Ivan Wyschnegradsky's 24 Preludes, Op. 22

John Clough had an interesting knack for making small, innocuous comments that would seem unimportant at the time but would later turn out to have startling ramifications.

I remember some time ago chatting with Charles Smith and John Clough in a fourth-floor hallway while Dr. Smith played fetch with his dog, Ransom. Somehow, the discussion turned to the topic of my dissertation. Dr. Smith wondered whether there might be a scale in the quarter-tone universe that had properties similar to the major scale—one that had things going for it like maximal evenness, the Myhill property, cardinality equals variety, and so on. Prof. Clough answered with a simple, "Yes, there is." The topic drifted (probably onto Ransom and his ball, the Zen of Retrievers, or some such thing) and that was the end of that.

Several months later, I started looking at Wyschnegradsky's Op. 22 in some detail, and I had found a scale like the one Dr. Smith had been wondering about. Shortly thereafter, John's health had taken a turn for the worse, and we never had a chance to talk about this scale. I think John would have found this set of preludes very interesting.

I had discovered that Wyschnegradsky's scale exhibits nearly all of the properties that make the major scale special. Not only that, but Wyschnegradsky employs a sort of tonic tetrachord embedded within his scale that plays a role analogous to that of the tonic triad in the major scale. This tetrachord provides me with a way to differentiate chord tones from non-chord tones. I believe that Wyschnegradsky uses non-chord tones as more than mere decorative embellishments; these non-chord tones represent true prolongations of structural harmonies.