csong@2: # This python file is a collection of basic functions that are used in the syncopation models. 
csong@2: 
csong@2: import math
csong@2: 
csong@2: # The concatenation function is used to concatenate two sequences.
csong@2: def concatenate(seq1,seq2):
csong@2: 	return seq1+seq2
csong@2: 
csong@2: # The repetition function is to concatenate a sequence to itself for 'times' number of times.
csong@2: def repeat(seq,times):
csong@2: 	new_seq = list(seq)
csong@2: 	if times >= 1:
csong@2: 		for i in range(times-1):
csong@2: 			new_seq = concatenate(new_seq,seq)
csong@2: 	else:
csong@2: 		#print 'Error: repetition times needs to be no less than 1.'
csong@2: 		new_seq = []
csong@2: 	return new_seq
csong@2: 
csong@2: # The subdivision function is to equally subdivide a sequence into 'divisor' number of segments.
csong@2: def subdivide(seq,divisor):
csong@2: 	subSeq = []
csong@2: 	if len(seq) % divisor != 0:
csong@2: 		print 'Error: rhythmic sequence cannot be equally subdivided.'
csong@2: 	else:
csong@2: 		n = len(seq) / divisor
csong@2: 		start , end = 0, n
csong@2: 		for i in range(divisor):
csong@2: 			subSeq.append(seq[start : end])
csong@2: 			start = end
csong@2: 			end = end + n	
csong@2: 	return subSeq
csong@2: 
csong@2: 
csong@2: # The ceiling function is to round each number inside a sequence up to its nearest integer.
csong@2: def ceiling(seq):
csong@2: 	seq_ceil = []
csong@2: 	for s in seq:
csong@2: 		seq_ceil.append(int(math.ceil(s)))
csong@2: 	return seq_ceil
csong@2: 
csong@2: # The find_divisor function returns a list of all possible divisors for a length of sequence.
csong@2: def find_divisor(number):
csong@2: 	divisors = [1]
csong@2: 	for i in range(2,number+1):
csong@2: 		if number%i ==0:
csong@2: 			divisors.append(i)
csong@2: 	return divisors
csong@2: 
csong@2: # The find_divisor function returns a list of all possible divisors for a length of sequence.
csong@2: def find_prime_factors(number):
csong@20: 	primeFactors = find_divisor(number)
csong@2: 	
csong@20: 	# remove 1 because 1 is not prime number
csong@20: 	del primeFactors[0]
csong@2: 
csong@20: 	# reversely traverse all the divisors list and once find a non-prime then delete
csong@20: 	for i in range(len(primeFactors)-1,0,-1):
csong@20: 	#	print primeFactors[i], is_prime(primeFactors[i])
csong@20: 		if not is_prime(primeFactors[i]):
csong@20: 			del primeFactors[i]
csong@2: 
csong@20: 	return primeFactors
csong@20: 
csong@20: def is_prime(number):
csong@20: 	isPrime = True
csong@20: 	# 0 or 1 is not prime numbers
csong@20: 	if number < 2:
csong@20: 		isPrime = False
csong@20: 	# 2 is the only even prime number
csong@20: 	elif number == 2:
csong@20: 		pass
csong@20: 	# all the other even numbers are non-prime
csong@20: 	elif number % 2 == 0:
csong@20: 		isPrime = False
csong@20: 	else:
csong@20: 		for odd in range(3, int(math.sqrt(number) + 1), 2):
csong@20: 			if number % odd == 0:
csong@20: 				isPrime = False
csong@20: 	return isPrime
csong@2: 
csong@2: # The min_timeSpan function searches for the shortest possible time-span representation for a sequence.
csong@2: def get_min_timeSpan(seq):
csong@20: 	minTimeSpan = [1]
csong@2: 	for d in find_divisor(len(seq)):
csong@2: 		segments = subdivide(seq,d)
csong@2: 		if len(segments)!=0:
csong@20: 			del minTimeSpan[:]
csong@2: 			for s in segments:
csong@20: 				minTimeSpan.append(s[0])
csong@20: 			if sum(minTimeSpan) == sum(seq):
csong@2: 				break
csong@20: 	return minTimeSpan
csong@2: 
csong@2: # get_note_indices returns all the indices of all the notes in this sequence
csong@20: def get_note_indices(sequence):
csong@20: 	noteIndices = []
csong@2: 
csong@20: 	for index in range(len(sequence)):
csong@20: 		if sequence[index] != 0:
csong@20: 			noteIndices.append(index)
csong@2: 
csong@20: 	return noteIndices
csong@2: 
csong@2: # The get_H returns a sequence of metrical weight for a certain metrical level (horizontal),
csong@2: # given the sequence of metrical weights in a hierarchy (vertical) and a sequence of subdivisions.
csong@19: def get_H(weightSequence,subdivisionSequence, level):
csong@2: 	H = []
csong@2: 	#print len(weight_seq), len(subdivision_seq), level
csong@19: 	if (level <= len(subdivisionSequence)-1) and (level <= len(weightSequence)-1):
csong@2: 		if level == 0:
csong@19: 			H = repeat([weightSequence[0]],subdivisionSequence[0])
csong@2: 		else:
csong@19: 			H_pre = get_H(weightSequence,subdivisionSequence,level-1)
csong@2: 			for h in H_pre:
csong@19: 				H = concatenate(H, concatenate([h], repeat([weightSequence[level]],subdivisionSequence[level]-1)))
csong@2: 	else:
csong@2: 		print 'Error: a subdivision factor or metrical weight is not defined for the request metrical level.'
csong@2: 	return H
csong@2: 
csong@19: # # The get_subdivision_seq function returns the subdivision sequence of several common time-signatures defined by GTTM, 
csong@19: # # or ask for the top three level of subdivision_seq manually set by the user.
csong@19: # def get_subdivision_seq(timesig, L_max):
csong@19: # 	subdivision_seq = []
csong@2: 
csong@19: # 	if timesig == '2/4' or timesig == '4/4':
csong@19: # 		subdivision_seq = [1,2,2]
csong@19: # 	elif timesig == '3/4' or timesig == '3/8':
csong@19: # 		subdivision_seq = [1,3,2]
csong@19: # 	elif timesig == '6/8':
csong@19: # 		subdivision_seq = [1,2,3]
csong@19: # 	elif timesig == '9/8':
csong@19: # 		subdivision_seq = [1,3,3]
csong@19: # 	elif timesig == '12/8':
csong@19: # 		subdivision_seq = [1,4,3]
csong@19: # 	elif timesig == '5/4' or timesig == '5/8':
csong@19: # 		subdivision_seq = [1,5,2]
csong@19: # 	elif timesig == '7/4' or timesig == '7/8':
csong@19: # 		subdivision_seq = [1,7,2]
csong@19: # 	elif timesig == '11/4' or timesig == '11/8':
csong@19: # 		subdivision_seq = [1,11,2]
csong@19: # 	else:
csong@19: # 		print 'Time-signature',timesig,'is undefined. Please indicate subdivision sequence for this requested time-signature, e.g. [1,2,2] for 4/4 meter.'
csong@19: # 		for i in range(3):
csong@19: # 			s = int(input('Enter the subdivision factor at metrical level '+str(i)+':'))
csong@19: # 			subdivision_seq.append(s)
csong@2: 
csong@19: # 	if L_max > 2:
csong@19: # 		subdivision_seq = subdivision_seq + [2]*(L_max-2)
csong@19: # 	else:
csong@19: # 		subdivision_seq = subdivision_seq[0:L_max+1]
csong@2: 	
csong@19: # 	return subdivision_seq
csong@2: 
csong@9: 
csong@13: def get_rhythm_category(velocitySequence, subdivisionSequence):
csong@13: 	'''
csong@13: 	The get_rhythm_category function is used to detect rhythm category: monorhythm or polyrhythm.
csong@13: 	For monorhythms, all prime factors of the length of minimum time-span representation of this sequence are
csong@13: 	elements of its subdivision_seq, otherwise it is polyrhythm; 
csong@13: 	e.g. prime_factors of polyrhythm 100100101010 in 4/4 is [2,3] but subdivision_seq = [1,2,2] for 4/4 
csong@13: 	'''
csong@13: 	rhythmCategory = 'mono'
csong@13: 	for f in find_prime_factors(len(get_min_timeSpan(velocitySequence))):
csong@13: 		if not (f in subdivisionSequence): 
csong@13: 			rhythmCategory = 'poly'
csong@9: 			break
csong@13: 	return rhythmCategory
csong@13: 
csong@13: def string_to_sequence(inputString):
csong@13: 	return map(int, inputString.split(','))
csong@9: 
csong@9: 
csong@2:  # The split_by_bar function seperates the score representation of rhythm by bar lines, 
csong@2:  # resulting in a list representingbar-by-bar rhythm sequence,
csong@2:  # e.g. rhythm = ['|',[ts1,td1,v1], [ts2,td2,v2], '|',[ts3,td3,v3],'|'...]
csong@2:  # rhythm_bybar = [ [ [ts1,td1,v1], [ts2,td2,v2] ], [ [ts3,td3,v3] ], [...]]
csong@2: # def split_by_bar(rhythm):
csong@2: # 	rhythm_bybar = []
csong@2: # 	bar_index = []
csong@2: # 	for index in range(len(rhythm)):
csong@2: # 		if rhythm[index] == '|':
csong@2: 
csong@2: # 	return rhythm_bybar
csong@2: 
csong@2: # def yseq_to_vseq(yseq):
csong@2: # 	vseq = []
csong@2: 
csong@2: # 	return vseq
csong@2: 
csong@2: 
csong@2: # # testing
csong@20: # print find_prime_factors(10)
csong@20: # print find_prime_factors(2)
csong@20: # print find_prime_factors(12)
csong@20: 
csong@20: 
csong@20: # print is_prime(1)       # False
csong@20: # print is_prime(2)       # True
csong@20: # print is_prime(3)       # True
csong@20: # print is_prime(29)      # True
csong@20: # print is_prime(345)     # False
csong@20: # print is_prime(999979)  # True
csong@20: # print is_prime(999981)  # False