Harry Partch's 43-tone scale

[2][failed verification] The first of Partch's "four concepts" is "The scale of musical intervals begins with absolute consonance (1 to 1) and gradually progresses into an infinitude of dissonance, the consonance of the intervals decreasing as the odd numbers of their ratios increase.

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.

[citation needed] Although theorists like Hindemith and Schoenberg have suggested that the 11th harmonic is implied by, e.g. F♯ in the key of C,[citation needed] Partch's opinion is that it is simply too far out of tune, and "if the ear does not realize an implication, it does not exist.

First, the scale only contains a complete set of chords (otonalities and utonalities) based on one tonic pitch.

[8] A constant structure giving one the property of anytime a ratio appears it will be subtended by the same number of steps.