Do two scales lie on the same ray? — same

Two scales which lie on the same ray from edoo() (the perfectly even scale) differ only in their saturation and are said to belong to the same "hue." They are not only members of a large "color" but also a much more specific structure which preserves properties such as ratio() and the precise shape of brightnessgraph(). same_hue() tests whether two scales have this close relationship.

Usage

same_hue(set_1, set_2, edo = 12, rounder = 10)

Arguments

set_1, set_2: Numeric vectors of pitch-classes in the sets. Must be of same length.
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.

Value

Boolean: are the sets of the same hue? NB: TRUE for identical sets (even perfectly even scales); FALSE for scales which are related by "involution."

Examples

set39 <- c(0, 5, 9, 10, 14, 16, 21)
set53 <- c(0, 7, 13, 16, 22, 26, 33)
set39 <- convert(set39, 39, 12)
set53 <- convert(set53, 53, 12)
same_hue(set39, set53)
#> [1] TRUE
# Since they have the same hue, we can resaturate one to become the other:
relative_evenness <- evenness(set53)/evenness(set39)
set53
#> [1] 0.000000 1.584906 2.943396 3.622642 4.981132 5.886792 7.471698
saturate(relative_evenness, set39)
#> [1] 0.000000 1.584906 2.943396 3.622642 4.981132 5.886792 7.471698

# These two hexachords belong to the same quasi-pairwise well formed 
# color (see "Modal Color Theory," p. 37), but not to the same hue: 
guidonian_1 <- c(0, 2, 4, 5, 7, 9)
guidonian_2 <- convert(guidonian_1, 13, 12)
isTRUE(all.equal(signvector(guidonian_1), signvector(guidonian_2)))
#> [1] TRUE
same_hue(guidonian_1, guidonian_2)
#> [1] FALSE