A type synonym is defined for our main numerical representation, this allows us to easily change the precision.

A datatype that wraps around an (musical) datatype, adding information about the musical time to this datatype. Musical time is stored as a list of BeatTime time stamps that can optionally be augmented with information about the Beat position of the particular time stamp inside the bar.

For now, we fix the number of available beats to four, because this is also hard-coded into the bar and beat-tracker.

Represents a musical time stamp, which is a NumData possibly augmented with a Beat denoting the position of the time stamp within a bar.

alternative Timed constructor

alternative Timed constructor

Returns the start time stamp

Returns the start Beat

Returns the onset time stamp

Returns the offset time stamp

Returns the duration of Timed

wraps a datatype in Timed

Given a list of Timed values, returns the end time of the latest element in the list.

merges consecutive Timed values that store the same element (using ('(==)'). For example:

>>> mergeTimed [timed "c" 0 1, timed "c" 1 2, timed "d" 3 4, timed "d" 4 5, timed "e" 5 6]
>>> [Timed {getData = "c", getTimeStamps = [(0.0),(1.0),(2.0)]}
>>> ,Timed {getData = "d", getTimeStamps = [(3.0),(4.0),(5.0)]}
>>> ,Timed {getData = "e", getTimeStamps = [(5.0),(6.0)]}]

Does exactly what mergeTimed does, but allows for a custom equality function

the inverse of mergeTimed, expanding the list Timed elements to all timestamps stored in the getTimeStamps list. N.B.

>>> expandTimed (mergeTimed x) = x :: [Timed a]

also,

>>> (expandTimed cs) = cs

and,

>>> mergeTimed (mergeTimed (mergeTimed cs)) = (mergeTimed cs)

hold. This has been tested on the first tranche of 649 Billboard songs.

concatenates the BeatTime timestamps of two Timeds and creates a new Timed that stores the first argument. N.B. this function uses timeComp to allow for very small timing deviations

Splits a Timed in two Timeds at the specified position. If the position is out of range, an error is thrown.

>>> splitTimed (Timed "x" [Time 2, Time 5]) 4
>>> ( Timed {getData = "x", getTimeStamps = [(2.0),(4.0)]}
>>> , Timed {getData = "x", getTimeStamps = [(4.0),(5.0)]} )

returns the next beat, e.g. nextBeat Two = Three . Following the (current) definition of Beat, we still assume 4/4, in the future this function should also have the meter as an argument.

returns the previous Beat, similar to prevBeat.

returns the next beat, e.g. nextBeat Two = Three . Following the (current) definition of Beat, we still assume 4/4, in the future this function should also have the meter as an argument.

drops the time (with or without Beat) information of a list Timed data structure

Returns the NumData timestamp, given a BeatTime

compares to NumData timestamps taking a rounding error roundingError into account.

When reducing and expanding Timed types there might be rounding errors in the floating point time stamps. The roundingError parameter sets the acceptable rounding error that is used in the comparison of time stamps (e.g. see timeComp)

Returns the NumData timestamp, given a BeatTime

Pretty prints a single Timed

Pretty prints a list of Timeds, one per line