schoenberg {schoenberg}

Generate a 12-tone matrix using Arnold Schoenberg's serialism technique.

Description

Generate a 12-tone matrix using Arnold Schoenberg's serialism technique.

Usage

schoenberg(prime0 = NULL, tone0 = NULL, accidentals = NULL, seed = NULL)

Arguments

prime0

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 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.

tone0

Optional: Name of the note to use as the lead tone of the matrix.

accidentals

Optional: Character scalar that determines whether accidentals should be represented as sharps (accidentals = "sharps") or flats (accidentals = "flats"); default value is NULL. accidentals can also be set to "integers" when one wishes to obtain a 12-tone matrix of numeric indices rather than notes. When accidentals is 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.

seed

Optional: Seed value to use in generating random matrices. Set this to a numeric value when matrices need to be reproducible.

Value

A 12-tone matrix of the "schoenberg" class with prime series on the rows and inverted series on the columns.

References

Schoenberg, A. (1923). 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"))