cps_scale_table: Create Combination Product Set Scale Table

In AlgoCompSynth/eikosany: Algorithmic Composition With Erv Wilson's Combination Product Sets

Create Combination Product Set Scale Table

Description

Creates a scale table from a combination product set definition

Usage

cps_scale_table(harmonics = c(1, 3, 5, 7, 9, 11), choose = 3, root_divisor)

Arguments

harmonics	a vector of the harmonics to use - defaults to the first six odd numbers, the harmonics that define the 1-3-5-7-9-11 Eikosany.
choose	the number of harmonics to choose for each combination - defaults to 3, the number of harmonics for each combination in the Eikosany.
root_divisor	a divisor that scales one of the products to 1/1. Most published CPS scales just use the smallest of the products for this, but Erv Wilson used 1x3x11 for the Eikosany, because that maps 1x5x11 to concert pitches for A: 55, 110, 220, 440 etc. There is no default value.

Value

a data.table with six columns:

• note_name: the product of harmonics that defines the note (character)

• ratio: the ratio that defines the note, as a number >= 1 and < 2

• ratio_frac: the ratio as a vulgar fraction (character)

• ratio_cents: the ratio in cents (hundredths of a semitone)

• interval_cents: interval between this note and the previous note

• degree: scale degree from zero to (number of notes) - 1

Examples

# the defaults yield the 1-3-5-7-9-11 Eikosany.

# Erv Wilson's design
print(eikosany <- cps_scale_table(root_divisor = 33))

# The usual public Eikosany
print(eikosany <- cps_scale_table(root_divisor = 15))

# the 1-3-5-7 Hexany
hexany_harmonics <- c(1, 3, 5, 7)
hexany_choose <- 2
print(hexany <-
  cps_scale_table(hexany_harmonics, hexany_choose, 3)
)

# the 1-7-9-11-13 2)5 Dekany

dekany_harmonics <- c(1, 7, 9, 11, 13)
dekany_choose <- 2
print(dekany <-
  cps_scale_table(dekany_harmonics, dekany_choose, 7)
)

# We might want to print out sheet music for a conventional keyboard
# player, since the synthesizer is mapping MIDI note numbers to pitches.
# We assume at least a 37-key synthesizer with middle C on the left,
# so the largest CPS scale we can play is a 35-note "35-any", made from
# seven harmonics taken three at a time.
harmonics_35 <- c(1, 3, 5, 7, 9, 11, 13)
choose_35 <- 3
print(any_35 <-
  cps_scale_table(harmonics_35, choose_35, root_divisor = 15)
)

AlgoCompSynth/eikosany documentation built on Nov. 25, 2024, 5:22 p.m.