name-bohlen-intervals.py

import re
from fractions import Fraction

def interval_difference(interval1, interval2):
	interval_difference = (e1 - e2 for (e1, e2) in zip(interval1, interval2))
	return tuple(interval_difference)

def interval_sum(interval1, interval2):
	interval_sum = (e1 + e2 for (e1, e2) in zip(interval1, interval2))
	return tuple(interval_sum)

def ab_to_natural_gravity(a, b):
	if a == 0:
		return 0
	if a == 1 and b <= 0:
		return 0
	if a == 1 and b >= 1:
		return 1
	if a == 2:
		return 1
	if a == 3:
		return 2
	if a == 4:
		return 3
	if a == 5:
		return 3
	if a == 6:
		return 4
	if a == 7:
		return 5
	if a == 8 and b <= 3:
		return 5
	if a == 8 and b >= 4:
		return 6

def pprint(interval_string):
	interval_string = re.sub(r"dP", r"d", interval_string)
	interval_string = re.sub(r"AP", r"A", interval_string)
	interval_string = re.sub(r"GrP", r"Gr", interval_string)
	interval_string = re.sub(r"AcP", r"Ac", interval_string)
	interval_string = re.sub(r"dm", r"d", interval_string)
	interval_string = re.sub(r"AM", r"A", interval_string)
	return interval_string

def interval_to_frequency_ratio(interval):
	(a, b, c) = interval
	frequency_ratio = Fraction(27, 25) ** a * Fraction(375, 343) ** b * Fraction(245, 243) ** c
	return frequency_ratio

def interval_to_quality(interval):
	#print(interval, flush=True)
	a, b, c = interval
	if a >= 9:
		return interval_to_quality(interval_difference((a, b, c), (9, 4, 6)))
	if a < 0:
		return interval_to_quality(interval_sum((a, b, c), (9, 4, 6)))
	base_interval_to_quality = {
		(0, 0, 0): "P",
		(1, 0, 0): "m",
		(1, 1, 1): "M",
		(2, 1, 1): "P",
		(3, 1, 2): "m",
		(3, 2, 2): "M",
		(4, 2, 3): "P",
		(5, 2, 3): "P",
		(6, 2, 4): "m",
		(6, 3, 4): "M",
		(7, 3, 5): "P",
		(8, 3, 5): "m",
		(8, 4, 6): "M",
	}
	if interval in base_interval_to_quality:
		return base_interval_to_quality[interval]
	natural_gravity = ab_to_natural_gravity(a, b)
	gravity_difference = c - natural_gravity
	if gravity_difference < 0:
		return "Gr" * abs(gravity_difference) + interval_to_quality((a, b, c - gravity_difference))
	if gravity_difference > 0:
		return "Ac" * gravity_difference + interval_to_quality((a, b, c - gravity_difference))
	if a == 0:
		if b < 0:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 0:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 1:
		if b < 0:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 1:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 2:
		if b < 1:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 1:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 3:
		if b < 1:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 2:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 4:
		if b < 2:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 2:
			return "A" + interval_to_quality((a, b -1, c))
	if a == 5:
		if b < 2:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 2:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 6:
		if b < 2:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 3:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 7:
		if b < 3:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 3:
			return "A" + interval_to_quality((a, b - 1, c))
	if a == 8:
		if b < 3:
			return "d" + interval_to_quality((a, b + 1, c))
		if b > 4:
			return "A" + interval_to_quality((a, b - 1, c))

def name_interval(interval):
	(a, b, c) = interval
	ordinal = a + 1
	name = interval_to_quality(interval) + str(ordinal)
	name = pprint(name)
	return name

intervals = [
	(0, 0, 0), # P1
	(1, 0, 0), # m2
	(1, 1, 1), # M2
	(2, 1, 1), # P3
	(3, 1, 2), # m4
	(3, 2, 2), # M4
	(4, 2, 3), # P5
	(5, 2, 3), # P6
	(6, 2, 4), # m7
	(6, 3, 4), # M7
	(7, 3, 5), # P8
	(8, 3, 5), # m9
	(8, 4, 6), # M9
	(9, 4, 6), # P10
	(0, 0, 1), # Ac1
	(0, 1, 0), # A1
	(1, 0, 1), # Acm2
]

for interval in intervals:
	name = name_interval(interval)
	frequency_ratio = interval_to_frequency_ratio(interval)
	print(interval, ":", name, "::", frequency_ratio)