Reference

Follow-Up, from July 2006 (Vol.29 No.7):

"Naughty But Nice," my feature article on the subject of euphonic distortion (Stereophile, April 2006), prompted an e-mail correspondence with Earl Geddes, co-originator (with Lidia Lee) of the GedLee distortion metric, which I mentioned in the piece. Geddes asked me for the polynomial coefficients I'd used to generate the four different distortion patterns, from which it emerged that, for three distinct reasons, the GedLee metric figures quoted in my article require correction.

First, I was guilty of a keying error with the GedLee distortion metric (G_m) for Pattern 3, which should have appeared as 0.082, not 0.82. Second, I failed to normalize the polynomial coefficients correctly prior to calculating the metric, as a result of which the metric was slightly underestimated for some of the patterns. The corrected G_m figures are:

Pattern 1: 0.16 (not 0.15)
Pattern 2: 0.015 (unchanged)
Pattern 3: 0.084 (not 0.082)
Pattern 4: 0.13 (not 0.12)

Third, although in the AES paper (footnote 1) describing the GedLee metric the equation given for calculating it includes an overall square root, Geddes tells me that better correlation with perceived distortion is achieved without this, in which case all the figures above need to be squared. The G_m figures for the four patterns are then (to two significant figures):

Pattern 1: 0.024
Pattern 2: 0.00022
Pattern 3: 0.0070
Pattern 4: 0.016

This revision does not alter the GedLee metric's audibility criteria. Geddes tells me, "According to our data the distortion should only be mildly audible for G_m values of 2 or less, and less than a value of 1 the subjects appeared to be guessing, indicating that perception of distortion below a G_m value of 1.0 cannot be said to be statistically significant."

As the revised metric value for all the distortion patterns I listened to for "Naughty But Nice" are very much less than 1, they ought all to be inaudible, reinforcing the comment I had already made to this effect in the article. My listening results are consequently at odds with the GedLee metric, but a number of factors may account for this.

First, my results were obtained informally, not under the blind listening conditions that were used during the metric's development. Second, Geddes acknowledges that "The G_m metric was not really developed for these very low level, fairly benign nonlinearities, and would likely need some more refinement to be applicable in these situations...Where it works best is for the more obscure nonlinearities, like crossover distortion, where THD is completely false in its ability to describe the audibility of this type of distortion. Owing to the fact that we were trying to show how THD could easily be fooled, our study focused on the more blatant situations and distortion levels that were much higher than what you used.

"That said, the information from our metric has already led us to major new discoveries that were heretofore not fully appreciated—like the audibility of group delay. Had I not realized that it could not be nonlinear distortion that I was hearing, I never would have questioned what it was, and never would have discovered the alternative perceptual issue of the perception being nonlinear instead of the system."

Earl Geddes and Lidia Lee are currently investigating the audibility of group-delay distortion and hope to present, at the San Francisco AES convention in October, a paper on their results that may put the significance of loudspeaker diffraction effects in an entirely new light. As this is a subject I have visited in these pages before ("Cutting Corners," Stereophile, July 2004), and as I have never accepted the de facto industry consensus that diffraction effects are benign, this is work I hope to be able to relate to you in due course.

Meanwhile, readers interested in using my AddDistortion utility for their own listening experiments should know that I have recently posted a revised version (v2.1) on my freeware page. This new version normalizes the transfer characteristic coefficients such that the output signal contains the input signal at precisely the same amplitude, which previously was not the case. As it is not possible to arrange that the input signal and (distorted) output signal have the same loudness at all signal levels, this strikes me as probably the best compromise.—Keith Howard

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Footnote 1: Earl Geddes and Lidia Lee, "Auditory Perception of Nonlinear Distortion—Theory," Preprint 5890, AES 115th Convention, October 2003.