Construction
Partch chose the 11 limit (i.e. all rational numbers with odd factors of numerator and denominator not exceeding 11) as the basis of his music, because the 11th harmonic is the first that is utterly foreign to Western ears. The seventh harmonic is poorly approximated by 12-tone equal temperament, but it appears in ancient Greek scales, is well-approximated by meantone temperament, and it is familiar from the barbershop quartet; the ninth harmonic is comparatively well approximated by equal temperament and it exists in Pythagorean tuning (because 3 × 3 = 9); but the 11th harmonic falls right in the middle between two pitches of 12-tone equal temperament. Although theorists like Hindemith and Schoenberg have suggested that the 11th harmonic is implied by, e.g. F# in the key of C, the fact is that it is simply too far out of tune, and "if the ear does not realize an implication, it does not exist."
When asked why he did not include 13, Partch replied, "When a hungry man has a large table of aromatic and unusual viands spread before him, he is unlikely to go tramping along the seashore and in the woods for still other exotic fare." In other words, two completely foreign harmonic elements would simply be too much, and Partch was satisfied with 11.
Read more about this topic: Harry Partch's 43-tone Scale
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