ps_scale_table: Create Product Set Scale Table

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

Create Product Set Scale Table

Description

Creates a scale table from a product set definition

Usage

ps_scale_table(
  ps_def = c("1x3x5", "5x9x11", "1x7x9", "1x3x11", "3x5x9", "1x5x7", "3x9x11", "1x7x11",
    "5x7x9", "3x5x11", "1x3x7", "7x9x11", "1x5x9", "3x7x9", "5x7x11", "1x9x11", "3x5x7",
    "1x3x9", "1x5x11", "3x7x11"),
  root_divisor
)

Arguments

ps_def	the product set scale definition. This is a character vector of products. Each product is a set of any number of integers separated by a lower-case "x". For example, the ps_def of the 1-3-5-7 Hexany is c("1x3", "1x5", "1x7", "3x5", "3x7", "5x7") The default is the ps_def for the 1-3-5-7-9-11 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 given product set definition, re-ordered by the degrees of the resulting scale (character)

• ratio: the ratio that defines the note, as a number between 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

See Also

offset_matrix()

Examples

# the default yields the 1-3-5-7-9-11 Eikosany
print(eikosany <- ps_scale_table(root_divisor = 33))

# Kraig Grady's Eikosany as two complementary extended Dekanies
# See _Microtonality and the Tuning Systems of Erv Wilson_, pages 127 - 131
# for the process used to create these scales
print(grady_a <- ps_scale_table(c(
  "1x3x11",
  "1x9",
  "3x9x11",
  "1x7x11",
  "1x3x7",
  "7x9x11",
  "3x7x9",
  "1x9x11",
  "1x3x9",
  "1x7",
  "3x7x11",
  "1x7x9"
), root_divisor = 33))
print(grady_a_offsets <- offset_matrix(grady_a))
print(grady_b <- ps_scale_table(c(
  "3x5x11",
  "1x5x9",
  "3x5x9x11",
  "5x7x11",
  "3x5x7",
  "1x5x11",
  "1x3x5",
  "5x9x11",
  "3x5x9",
  "1x5x7",
  "3x5x7x11",
  "5x7x9"
), root_divisor = 3*5*11))
print(grady_b_offsets <- offset_matrix(grady_b))

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