Quotation:
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The
Pierce scale The Pierce scale was actually first discovered by H. Bohlen (1978), who published an article in Acustica, in which he described the scale almost exactly as we have done here. The work was not known to us at the time we did our research or prepared the draft for this article. However, now that we have read the Bohlen paper, we believe that it is clear that he proposed exactly the same scale including the tempered form of the scale using the 13th root of 3 as the tempered factor and including timbres which have only odd partials such as a square wave for playing this scale. Bohlen derived his scale from a theory of combination tones and, in particular, combination tones involving 3*f 1 - f 2 . We derived the scale based on experimental measurements of the intonational sensitivity of the 3:5:7 and 5:7:9 chords. The two sources for the scale, although different, are not in conflict, since Bohlen's derivation was primarily theoretical and ours was primarily experimental. We find it heartening that we arrived at the same result from a completely different direction. Obviously there is no question about who derived the scale first, since Bohlen published a decade sooner than we did. |
End of quotation.
(Actually, there is a typo in this paper. The frequencies of the combination tones should read 2·f1-f2, rather than 3·f1-f2.)