maxeven

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 (<code>card</code>) 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).

Analysis of musical scales (& modes, grooves, etc.) in the vein of
Sherrill 2025 <https://collections.lib.utah.edu/ark:/87278/s6d2gr78>.
The initials MCT in the package title refer to the article's title: "Modal
Color Theory." Offers support for conventional musical pitch class set
theory as developed by Forte (1973, ISBN: 9780300016109) and David Lewin
(1987, ISBN: 9780300034936), as well as for the continuous geometries of
Callender, Quinn, & Tymoczko (2008) <doi:10.1126/science.1153021>.
Identifies structural properties of scales and calculates derived values
(sign vector, color number, brightness ratio, etc.). Creates plots such as
"brightness graphs" which visualize these properties.

Paul Sherrill

musicMCT

Analyze the Structure of Musical Scales

maxeven function

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

Arguments

Maximally even scales — maxeven

<dl>

<dt>card</dt>
<dd>Number of notes in the scale. Numeric.</dd>


<dt>edo</dt>
<dd>Number of unit steps in an octave. Defaults to <code>12</code>.</dd>


<dt>floor</dt>
<dd>Boolean determining how to quantize. Defaults to <code>TRUE</code> causing the
quantization to round down. If <code>FALSE</code> rounds to the nearest value.</dd>

</dl>

maxeven: Maximally even scales

Description

Usage

Value

Arguments

Examples