Nothing
R/schoenberg.R
In schoenberg: Tools for 12-Tone Musical Composition
#' Generate a 12-tone matrix using Arnold Schoenberg's serialism technique.
#'
#' @param prime0 \emph{Optional}: Vector of notes or numeric note indices to use in forming the matrix.
#' If the vector is numeric, the values must span from 0 - 11, where 0 is the lead tone (unless \code{tone0} is specified, note 0 will be treated as "C").
#' If supplying note names, use capital letters for the note names, use "#" to indicate sharps, and use "b" to indicate flats.
#' @param tone0 \emph{Optional}: Name of the note to use as the lead tone of the matrix.
#' @param accidentals \emph{Optional}: Character scalar that determines whether accidentals should be represented as sharps (\code{accidentals} = "sharps") or flats (\code{accidentals} = "flats"); default value is \code{NULL}.
#' \code{accidentals} can also be set to "integers" when one wishes to obtain a 12-tone matrix of numeric indices rather than notes.
#' When \code{accidentals} is \code{NULL}, matrices created from pre-specified vectors of notes will use the original set of accidentals, whereas
#' random matrices and matrices created from vectors of numeric indices will default to sharp notation.
#' @param seed \emph{Optional}: Seed value to use in generating random matrices. Set this to a numeric value when matrices need to be reproducible.
#'
#' @return A 12-tone matrix of the "schoenberg" class with prime series on the rows and inverted series on the columns.
#' @export
#'
#' @references
#' Schoenberg, A. (1923). \emph{Fünf klavierstücke [Five piano pieces], Op. 23, Movement 5: Walzer}.
#' Copenhagen, Denmark: Wilhelm Hansen.
#'
#' @examples
#' #### Generating Random 12-Tone Matrices ####
#' # The schoenberg() function can generate completely random 12-tone matrices:
#' schoenberg()
#'
#' # Or you can specify a seed value so that your matrices are reproducible:
#' schoenberg(seed = 42)
#'
#'
#' #### Generating 12-Tone Matrices From a Specified Vector of Notes ####
#' # For illustration, let's create two equivalent vectors of note information
#' # for Schoenberg's first 12-tone serialist work: Walzer from Opus 23.
#'
#' # First, let's create one vector with note labels:
#' prime01 <- c("C#", "A", "B", "G", "Ab", "F#", "A#", "D", "E", "Eb", "C", "F")
#'
#' # Next, let's create an equivalent vector using numeric indices instead of notes:
#' prime02 <- c(1, 9, 11, 7, 8, 6, 10, 2, 4, 3, 0, 5)
#'
#'
#' # Now, let's generate a 12-tone matrix from our note-based vector:
#' schoenberg(prime0 = prime01)
#'
#' # And let's generate a matrix from our number-based vector:
#' schoenberg(prime0 = prime02)
#'
#' # Schoenberg used a mix of sharps and flats in his notation, wich lost in translation with the
#' # numeric-index approach. Let's re-create our note-based matrix using only sharps:
#' schoenberg(prime0 = prime01, accidentals = "sharps")
#'
#' # These two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, accidentals = "sharps") == schoenberg(prime0 = prime02))
#'
#'
#' # Matrices can also be generated with flat notation by setting accidentals to "flats":
#' schoenberg(prime0 = prime01, accidentals = "flats")
#' schoenberg(prime0 = prime02, accidentals = "flats")
#'
#' # As before, these two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, accidentals = "flats") ==
#' schoenberg(prime0 = prime02, accidentals = "flats"))
#'
#'
#' # We can also manipulate the output of the schoenberg() function
#' # so that the lead tone of the matrix is a particular note.
#' # This works with either note-based or number-based input vectors:
#' schoenberg(prime0 = prime01, tone0 = "C", accidentals = "sharps")
#' schoenberg(prime0 = prime02, tone0 = "C")
#'
#' # And, as before, these two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, tone0 = "C", accidentals = "sharps") ==
#' schoenberg(prime0 = prime02, tone0 = "C"))
schoenberg <- function(prime0 = NULL, tone0 = NULL, accidentals = NULL, seed = NULL){
if(!is.null(accidentals)){
if(!is.character(accidentals))
stop("When 'accidentals' is not NULL, it must be a character scalar", call. = FALSE)
if(length(accidentals) > 1){
accidentals <- accidentals[1]
warning("When 'accidentals' is not NULL, it must be a scalar - only the first value was used", call. = FALSE)
}
if(!(accidentals %in% c("sharps", "flats", "integers")))
stop("When 'accidentals' is not NULL, it must be 'sharps', 'flats', or 'integers'")
}
set.seed(seed)
if(is.null(prime0)) prime0 <- sample(0:11, 12)
note_list <- list("0" = c("B#", "C", "Dbb"),
"1" = c("C#", "Db"),
"2" = c("D", "C##", "Ebb"),
"3" = c("D#", "Eb"),
"4" = c("E", "Fb", "D##"),
"5" = c("F", "E#", "Gbb"),
"6" = c("F#", "Gb"),
"7" = c("G", "F##", "Abb"),
"8" = c("G#", "Ab"),
"9" = c("A", "G##", "Bbb"),
"10" = c("A#", "Bb"),
"11" = c("B", "Cb"))
note_vec <- unlist(note_list)
if(!is.numeric(prime0)){
.prime0 <- prime0 <- as.character(prime0)
if(!all(prime0 %in% note_vec))
stop("Notes in 'prime0' are limited to the following notation: \n", paste(note_vec, collapse = ", "), call. = FALSE)
for(i in as.character(0:11)) prime0[prime0 %in% note_list[[i]]] <- i
prime0 <- as.numeric(prime0)
.key <- NULL
}else{
if(is.null(accidentals))
accidentals <- "sharps"
}
if(!all(prime0 <= 11 & prime0 >= 0))
stop("Values in 'prime0' must range from 0 to 11", call. = FALSE)
if(!all(round(prime0) == zapsmall(prime0)))
stop("Values in 'prime0' must be integers", call. = FALSE)
if(any(duplicated(prime0)))
stop("Notes in 'prime0' must be unique", call. = FALSE)
if(!is.null(tone0)){
.key <- as.numeric(names(which(unlist(lapply(note_list, function(x) tone0 %in% x)))))
}else{
.key <- NULL
}
key <- prime0[1]
prime0 <- prime0 - key
prime0[prime0 < 0] <- prime0[prime0 < 0] + 12
if(!is.null(.key)) key <- .key
inv <- prime0[1]
for(i in 2:12){
add <- prime0[i - 1] - prime0[i]
inv[i] <- inv[i - 1] + add
}
inv[inv < 0] <- inv[inv < 0] + 12
mat <- matrix(NA, 12, 12)
mat[1,] <- prime0
mat[,1] <- inv
colnames(mat) <- paste0("I", prime0)
rownames(mat) <- paste0("P", inv)
for(i in 2:12){
mat[-1,2:12] <- matrix(mat[-1,1], 11, 11) + matrix(mat[1,-1], 11, 11, byrow = T)
mat[mat > 11] <- mat[mat > 11] - 12
}
out <- mat + key
out[out > 11] <- out[out > 11] - 12
out[1:length(out)] <- as.character(out)
if(is.null(accidentals)){
for(i in as.character(0:11))
out[out == i] <- .prime0[.prime0 %in% note_list[[i]]]
}else if(accidentals == "flats"){
out[out == "0"] <- "C"
out[out == "1"] <- "Db"
out[out == "2"] <- "D"
out[out == "3"] <- "Eb"
out[out == "4"] <- "E"
out[out == "5"] <- "F"
out[out == "6"] <- "Gb"
out[out == "7"] <- "G"
out[out == "8"] <- "Ab"
out[out == "9"] <- "A"
out[out == "10"] <- "Bb"
out[out == "11"] <- "B"
}else if(accidentals == "sharps"){
out[out == "0"] <- "C"
out[out == "1"] <- "C#"
out[out == "2"] <- "D"
out[out == "3"] <- "D#"
out[out == "4"] <- "E"
out[out == "5"] <- "F"
out[out == "6"] <- "F#"
out[out == "7"] <- "G"
out[out == "8"] <- "G#"
out[out == "9"] <- "A"
out[out == "10"] <- "A#"
out[out == "11"] <- "B"
}
out <- data.frame(out)
class(out) <- c("schoenberg", "data.frame")
out
}
#' Re-express a "schoenberg" class object with a different lead tone or different notation of accidentals.
#'
#' @param tone_mat Object of the class "schoenberg" produced by the \code{schoenberg()} function.
#' @param tone0 \emph{Optional}: Name of the note to use as the lead tone of the matrix.
#' @param accidentals \emph{Optional}: Character scalar that determines whether accidentals should be represented as sharps (\code{accidentals} = "sharps") or flats (\code{accidentals} = "flats"); default value is \code{NULL}.
#' \code{accidentals} can also be set to "integers" when one wishes to obtain a 12-tone matrix of numeric indices rather than notes.
#' When \code{accidentals} is \code{NULL}, matrices created from pre-specified vectors of notes will use the original set of accidentals, whereas
#' random matrices and matrices created from vectors of numeric indices will default to sharp notation.
#'
#' @return A 12-tone matrix of the "schoenberg" class with prime series on the rows and inverted series on the columns.
#' @export
#'
#' @examples
#' # Let's create a vector of notes to use in creating our inital 'tone_mat' matrix based
#' # on Schoenberg's Walzer from Opus 23
#' prime01 <- c("C#", "A", "B", "G", "Ab", "F#", "A#", "D", "E", "Eb", "C", "F")
#' tone_mat <- schoenberg(prime0 = prime01)
#'
#' # Now, let's change the lead tone to "C":
#' rekey(tone_mat = tone_mat, tone0 = "C")
#'
#' # And let's also change the accidentals to flats:
#' rekey(tone_mat = tone_mat, tone0 = "C", accidentals = "flats")
rekey <- function(tone_mat, tone0 = NULL, accidentals = NULL){
if(!("schoenberg" %in% class(tone_mat) ))
stop("'tone_mat' must be of class 'schoenberg'", call. = FALSE)
schoenberg(prime0 = as.matrix(tone_mat)[1,], tone0 = tone0, accidentals = accidentals)
}
Try the schoenberg package in your browser
Any scripts or data that you put into this service are public.
schoenberg documentation built on May 2, 2019, 4:04 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
#' Generate a 12-tone matrix using Arnold Schoenberg's serialism technique.
#'
#' @param prime0 \emph{Optional}: Vector of notes or numeric note indices to use in forming the matrix.
#' If the vector is numeric, the values must span from 0 - 11, where 0 is the lead tone (unless \code{tone0} is specified, note 0 will be treated as "C").
#' If supplying note names, use capital letters for the note names, use "#" to indicate sharps, and use "b" to indicate flats.
#' @param tone0 \emph{Optional}: Name of the note to use as the lead tone of the matrix.
#' @param accidentals \emph{Optional}: Character scalar that determines whether accidentals should be represented as sharps (\code{accidentals} = "sharps") or flats (\code{accidentals} = "flats"); default value is \code{NULL}.
#' \code{accidentals} can also be set to "integers" when one wishes to obtain a 12-tone matrix of numeric indices rather than notes.
#' When \code{accidentals} is \code{NULL}, matrices created from pre-specified vectors of notes will use the original set of accidentals, whereas
#' random matrices and matrices created from vectors of numeric indices will default to sharp notation.
#' @param seed \emph{Optional}: Seed value to use in generating random matrices. Set this to a numeric value when matrices need to be reproducible.
#'
#' @return A 12-tone matrix of the "schoenberg" class with prime series on the rows and inverted series on the columns.
#' @export
#'
#' @references
#' Schoenberg, A. (1923). \emph{Fünf klavierstücke [Five piano pieces], Op. 23, Movement 5: Walzer}.
#' Copenhagen, Denmark: Wilhelm Hansen.
#'
#' @examples
#' #### Generating Random 12-Tone Matrices ####
#' # The schoenberg() function can generate completely random 12-tone matrices:
#' schoenberg()
#'
#' # Or you can specify a seed value so that your matrices are reproducible:
#' schoenberg(seed = 42)
#'
#'
#' #### Generating 12-Tone Matrices From a Specified Vector of Notes ####
#' # For illustration, let's create two equivalent vectors of note information
#' # for Schoenberg's first 12-tone serialist work: Walzer from Opus 23.
#'
#' # First, let's create one vector with note labels:
#' prime01 <- c("C#", "A", "B", "G", "Ab", "F#", "A#", "D", "E", "Eb", "C", "F")
#'
#' # Next, let's create an equivalent vector using numeric indices instead of notes:
#' prime02 <- c(1, 9, 11, 7, 8, 6, 10, 2, 4, 3, 0, 5)
#'
#'
#' # Now, let's generate a 12-tone matrix from our note-based vector:
#' schoenberg(prime0 = prime01)
#'
#' # And let's generate a matrix from our number-based vector:
#' schoenberg(prime0 = prime02)
#'
#' # Schoenberg used a mix of sharps and flats in his notation, wich lost in translation with the
#' # numeric-index approach. Let's re-create our note-based matrix using only sharps:
#' schoenberg(prime0 = prime01, accidentals = "sharps")
#'
#' # These two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, accidentals = "sharps") == schoenberg(prime0 = prime02))
#'
#'
#' # Matrices can also be generated with flat notation by setting accidentals to "flats":
#' schoenberg(prime0 = prime01, accidentals = "flats")
#' schoenberg(prime0 = prime02, accidentals = "flats")
#'
#' # As before, these two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, accidentals = "flats") ==
#' schoenberg(prime0 = prime02, accidentals = "flats"))
#'
#'
#' # We can also manipulate the output of the schoenberg() function
#' # so that the lead tone of the matrix is a particular note.
#' # This works with either note-based or number-based input vectors:
#' schoenberg(prime0 = prime01, tone0 = "C", accidentals = "sharps")
#' schoenberg(prime0 = prime02, tone0 = "C")
#'
#' # And, as before, these two approaches produce identical outputs:
#' all(schoenberg(prime0 = prime01, tone0 = "C", accidentals = "sharps") ==
#' schoenberg(prime0 = prime02, tone0 = "C"))
schoenberg <- function(prime0 = NULL, tone0 = NULL, accidentals = NULL, seed = NULL){
if(!is.null(accidentals)){
if(!is.character(accidentals))
stop("When 'accidentals' is not NULL, it must be a character scalar", call. = FALSE)
if(length(accidentals) > 1){
accidentals <- accidentals[1]
warning("When 'accidentals' is not NULL, it must be a scalar - only the first value was used", call. = FALSE)
}
if(!(accidentals %in% c("sharps", "flats", "integers")))
stop("When 'accidentals' is not NULL, it must be 'sharps', 'flats', or 'integers'")
}
set.seed(seed)
if(is.null(prime0)) prime0 <- sample(0:11, 12)
note_list <- list("0" = c("B#", "C", "Dbb"),
"1" = c("C#", "Db"),
"2" = c("D", "C##", "Ebb"),
"3" = c("D#", "Eb"),
"4" = c("E", "Fb", "D##"),
"5" = c("F", "E#", "Gbb"),
"6" = c("F#", "Gb"),
"7" = c("G", "F##", "Abb"),
"8" = c("G#", "Ab"),
"9" = c("A", "G##", "Bbb"),
"10" = c("A#", "Bb"),
"11" = c("B", "Cb"))
note_vec <- unlist(note_list)
if(!is.numeric(prime0)){
.prime0 <- prime0 <- as.character(prime0)
if(!all(prime0 %in% note_vec))
stop("Notes in 'prime0' are limited to the following notation: \n", paste(note_vec, collapse = ", "), call. = FALSE)
for(i in as.character(0:11)) prime0[prime0 %in% note_list[[i]]] <- i
prime0 <- as.numeric(prime0)
.key <- NULL
}else{
if(is.null(accidentals))
accidentals <- "sharps"
}
if(!all(prime0 <= 11 & prime0 >= 0))
stop("Values in 'prime0' must range from 0 to 11", call. = FALSE)
if(!all(round(prime0) == zapsmall(prime0)))
stop("Values in 'prime0' must be integers", call. = FALSE)
if(any(duplicated(prime0)))
stop("Notes in 'prime0' must be unique", call. = FALSE)
if(!is.null(tone0)){
.key <- as.numeric(names(which(unlist(lapply(note_list, function(x) tone0 %in% x)))))
}else{
.key <- NULL
}
key <- prime0[1]
prime0 <- prime0 - key
prime0[prime0 < 0] <- prime0[prime0 < 0] + 12
if(!is.null(.key)) key <- .key
inv <- prime0[1]
for(i in 2:12){
add <- prime0[i - 1] - prime0[i]
inv[i] <- inv[i - 1] + add
}
inv[inv < 0] <- inv[inv < 0] + 12
mat <- matrix(NA, 12, 12)
mat[1,] <- prime0
mat[,1] <- inv
colnames(mat) <- paste0("I", prime0)
rownames(mat) <- paste0("P", inv)
for(i in 2:12){
mat[-1,2:12] <- matrix(mat[-1,1], 11, 11) + matrix(mat[1,-1], 11, 11, byrow = T)
mat[mat > 11] <- mat[mat > 11] - 12
}
out <- mat + key
out[out > 11] <- out[out > 11] - 12
out[1:length(out)] <- as.character(out)
if(is.null(accidentals)){
for(i in as.character(0:11))
out[out == i] <- .prime0[.prime0 %in% note_list[[i]]]
}else if(accidentals == "flats"){
out[out == "0"] <- "C"
out[out == "1"] <- "Db"
out[out == "2"] <- "D"
out[out == "3"] <- "Eb"
out[out == "4"] <- "E"
out[out == "5"] <- "F"
out[out == "6"] <- "Gb"
out[out == "7"] <- "G"
out[out == "8"] <- "Ab"
out[out == "9"] <- "A"
out[out == "10"] <- "Bb"
out[out == "11"] <- "B"
}else if(accidentals == "sharps"){
out[out == "0"] <- "C"
out[out == "1"] <- "C#"
out[out == "2"] <- "D"
out[out == "3"] <- "D#"
out[out == "4"] <- "E"
out[out == "5"] <- "F"
out[out == "6"] <- "F#"
out[out == "7"] <- "G"
out[out == "8"] <- "G#"
out[out == "9"] <- "A"
out[out == "10"] <- "A#"
out[out == "11"] <- "B"
}
out <- data.frame(out)
class(out) <- c("schoenberg", "data.frame")
out
}
#' Re-express a "schoenberg" class object with a different lead tone or different notation of accidentals.
#'
#' @param tone_mat Object of the class "schoenberg" produced by the \code{schoenberg()} function.
#' @param tone0 \emph{Optional}: Name of the note to use as the lead tone of the matrix.
#' @param accidentals \emph{Optional}: Character scalar that determines whether accidentals should be represented as sharps (\code{accidentals} = "sharps") or flats (\code{accidentals} = "flats"); default value is \code{NULL}.
#' \code{accidentals} can also be set to "integers" when one wishes to obtain a 12-tone matrix of numeric indices rather than notes.
#' When \code{accidentals} is \code{NULL}, matrices created from pre-specified vectors of notes will use the original set of accidentals, whereas
#' random matrices and matrices created from vectors of numeric indices will default to sharp notation.
#'
#' @return A 12-tone matrix of the "schoenberg" class with prime series on the rows and inverted series on the columns.
#' @export
#'
#' @examples
#' # Let's create a vector of notes to use in creating our inital 'tone_mat' matrix based
#' # on Schoenberg's Walzer from Opus 23
#' prime01 <- c("C#", "A", "B", "G", "Ab", "F#", "A#", "D", "E", "Eb", "C", "F")
#' tone_mat <- schoenberg(prime0 = prime01)
#'
#' # Now, let's change the lead tone to "C":
#' rekey(tone_mat = tone_mat, tone0 = "C")
#'
#' # And let's also change the accidentals to flats:
#' rekey(tone_mat = tone_mat, tone0 = "C", accidentals = "flats")
rekey <- function(tone_mat, tone0 = NULL, accidentals = NULL){
if(!("schoenberg" %in% class(tone_mat) ))
stop("'tone_mat' must be of class 'schoenberg'", call. = FALSE)
schoenberg(prime0 = as.matrix(tone_mat)[1,], tone0 = tone0, accidentals = accidentals)
}
Try the schoenberg package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.