R/OPTC_test.R

In musicMCT: Analyze the Structure of Musical Scales

#' Does a scale lie in the canonical fundamental domain for OPTC symmetries?
#'
#' Modal Color Theory is capable of describing "scales" (perhaps "melodies" might be more accurate)
#' which do all sorts of non-scalar things, like repeating notes, ascending and descending 
#' inconsistently, not observing octave equivalence, and so on. This function tests whether
#' an input has a 'well-behaved' form in that it starts on `0`, only ascends, doesn't repeat
#' pitches, and doesn't go above the octave. If you find an interesting scale structure
#' represented by a set that *doesn't* satisfy these constraints, you can always desaturate it
#' until it does (i.e. call something like `saturate(.1, my_scale_with_bad_OPTCs)`).
#'
#' @inheritParams tnprime
#' @inheritParams fpunique
#' @param single_answer Should the function return a single value of `TRUE` or `FALSE`? Defaults
#'   to `TRUE`. If set to `FALSE`, returns a vector of 4 Boolean values that indicate whether
#'   the scale individually passes O, P, T, and C criteria for being in the fundamental domain.
#'
#' @returns Either a single Boolean value or a vector of 4 Boolean values, depending on the
#'   `single_answer` argument.
#'
#' @examples
#' major_triad_normal_form <- c(0, 4, 7)
#' major_triad_open_spacing <- c(0, 7, 16)
#' major_triad_voice_crossing <- c(0, 7, 4)
#' major_triad_on_des <- c(1, 5, 8)
#' major_triad_doubled_third_omit_5 <- c(0, 4, 4)
#' example_triads <- cbind(major_triad_normal_form,
#'				   major_triad_open_spacing,
#'				   major_triad_voice_crossing,
#'				   major_triad_on_des,
#'				   major_triad_doubled_third_omit_5)
#' 
#' apply(example_triads, 2, optc_test)
#' optc_test(major_triad_voice_crossing, single_answer=FALSE)
#'
#' @export
optc_test <- function(set, edo=12, rounder=10, single_answer=TRUE) {
  basically_zero <- 10^(-rounder)
  step_sizes <- sim(sort(set), edo=edo)[2,]

  satisfies_O <- max(set) < edo
  satisfies_P <- isTRUE( all.equal(set, sort(set), tolerance=basically_zero) )
  satisfies_T <- abs(set[1]) < basically_zero
  satisfies_C <- min(abs(step_sizes)) > basically_zero

  if (single_answer == FALSE) {
    res <- c(satisfies_O, satisfies_P, satisfies_T, satisfies_C)
    names(res) <- c("O", "P", "T", "C")
    return(res)
  }

  return(satisfies_O && satisfies_P && satisfies_T && satisfies_C)
}