Euphonic Distortion: Naughty but Nice?:
Page 2 The AddDistortion utility I've written to apply different patterns of nonlinear distortion can be downloaded from my website. I invite anyone who wishes to satisfy themselves on the subjective effects to try it for themselves. The software processes mono 16-bit/44.1kHz WAV files only, but the two channels of a stereo source signal can easily be separated, and the distorted versions recombined, by using either a software editor or two other utilities available on my site: ChannelIsolate and ChannelCombine, which do as their names suggest.

I used AddDistortion to apply four different patterns of nonlinearity, summarized in the accompanying Table 1, to seven stereo WAV files ripped from the European Broadcasting Union's Sound Quality Assessment Material (SQAM) CD. This contains numerous single-instrument recordings and a few of small ensembles. I chose tracks covering a variety of different frequency ranges and with a variety of inherent harmonic content. These comprised a vocal quartet and its alto part alone (tracks 45 and 48), a wind ensemble (track 67), flute (track 13), harpsichord (track 40), piano (track 60), and violin (track 8). Most of these were edited to remove the silences between sections, so as to make the tracks shorter and thereby speed up the processing (which is time-consuming because it involves 24-fold up- and downsampling on either side of the distortion synthesis). In the case of the harpsichord track, the content was also amplified so that the signal peaked closer to 0dBFS.

The harmonic amplitudes specified in the table may seem surprisingly high, but the first surprise awaiting you when you experiment with distortion synthesis is just how large the distortion must be to become audible. 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. Patterns 3 and 4 comprise, respectively, the odd- and even-order harmonics only of Pattern 1. THD, Shorter-weighted THD, and GedLee distortion metric (footnotes 5, 6) (G_m) figures are given for all three patterns. 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 G_m value, despite having a significantly lower THD than Pattern 1.

Figs.1–4 show the spectra that result from applying these patterns to a full-scale sinewave using AddDistortion, and confirm the accuracy of the distortion synthesis. Fig.5 shows how the harmonic amplitudes of Pattern 1 fall away as the sinewave amplitude is reduced to –10, –20, and –30dBFS. Fig.6 shows the result of applying Pattern 1 to a 19+20kHz twin-tone input and confirms that intermodulation distortion is also introduced by the processing, just as in a real device. Note also the absence of any spuriae resulting from aliasing of above-band distortion components, which proves the efficacy of the filters used in the up- and downsampling.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5a

Fig. 5b

Fig. 5c

Fig. 6

Listening
Of course, it is impossible to listen to any synthesized distortion pattern in isolation, because the replay equipment will inevitably add nonlinearities of its own. But the nonlinearities are of such high amplitude in Patterns 1–4 that they can be expected to dominate that of most replay systems other than those employing some tube amplification. I used two different setups for my listening: I replayed the processed WAV files direct from hard disk via a HeadRoom Total BitHead and Sennheiser HD650 headphones, and I burned them to CD-R for replay via a system comprising a Pioneer DV-939A disc player, TacT Audio RCS 2.2X digital equalizer/processor, home-grown passive preamp, Exposure XVIII monoblock power amplifiers, and B&W 805S speakers. To ensure that any side effect of the distortion processing didn't affect the listening results, I compared the distorted files not with the original but with a file that had been processed by AddDistortion, but with all the harmonics set to the default amplitude of –250dBr.

This type of listening exercise can rapidly drive you nuts, particularly as none of the distortion patterns proved to have a gross effect on sound quality. Nor would you expect them to, given the tiny, difficult-to-spot differences revealed by spectral analysis of the undistorted and distorted music signals. But after a number of listening sessions—kept short to keep my ears fresh—over both headphones and loudspeakers, I did feel that I could detect differences. I found two of the recordings—of the violin and the harpsichord—particularly insightful, I surmise because both instruments have a rich enough harmonic structure to generate significant numbers of intermodulation products.

The most important finding was that none of the different patterns of nonlinearity sounded in any way preferable to the undistorted reference. They all sounded worse, albeit in different ways. 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. But I thought I could also detect it just beginning to muddy the presentation. 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. Although Patterns 3 and 4 both introduce less distortion than Pattern 1, it was Pattern 1 that proved less subjectively annoying. While I could hear its effect, it did not threaten to send me screaming from the room after 10 minutes' listening.

As already described, it has long been known that THD is a poor indicator of nonlinear distortion's subjective impact, and so it proved once again here. Shorter's n-squared weighting regime didn't correlate well either. The GedLee metric was a much better indicator, although my listening suggested that it underestimates the relative subjective annoyance of Pattern 4.

There is a little support in these findings for Hiraga's thesis, in that Pattern 1—with its full complement of even- and odd-order harmonics—indeed proved preferable to the denuded harmonic Patterns 3 and 4. But neither Pattern 1 nor Pattern 2 sounded preferable to the undistorted reference. I entreat those with a particular interest in this issue to repeat my experiments and judge for themselves, but for me the issue is now settled. Unless and until somebody comes up with a "magic" pattern of nonlinearity that truly enhances sound quality, I will believe euphonic distortion to be a fantasy. The only "good" nonlinear distortion is that of a nature and amplitude such that the human ear cannot detect it.

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Footnote 5: Earl R. Geddes and Lidia W. Lee, "Auditory Perception of Nonlinear Distortion: Theory" and "Auditory Perception of Nonlinear Distortion," Preprints 5890 and 5891, 115th AES Convention, October 2003.

Footnote 6: Keith Howard, "Weighting Up," Hi-Fi News, March 2005.