Partch presents 4 "basic monophonic concepts": •
Consonance and dissonance: "The ear informs us that tones which are in small-number proportion, say in the relation of 2 to 1, are strong, clear, powerful, consonant." • "The smaller the number involved in the interval ratio|[interval] ratios, the more consonant the ratio; the larger the numbers, the more dissonant". • "Dual Identity": "Every ratio of a Monophonic system is at least a dual identity." • "
Odentity [is] determined by the odd-number ratio component of the numerator, and another one, the Udentity [is] determined by the odd-number component of the denominator. A ratio thus always belongs to two tonalities, an Otonality in accordance with its
Odentity, and an Utonality in accordance with its Udentity." •
Minor: "Under-number Tonality, or Utonality ("minor"), is the immutable faculty of ratios, which in turn represent an immutable faculty of the human ear." • See:
Arithmetic progression and
Undertone series • History: Music has appeared to have advanced up the
harmonic series throughout history. •
Pythagorean tuning is 3-limit, "just intonation" often refers to
5-limit tuning, while Partch uses an 11-
limit tuning. Partch admirer
Ben Johnston uses 31-limit or higher "
extended just intonation". See:
Emancipation of the dissonance ==Editions==