In music theory and tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is the Otonality and one the Utonality. Thus the n-limit tonality diamond is an arrangement in diamond-shape of the set of rational numbers r, , such that the odd part of both the numerator and the denominator of r, when reduced to lowest terms, is less than or equal to the fixed odd number n. Equivalently, the diamond may be considered as a set of pitch classes, where a pitch class is an equivalence class of pitches under octave equivalence. The tonality diamond is often regarded as comprising the set of consonances of the n-limit. Although originally invented by Max Friedrich Meyer, the tonality diamond is now most associated with Harry Partch.
The Quadrangularis Reversum, an instrument constructed by Harry Partch based on the 11-limit tonality diamond
Harry Partch was an American composer, music theorist, and creator of unique musical instruments. He composed using scales of unequal intervals in just intonation, and was one of the first 20th-century composers in the West to work systematically with microtonal scales, alongside Lou Harrison. He built his own instruments in these tunings on which to play his compositions, and described the method behind his theory and practice in his book Genesis of a Music (1947).
c. 1952
Partch's parents, Virgil and Jennie (1888).
Partch in 1919
Partch (center) directing four college students in rehearsal