies, and tone amplitudes for measuring THD and IM, and the relationship depends on which set(s) of tones you chose to compare.

My point is that if you have IM, you have THD and vice versa. They are basically equally important because they are like two sides of the same coin, and the coin is named nonlinear distortion. Harmonic distortion can possibly be euphonic or at least hard to detect because it is often masked by the harmonics that are already naturally in the music. IM has this nasty strong tendency to sound ugly to most people, except possibly people who like things like Punk Rock or Heavy Metal. Thing is, Deep Purple sounds better to me on a measurably clean system than a dirty one. The fact that the mainstream of audio is highly dependent on the existence of gear with vanishing or at least inaudible distortion is a matter of historical fact. Of course like most avocations there are many tiny niches in audio that may defy conventional logic.

Excellent posts Arny, and it seems you read my mind. This is from an article I just submitted to audioXpress magazine that will be published in a few months:

It’s worth mentioning that for static waveforms, symmetrical wave shapes contain only odd numbered harmonics, and asymmetrical shapes contain both odd and even harmonics. So square waves and triangle waves contain only odd harmonics, where sawtooth and pulse waves contain both types. Also note that ... intermodulation distortion (IMD) is always added along with harmonic distortion unless the input source is a single frequency. This is true for all electronic devices, including gear with tubes and transformers, and analog tape recorders. I smile when I see people refer to tube gear as producing mainly even-order harmonics, and solid state gear being mainly odd. Every device that adds even numbered harmonics also adds odd harmonics. Further, when playing music, any type of harmonic distortion always adds a similar amount of IMD.

Thanks.

There are several related myths about "Tube sound".

One is that tubed push-pull amplifiers, particularly when well-balanced inherently cancel even order distortion, and this often shows up in measurements. Yet the myth about even order distortion is still ascribed to them even though in theory it can't and in practice it doesn't really apply.  The same cancellation takes place in push-pull SS amps, with the same favorable results. Yet somehow the golden ears don't seem to hear this difference. 

The other relevant critical factoid is that single-ended amps, whether amps or preamps actually create a mixture of odd and even distortion that is again an inherent part of their basic operation which is exponential.  Again the facts don't support the even order distortion myth, but that doesn't stop people from mindlessly applying it.

IME the most useful application of the information about the harmonic content of  sawtooth waves is analog music synths, and digital synths that mimic them closely.