Data.PcSets
Contents
Description
- class PcSet a where
- class PcSet a => Selective a where
- complement :: a -> a
- class PcSet a => Inclusive a where
- data GenSet
- data StdSet
- data GenRow
- data StdRow
- genset :: Int -> [Int] -> GenSet
- stdset :: [Int] -> StdSet
- genrow :: Int -> [Int] -> GenRow
- stdrow :: [Int] -> StdRow
- transpose :: PcSet a => Int -> a -> a
- invert :: PcSet a => a -> a
- invertXY :: PcSet a => Int -> Int -> a -> a
- zero :: PcSet a => a -> a
- retrograde :: PcSet a => a -> a
- rotate :: PcSet a => Int -> a -> a
- sort :: (PcSet a, Selective a) => a -> a
- normal :: (PcSet a, Selective a) => a -> a
- reduced :: (PcSet a, Selective a) => a -> a
- prime :: (PcSet a, Selective a) => a -> a
- cardinality :: (PcSet a, Selective a) => a -> Int
- binaryValue :: (PcSet a, Selective a) => a -> Integer
- avec :: (PcSet a, Selective a) => a -> [Int]
- cvec :: (PcSet a, Selective a) => a -> [Int]
- ivec :: (PcSet a, Selective a) => a -> [Int]
- rowP :: (PcSet a, Inclusive a) => Int -> a -> a
- rowR :: (PcSet a, Inclusive a) => Int -> a -> a
- rowI :: (PcSet a, Inclusive a) => Int -> a -> a
- rowRI :: (PcSet a, Inclusive a) => Int -> a -> a
Classes
The broadest class of Pitch Class Set. All members of this class
have a modulus which restricts their elements in some way. They
also have pMap, a method for lifting integer list functions to act
on set elements. The modulus corresponds to the underlying system
of equivalent pitch classes, for example, 12-TET = modulus 12.
Methods
Determines the range of possible elements of the set,
from 0 to (m-1). If m = 0, the set can only be empty.
Returns the elements of the set as a list.
pMap :: ([Int] -> [Int]) -> a -> aSource
Maps an integer list function across the members of the set, and returns the results in a new set of the same type.
class PcSet a => Selective a whereSource
Selective Pitch Class Sets can have elements in a range of values
permitted by their modulus. They can have as few as 0 (the empty
set) or as many as all. The set complement operation only makes
sense for Selective sets.
Methods
complement :: a -> aSource
Returns a new PcSet which is the complement of the original:
it contains all the elements which the original does not.
class PcSet a => Inclusive a whereSource
Inclusive Pitch Class Sets, or Tone Rows, have all the possible
elements permitted by their modulus. The most important
characteristic of a Tone Row is not its elements, but the
ordering of its elements.
Types
Selective (Sets)
General Pitch Class Set. This represents a Pitch Class Set that
can have a modulus of any positive integer value, representing
the number of equivalent pitch classes in a given system; for
example, 19-TET would be a modulus 19 set. The members of a the
set can be as few as zero and as many as all possible values.
Standard Pitch Class Set. This represents the traditional definition of a pitch class set, based on 12-TET, with the pitch classes numbered C = 0, C#/Db = 1, D = 2, and so on up to B = 11. This set can have anywhere from zero to 12 members (the empty set vs. the chromatic scale).
Inclusive (Rows)
Standard Tone Row. This is the traditional Tone Row, a collection
of all the elements [0..11], based on 12-TET. As with GenRow,
the most significant information in this type of set is the ordering
of the elements. Since this is always a complete set, this set
always has a length of 12.
Constructors
Selective (Sets)
stdset :: [Int] -> StdSetSource
Constructor for Standard Pitch Class Sets. This constructor accepts
any [Int] values for elements. The modulus is always 12 (12-TET).
Inclusive (Rows)
genrow :: Int -> [Int] -> GenRowSource
Constructor for General Tone Rows. This constructor accepts any Int
value for modulus, and any [Int] values for an input list. Zero
modulus always returns an empty set; a negative modulus is always
taken as positive (see GenSet). If the input list of elements is
incomplete, the remaining elements are filled in at the end, in order.
General Operations (All Sets)
Transformations
transpose :: PcSet a => Int -> a -> aSource
Returns a new PcSet which is the original transposed by n.
invert :: PcSet a => a -> aSource
Returns a new PcSet which is the standard inverse of the original,
that is, about an axis containing pitch class 0.
invertXY :: PcSet a => Int -> Int -> a -> aSource
Inversion around an axis specified by pitch classes x and y. This inverts the set in such a way that x becomes y and y becomes x.
zero :: PcSet a => a -> aSource
Returns a new PcSet in which the elements have been transposed
so that the first element is zero.
Permutations
retrograde :: PcSet a => a -> aSource
Returns a new PcSet with the elements of the original reversed.
rotate :: PcSet a => Int -> a -> aSource
Returns a new PcSet with the elements shifted n places to the left.
Selective Set Operations
Systematically Equivalent Forms
Scalar Quantities
cardinality :: (PcSet a, Selective a) => a -> IntSource
binaryValue :: (PcSet a, Selective a) => a -> IntegerSource
Binary Value. For a given Selective PcSet, this returns a
unique number relating to the elements of the set -- a measure
of the leftward packing of the sorted set (overall closeness
of each element to zero).
Vector Quantities
ivec :: (PcSet a, Selective a) => a -> [Int]Source
Interval Vector. Each element of the interval vector represents the number of intervals in the set for that particular interval class. Element 0 measures the number of 1-interval leaps; element 1 measures the number of 2-interval leaps, and so on, up to half of the modulus m.
Inclusive Set (Tone Row) Operations
rowP :: (PcSet a, Inclusive a) => Int -> a -> aSource
Returns a new Tone Row in which the elements are Prograde (in their original order) and transposed so that the first element is n.
rowR :: (PcSet a, Inclusive a) => Int -> a -> aSource
Returns a new Tone Row in which the elements are Retrograde (reversed compared to their original order) and transposed so that the first element is n.