coord_to_edo {musicMCT} | R Documentation |
Coordinate systems for scale representation
Description
Usually, it is most intuitive to music theorists to represent
a scale as a vector of the pitch-classes it contains. However, for certain
computations in the setting of Modal Color Theory, it is more convenient
to use a coordinate system with the "white" perfectly even scale as the
origin (because this is the point where all of the hyperplanes
in the arrangement defining scalar "colors" intersect). Therefore, these
two functions convert between the two coordinate systems: coord_to_edo
takes in a scale represented by its pitch classes and returns its
displacement vector from "white" and coord_from_edo
does the reverse.
Usage
coord_to_edo(set, edo = 12)
coord_from_edo(set, edo = 12)
Arguments
set |
Numeric vector of pitch-classes in the set |
edo |
Number of unit steps in an octave. Defaults to |
Details
It should be noted that the representative "white" scale used is not
necessarily the closest one to the scale in question. Instead, it is
the unique transposition of white that has 0 as its first coordinate.
This is natural in the context of Modal Color Theory, which essentially
always assumes transpositional equivalence with x_0 = 0
. The closest
transposition of "white" to set
will be the one that has the same sum
class as set
, guaranteeing that the voice leading between them is
"pure contrary" (Tymoczko 2011, 81ff; explored further in Straus 2018
doi:10.1215/00222909-7127694).
Value
Numeric vector of same length as set
. Same scale,
new coordinate system.
Examples
dominant_seventh_chord <- c(0, 2, 6, 9)
coord_to_edo(dominant_seventh_chord)
ait1 <- c(0, 1, 4, 6)
ait2 <- c(0, 1, 3, 7)
coord_to_edo(ait1)
coord_to_edo(ait2) # !
weitzmann_pentachord <- coord_from_edo(c(0, -1, 0, 0, 0)) # See note 53 of "Modal Color Theory"
convert(weitzmann_pentachord, 12, 60)
coord_to_edo(weitzmann_pentachord)