def _relabel_x(point_set):
	"""Relabels note onsets of the given point set.

	The note onsets relabeled to be integers in between 1 and the length of
	the point set. Returns the relabeled set, and a mapping dictionary with
	relabeled notes as keys and original points as the values. Notes played
	originally at the same time get the same note onset value.

	Assumes that the given point set is sorted.

	Args:
		point_set: The point set to relabel.

	Returns:
		A tuple: the point set relabeled, and a mapping dictionary with the
		relabeled points as keys and the original points as values.
	"""
	relabeled_set = []
	mapping = {}
	relabel_onset = 1
	old_onset = point_set[0][0]

	for point in point_set:
		if point[0] != old_onset:
			relabel_onset += 1

		old_onset = point[0]
		relabeled_point = (relabel_onset, point[1])
		relabeled_set.append(relabeled_point)
		mapping[relabeled_point] = point

	return relabeled_set, mapping