Module musx.frac
Adds methods to python's Fraction class for representing exact time, mensural tuples,
tuning ratios, etc.
Expand source code
###############################################################################
"""
Adds methods to python's Fraction class for representing exact time, mensural tuples,
tuning ratios, etc.
"""
from fractions import Fraction
def dotted(self, dots=1):
"""
Returns the 'dotted' value of the fraction, e.g. 1/4 with
one dot is 1/4 + 1/8 = 3/8, e.g. the time value of a dotted quarter.
Parameters
----------
dots : int
The number of dots to apply, each dot adds half the previous
value of the fraction.
Returns
-------
A new fraction representing the dotted value.
"""
if isinstance(dots, int) and dots > 0:
return self * (2 - Fraction(1, 2**dots))
raise ValueError(f"Dots value is not a positive integer: {dots}.")
def tuplets(self, num, intimeof=1):
"""
Returns a list of num sub-divisions (metric 'tuples') that sum to
value of fraction * num.
Parameters
----------
num : int
The number of tuples to return.
intimeof : int
A number that, when multiplied by the fraction itself,
represents the sum of all the tuplets in the list.
Examples
--------
>>> Fraction(1, 4).tuplets( 3)
[Fraction(1, 12), Fraction(1, 12), Fraction(1, 12)]
>>> Fraction(1, 4).tuplets(3, 2)
[Fraction(1, 6), Fraction(1, 6), Fraction(1, 6)]
"""
tup = Fraction(intimeof, num)
one = self * tup
return [one for _ in range(num)]
def tup(self, num):
"""
Returns the fraction representing num divisions of the current fraction.
Parameters
----------
num : int
The number to divide this fraction by.
Examples
--------
>>> Fraction(1, 4).tup(5)
Fraction(1, 20)
"""
if isinstance(num, int) and num > 0:
return Fraction(self._numerator, (self._denominator * num))
raise ValueError(f"Invalid tup divisor: {num}.")
def seconds(self, tempo=60, beat=None):
"""
Converts a fraction to floating point seconds according to a
given tempo and beat.
Parameters
----------
tempo : int
The tempo in beats per minute. Defaults to 60.
beat : Fraction
A fraction representing the beat. Defaults to 1/4 (quarter note).
Examples
--------
>>> Fraction(1,4).seconds(tempo=120)
0.5
Returns
-------
A floating point value in seconds.
"""
if beat is None:
beat = Fraction(1, 4)
elif isinstance(beat, int):
beat = Fraction(beat, 1)
if isinstance(beat, Fraction):
return (beat._denominator / beat._numerator) * (self._numerator / self._denominator) * (60 / tempo)
raise TypeError(f'Invalid beat: {beat}.')
# this adds the extensions to python's Fraction class.
Fraction.dotted = dotted
Fraction.tuplets = tuplets
Fraction.tup = tup
Fraction.seconds = seconds
if __name__ == "__main__":
passFunctions
def dotted(self, dots=1)-
Returns the 'dotted' value of the fraction, e.g. 1/4 with one dot is 1/4 + 1/8 = 3/8, e.g. the time value of a dotted quarter.
Parameters
dots:int- The number of dots to apply, each dot adds half the previous value of the fraction.
Returns
A new fraction representing the dotted value.
Expand source code
def dotted(self, dots=1): """ Returns the 'dotted' value of the fraction, e.g. 1/4 with one dot is 1/4 + 1/8 = 3/8, e.g. the time value of a dotted quarter. Parameters ---------- dots : int The number of dots to apply, each dot adds half the previous value of the fraction. Returns ------- A new fraction representing the dotted value. """ if isinstance(dots, int) and dots > 0: return self * (2 - Fraction(1, 2**dots)) raise ValueError(f"Dots value is not a positive integer: {dots}.") def seconds(self, tempo=60, beat=None)-
Converts a fraction to floating point seconds according to a given tempo and beat.
Parameters
tempo:int- The tempo in beats per minute. Defaults to 60.
beat:Fraction- A fraction representing the beat. Defaults to 1/4 (quarter note).
Examples
>>> Fraction(1,4).seconds(tempo=120) 0.5Returns
A floating point value in seconds.
Expand source code
def seconds(self, tempo=60, beat=None): """ Converts a fraction to floating point seconds according to a given tempo and beat. Parameters ---------- tempo : int The tempo in beats per minute. Defaults to 60. beat : Fraction A fraction representing the beat. Defaults to 1/4 (quarter note). Examples -------- >>> Fraction(1,4).seconds(tempo=120) 0.5 Returns ------- A floating point value in seconds. """ if beat is None: beat = Fraction(1, 4) elif isinstance(beat, int): beat = Fraction(beat, 1) if isinstance(beat, Fraction): return (beat._denominator / beat._numerator) * (self._numerator / self._denominator) * (60 / tempo) raise TypeError(f'Invalid beat: {beat}.') def tup(self, num)-
Returns the fraction representing num divisions of the current fraction.
Parameters
num:int- The number to divide this fraction by.
Examples
>>> Fraction(1, 4).tup(5) Fraction(1, 20)Expand source code
def tup(self, num): """ Returns the fraction representing num divisions of the current fraction. Parameters ---------- num : int The number to divide this fraction by. Examples -------- >>> Fraction(1, 4).tup(5) Fraction(1, 20) """ if isinstance(num, int) and num > 0: return Fraction(self._numerator, (self._denominator * num)) raise ValueError(f"Invalid tup divisor: {num}.") def tuplets(self, num, intimeof=1)-
Returns a list of num sub-divisions (metric 'tuples') that sum to value of fraction * num.
Parameters
num:int- The number of tuples to return.
intimeof:int- A number that, when multiplied by the fraction itself, represents the sum of all the tuplets in the list.
Examples
>>> Fraction(1, 4).tuplets( 3) [Fraction(1, 12), Fraction(1, 12), Fraction(1, 12)] >>> Fraction(1, 4).tuplets(3, 2) [Fraction(1, 6), Fraction(1, 6), Fraction(1, 6)]Expand source code
def tuplets(self, num, intimeof=1): """ Returns a list of num sub-divisions (metric 'tuples') that sum to value of fraction * num. Parameters ---------- num : int The number of tuples to return. intimeof : int A number that, when multiplied by the fraction itself, represents the sum of all the tuplets in the list. Examples -------- >>> Fraction(1, 4).tuplets( 3) [Fraction(1, 12), Fraction(1, 12), Fraction(1, 12)] >>> Fraction(1, 4).tuplets(3, 2) [Fraction(1, 6), Fraction(1, 6), Fraction(1, 6)] """ tup = Fraction(intimeof, num) one = self * tup return [one for _ in range(num)]