Test for transpositional symmetry

Does the set map onto itself at some transposition other than \(T_0\)? That is, does it map onto itself under \(T_n\) for some appropriate \(n\)? tsym() can return either TRUE/FALSE or an index of symmetry but defaults to the former. tsym_index() is a simple wrapper for tsym() that returns the latter. tsym_degree() counts the total number of transpositional symmetries.

Usage

tsym(set, return_index = FALSE, edo = 12, rounder = 10)

tsym_index(set, ...)

tsym_degree(set, ...)

Arguments

set

Numeric vector of pitch-classes in the set

return_index

Should the function return a specific index at which the set is symmetrical? Defaults to FALSE.

edo

Number of unit steps in an octave. Defaults to 12.

rounder

Numeric (expected integer), defaults to 10: number of decimal places to round to when testing for equality.

...

Arguments to be passed to tsym()

Value

By default, tsym() returns TRUE if the set has non-trivial transpositional symmetry, FALSE otherwise. If return_index is TRUE, returns a vector of transposition levels at which the set is symmetric, including 0. tsym_index() is a wrapper for tsym() which sets return_index to TRUE. tsym_degree() gives the degree of symmetry, which is simply the length of tsym_index()'s value.

Examples

tsym(sc(6, 34))
#> [1] FALSE
tsym(sc(6, 35))
#> [1] TRUE
tsym(edoo(5))
#> [1] TRUE

# Works for continuous values:
tsym(tc(j(dia), edoo(3)))
#> [1] TRUE


# Index and Degree:
tsym_index(c(0, 1, 3, 6, 7, 9))
#> [1] 0 6
tsym_degree(edoo(7))
#> [1] 7