maxeven: Maximally even scales

In musicMCT: Analyze the Structure of Musical Scales

Maximally even scales

Description

Scales which are "maximally even" divisions of some equal-tempered universe have several musically interesting properties. When a maximally even scale has a number of notes (card) that is coprime to the size of the equal-tempered universe, the maximally even scale is called a "non-degenerate well-formed" or "moment of symmetry" scale. When its size divides the equal temperament, it is a perfectly even scale. When it is neither coprime nor a divisor, it produces a scale with a structure like the octatonic (i.e. a union of perfectly even scales, or a well-formed scale with a period smaller than the octave). The scale is generated by quantizing a perfectly even scale to the chosen chromatic cardinality. Two quantization options are offered (rounding down and rounding to the nearest value).

Usage

maxeven(card, edo = 12, floor = TRUE)

Arguments

card	Number of notes in the scale. Numeric.
edo	Number of unit steps in an octave. Defaults to 12.
floor	Boolean determining how to quantize. Defaults to TRUE causing the quantization to round down. If FALSE rounds to the nearest value.

Value

Numeric vector of length card representing a scale of card notes.

Examples

maxeven(7, 12)
maxeven(6, 15)
maxeven(6, 15, floor=FALSE)

diatonic_in_19 <- maxeven(7, 19)
tresillo <- maxeven(3,8)

musicMCT documentation built on June 21, 2026, 9:06 a.m.