Skip to contents

All intervals from one set to another

Source: R/lewin.R
ifunc.Rd

David Lewin's interval function (IFUNC) calculates all the intervals from some source set x to some goal set y. See Lewin, Generalized Musical Intervals and Transformations (New Haven, CT: Yale University Press, 1987), 88. Lewin's definition of the IFUNC depends on the GIS it applies to, but this package's ifunc() is less flexible. It uses only ordered pitch-class intervals as the group of IVLS to be measured. Its intervals can, however, be any continuous value and are not restricted to integers mod edo. The format of the result depends on whether non-integer intervals occur.

Usage

ifunc(
  x,
  y = NULL,
  edo = 12,
  rounder = 10,
  display_digits = 2,
  show_zeroes = TRUE
)

Arguments

x

The source set from which the intervals originate

y

The goal set to which the intervals lead. Defaults to NULL, in which case ifunc() gives the intervals from x to itself.

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.

display_digits

Integer: how many digits to display when naming any non-integral interval sizes. Defaults to 2.

show_zeroes

Boolean: if x and y belong to a single mod edo universe, should 0 values be listed for any intervals mod edo which do not occur in their IFUNC? Defaults to TRUE.

Value

Numeric vector counting the number of occurrences of each interval. The names() of the result indicate which interval size is counted by each entry. If x and y both belong to a single mod edo universe (and show_zeroes=TRUE), the result is a vector of length edo and includes explicit 0 results for missing intervals. If x and y must be measured in continuous pitch-class space, no missing intervals are identified (since there would be infinitely many to list).

Examples

ifunc(c(0, 3, 7))
#>  0  1  2  3  4  5  6  7  8  9 10 11 
#>  3  0  0  1  1  1  0  1  1  1  0  0 
ifunc(c(0, 3, 7), c(0, 4, 7))
#>  0  1  2  3  4  5  6  7  8  9 10 11 
#>  2  1  0  0  2  1  0  1  0  2  0  0 
ifunc(c(0, 4, 7), c(0, 3, 7))
#>  0  1  2  3  4  5  6  7  8  9 10 11 
#>  2  0  0  2  0  1  0  1  2  0  0  1 

ifunc(c(0, 2, 4, 7, 9), show_zeroes=FALSE)
#>  0  2  3  4  5  7  8  9 10 
#>  5  3  2  1  4  4  1  2  3 

just_dia <- j(dia)
ifunc(just_dia)
#>     0  1.11  1.82  2.03  2.94  3.15  3.86  4.98  5.19  5.90  6.09  6.80  7.01 
#>     7     2     2     3     1     3     3     5     1     1     1     1     5 
#>  8.13  8.84  9.05  9.96 10.17 10.88 
#>     3     3     1     3     2     2 
ifunc(just_dia, display_digits=4)
#>       0  1.1173  1.8240  2.0391  2.9413  3.1564  3.8631  4.9804  5.1955  5.9022 
#>       7       2       2       3       1       3       3       5       1       1 
#>  6.0977  6.8044  7.0195  8.1368  8.8435  9.0586  9.9608 10.1759 10.8826 
#>       1       1       5       3       3       1       3       2       2 

# See Lewin, GMIT p. 89:
lewin_x <- c(4, 10)
lewin_y1 <- c(9, 1, 5)
lewin_y2 <- c(7, 11, 9)
isTRUE(all.equal(ifunc(lewin_x, lewin_y1), ifunc(lewin_x, lewin_y2)))
#> [1] TRUE
apply(cbind(lewin_y1, lewin_y2), 2, fortenum)
#> lewin_y1 lewin_y2 
#>   "3-12"    "3-6"