modesscales

Modesscales are a conceptual framework used in music theory and algorithmic composition to describe and generate families of scales that combine modal structure with modular pitch division. The term blends the ideas of modes (modal patterns of step sizes) with scales (collections of pitches spanning an octave), highlighting the two foundations of a scale: its interval pattern and its division of the octave.

A modesscale is defined by two components: a mode pattern, which is a sequence of positive integers that sum to the octave, and a modulus, which determines how the octave is partitioned into equal steps. In a standard 12-tone context, the common Ionian pattern is 2-2-1-2-2-2-1, and the modulus is 12. By applying rotations of the pattern and, if desired, transpositions of the starting point, one obtains a family of modal scales within the chosen modulus. Using different moduli, such as 12, 24, or other divisions, yields microtonal variants that preserve the same modal skeleton while altering step sizes between pitches.

Applications of modesscales include algorithmic composition, tuning research, and educational tools for exploring how modal structures interact with different pitch divisions. They provide a compact way to generate related scales and to study how transposition and rotation affect sonority across temperaments and microtonal systems.

See also: musical scale, mode, temperament, microtonality, algorithmic composition.