roth_ineqmats {musicMCT} | R Documentation |
Hyperplane arrangements for Rothenberg arrangements
Description
The data file roth_ineqmats
represents the Rothenberg hyperplane arrangements
that make_roth_ineqmat()
generates. Just like the file ineqmats
, for large
computations it's faster simply to call on precalculated data rather than to run
make_roth_ineqmat()
many thousands of times. Thus the object roth_ineqmats
saves
the inequality matrices for scales of cardinality 1-24, to be called upon by
get_roth_ineqmat()
.
Usage
roth_ineqmats
Format
roth_ineqmats
A list with 24 entries. The nth entry of the list gives the inequality
matrix for n-note scales. Each inequality matrix itself is an m by (n+1)
matrix, where m is the number of hyperplanes in the relevant Rothenberg arrangement.
(The values m are currently only empirical: so far, no principled enumeration exists.)
The last column of the matrix contains constants that translate the hyperplane away
from the origin.
Source
The data in roth_ineqmats
can be recreated with the command
sapply(1:24, make_roth_ineqmat)
.