brightness_comparisons {musicMCT} | R Documentation |
Voice-leading brightness relationships for a scale's modes
Description
The essential step in creating the brightness graph of a scale's modes
is to compute the pairwise comparisons between all the modes. Which ones are strictly
brighter than others according to "voice-leading brightness" (see "Modal Color Theory," 6-7)?
This function makes those pairwise comparisons in a manner that's useful for more computation.
If you want a human-readable version of the same information, you should use brightnessgraph()
instead.
Usage
brightness_comparisons(set, edo = 12, rounder = 10)
Arguments
set |
Numeric vector of pitch-classes in the set |
edo |
Number of unit steps in an octave. Defaults to |
rounder |
Numeric (expected integer), defaults to |
Details
Note that the returned value shows all voice-leading brightness comparisons, not just the transitive reduction of those comparisons. (That is, dorian is shown as darker than ionian even though mixolydian intervenes in the brightness graph.)
Value
An n-by-n matrix where n is the size of the scale. Row i represents mode i of the scale
in comparison to all 7 modes. If the entry in row i, column j is -1
, then mode i is
"voice-leading darker" than mode j. If 1
, mode i is "voice-leading brighter". If 0, mode i
is neither brighter nor darker, either because contrary motion is involved or because mode i
is identical to mode j. (Entries on the principal diagonal are always 0.)
Examples
# Because the diatonic scale, sc7-35, is non-degenerate well-formed, the only
# 0 entries should be on its diagonal.
brightness_comparisons(sc(7, 35))
mystic_chord <- sc(6,34)
colSums(sim(mystic_chord)) # The sum brightnesses of the mystic chord's 6 modes
brightness_comparisons(mystic_chord)
# Almost all 0s because very few mode pairs are comparable.
# That's because nearly all modes have the same sum, which means they have sum-brightness
# ties, and voice-leading brightness can't break a sum-brightness tie.
# (See "Modal Color Theory," 7.)