Passing siteswap

Creates a passing siteswap object from a multi-juggler sequence in <A|B> notation. Each section separated by | gives one juggler's throws; a p suffix (e.g. "3p") marks a throw that passes to the next juggler. Fractional notation (e.g. "<4.5 3 3 | 3 4 3.5>") is also supported, where .5 throws are passes and the second juggler is half a beat later.

Usage

passingSiteswap(sequence = character(0))

Arguments

sequence

A single character string of passing siteswap notation, e.g. "<3p 3 3 3 3 3 | 3p 3 3 3 3 3>" or "<4.5 3 3 | 3 4 3.5>". Spaces within sections are ignored; <3p33|3p33> and <3p 3 3|3p 3 3> are equivalent.

Value

A passingSiteswap S7 object.

Details

In p-notation, both jugglers are fully synchronised: they throw on the same beat and alternate hands together. In fractional notation, the second juggler is offset by half a beat in the combined timeline.

Additional properties

@type

Always "passing" (read-only).

@is_fractional

TRUE for fractional notation; FALSE for p-notation.

@n_jugglers

Number of jugglers (sections in the sequence).

@sequences_by_juggler

List of character vectors, one per juggler, each giving the raw tokens (e.g. c("3p", "3", "3")).

@throws_by_juggler

List of numeric vectors, one per juggler, of throw heights (integers for p-notation; may include .5 for fractional).

@is_pass_by_juggler

List of logical vectors, one per juggler, indicating which throws are passes.

@period

Number of throws per juggler per cycle.

@symmetry

"symmetrical" when period is odd; "asymmetrical" when period is even.

@n_props

Total number of props (sum(all throws) / period).

@can_throw

TRUE if no two throws land on the same (juggler, beat, hand) triple (no collision).

@satisfies_average_theorem

TRUE if n_props is a whole number.

@valid

TRUE if both can_throw and satisfies_average_theorem are TRUE.

Examples

passingSiteswap("<3p 3 3 3 3 3 | 3p 3 3 3 3 3>")
#> ✔ '<3p 3 3 3 3 3 | 3p 3 3 3 3 3>' is valid passing siteswap
#> ℹ It uses 6 props across 2 jugglers
#> ℹ It is asymmetrical with period 6
passingSiteswap("<4p 3 | 3 4p>")
#> ✔ '<4p 3 | 3 4p>' is valid passing siteswap
#> ℹ It uses 7 props across 2 jugglers
#> ℹ It is asymmetrical with period 2

# Compact and spaced forms are equivalent
s1 <- passingSiteswap("<3p33|3p33>")
s2 <- passingSiteswap("<3p 3 3 | 3p 3 3>")
identical(s1@throws_by_juggler, s2@throws_by_juggler)
#> [1] TRUE

s <- passingSiteswap("<4p 3 | 3 4p>")
s@n_props
#> [1] 7
s@valid
#> [1] TRUE