Name Interval Coordinates Expressed In The Rank-6 Lilley-Johnston Basis

rank_6_coordinates_to_name.py

import re
from fractions import Fraction

def ordinal_to_suffix(degree):
	ds = str(degree)
	if ds[-1] == "1":
		if len(ds) > 1:
			if ds[-2] == "1":
				return "th"
		return "st"
	if ds[-1] == "2":
		if len(ds) > 1:
			if ds[-2] == "1":
				return "th"
		return "nd"
	if ds[-1] == "3":
		if len(ds) > 1:
			if ds[-2] == "1":
				return "th"
		return "rd"
	else:
		return "th"

def interval_name_to_english(interval_string):
	interval_string = re.sub(r"Sp", r"super-", interval_string)
	interval_string = re.sub(r"Sb", r"sub-", interval_string)
	interval_string = re.sub(r"Ac", r"acute ", interval_string)
	interval_string = re.sub(r"Gr", r"grave ", interval_string)
	interval_string = re.sub(r"m", r"minor ", interval_string)
	interval_string = re.sub(r"d", r"diminished ", interval_string)
	interval_string = re.sub(r"M", r"major ", interval_string)
	interval_string = re.sub(r"Pr", r"prominent-", interval_string)
	interval_string = re.sub(r"Re", r"recessed-", interval_string)
	interval_string = re.sub(r"P", r"perfect ", interval_string)
	interval_string = re.sub(r"De", r"descendant-", interval_string)
	interval_string = re.sub(r"As", r"ascendant-", interval_string)
	interval_string = re.sub(r"A", r"augmented ", interval_string)
	return interval_string


def tune_interval_in_comma_basis(interval):
	a, b, c, d, e, f = interval
	ratio = Fraction(81, 80) ** a * Fraction(25, 24) ** b * Fraction(128, 125) ** c * Fraction(36, 35) ** d * Fraction(33, 32) ** e * Fraction(65, 64) ** f
	return ratio

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"DeP", r"De", interval_string)
	interval_string = re.sub(r"SbP", r"Sb", interval_string)
	interval_string = re.sub(r"AsP", r"As", interval_string)
	interval_string = re.sub(r"SpP", r"Sp", interval_string)
	interval_string = re.sub(r"GrP", r"Gr", interval_string)
	interval_string = re.sub(r"PrP([0-9]+)", r"Pr\1", interval_string)
	interval_string = re.sub(r"ReP", r"Re", 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_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 interval_to_quality(interval):
	a, b, c, d, e, f = interval
	if c >= 7:
		return interval_to_quality(interval_difference((a, b, c, d, e, f), (3, 12, 7, 0, 0, 0)))
	if c < 0:
		return interval_to_quality(interval_sum((a, b, c, d, e, f), (3, 12, 7, 0, 0, 0)))
	base_interval_to_quality = {
		(0, 0, 0, 0, 0, 0): "P",
		(0, 1, 1, 0, 0, 0): "m",
		(0, 2, 1, 0, 0, 0): "M",
		(1, 3, 2, 0, 0, 0): "m",
		(1, 4, 2, 0, 0, 0): "M",
		(1, 5, 3, 0, 0, 0): "P",
		(2, 7, 4, 0, 0, 0): "P",
		(2, 8, 5, 0, 0, 0): "m",
		(2, 9, 5, 0, 0, 0): "M",
		(3, 10, 6, 0, 0, 0): "m",
		(3, 11, 6, 0, 0, 0): "M",
	}
	c_to_natural_gravity = {
		0: 0,
		1: 0,
		2: 1,
		3: 1,
		4: 2,
		5: 2,
		6: 3,
	}
	if interval in base_interval_to_quality:
		return base_interval_to_quality[interval]
	if f < 0:
		return "Re" + interval_to_quality((a, b, c, d, e, f + 1))
	if f > 0:
		return "Pr" + interval_to_quality((a, b, c, d, e, f - 1))
	if e < 0:
		return "De" + interval_to_quality((a, b, c, d, e + 1, f))
	if e > 0:
		return "As" + interval_to_quality((a, b, c, d, e - 1, f))
	if d < 0:
		return "Sb" + interval_to_quality((a, b, c, d + 1, e, f))
	if d > 0:
		return "Sp" + interval_to_quality((a, b, c, d - 1, e, f))
	natural_gravity = c_to_natural_gravity[c]
	gravity_difference = a - natural_gravity
	if gravity_difference < 0:
		return "Gr" * abs(gravity_difference) + interval_to_quality((a - gravity_difference, b, c, d, e, f))
	if gravity_difference > 0:
		return "Ac" * gravity_difference + interval_to_quality((a - gravity_difference, b, c, d, e, f))
	if c == 0:
		if b < 0:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 0:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 1:
		if b < 1:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 2:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 2:
		if b < 3:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 4:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 3:
		if b < 5:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 5:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 4:
		if b < 7:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 7:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 5:
		if b < 8:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 9:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))
	if c == 6:
		if b < 10:
			return "d" + interval_to_quality((a, b + 1, c, d, e, f))
		if b > 11:
			return "A" + interval_to_quality((a, b - 1, c, d, e, f))

def name_rank_6_interval(interval):
	(a, b, c, d, e, f) = interval
	ordinal = interval[2] + 1
	name = interval_to_quality(interval) + str(ordinal)
	name = pprint(name)
	return name

intervals = [
	(3, 10, 6, 0, 0, 0),
	(3, 10, 6, 1, 0, 1),
]
for interval in intervals:
	name = name_rank_6_interval(interval)
	frequency_ratio = tune_interval_in_comma_basis(interval)
	frequency_ratio_string = str(frequency_ratio.numerator) + "/" + str(frequency_ratio.denominator)
	#ordinal = interval[2] + 1
	#english_name = interval_name_to_english(name) + ordinal_to_suffix(ordinal)
	print(name, "=", list(interval), "#", frequency_ratio_string, "=", float(frequency_ratio))