Module:JI ratio finder

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This module depends on the following other modules: Module: Rational Module: Utils

Todo: add documentation

---

local utils = require('Module:Utils')
local interval = require('Module:Interval')
local rat = require('Module:Rational')
local p = {}

-- Finds candidate ratios up to a cent value and up to an integer limit
-- Ratios found this way will range from 0 cents to the given cent value
-- These ratios should then be filtered as needed
function p.find_candidate_ratios(cents, int_limit)
	local cents = cents or 1200
	local int_limit = int_limit or 99
	
	local candidate_ratios = {}
	
	for i = 1, int_limit do
		local denominator = i
		local numerator = i
		local is_within_cents = true
		
		repeat
			local current_ratio = rat.new(numerator, denominator)
			local is_simplified = utils._gcd(numerator, denominator) == 1
			is_within_cents = rat.cents(current_ratio) <= cents
			
			if is_simplified and is_within_cents then
				table.insert(candidate_ratios, current_ratio)
			end
			
			numerator = numerator + 1
			
		until not is_within_cents
	end
	
	return candidate_ratios
end

-- Filter ratios based on whether they're within a cent range
function p.filter_ratios_by_range(ratios, min_cents, max_cents)
	local ratios = ratios or { rat.new(5, 4), rat.new(81, 64), rat.new(9, 7) }
	local min_cents = min_cents or 380
	local max_cents = max_cents or 420
	
	local filtered_ratios = {}
	for i = 1, #ratios do
		local ratio_in_cents = rat.cents(ratios[i])
		if ratio_in_cents >= min_cents and ratio_in_cents <= max_cents then
			table.insert(filtered_ratios, ratios[i])
		end
	end
	
	return filtered_ratios
end

-- Filters ratios by prime limit
-- Filters out ratios whose prime factorizations contains primes larger than
-- the prime limit
function p.filter_ratios_by_prime_limit(ratios, prime_limit)
	local ratios = ratios or { rat.new(5, 4), rat.new(81, 64), rat.new(9, 7) }
	local prime_limit = prime_limit or 5
	
	local filtered_ratios = {}
	for i = 1, #ratios do
		if rat.max_prime(ratios[i]) <= prime_limit then
			table.insert(filtered_ratios, ratios[i])
		end
	end
	
	return filtered_ratios
end

-- Filters ratios by odd limit
-- Filters out ratios where, ignoring powers of 2, either the numerator or
-- denominator exceeds the odd limit
function p.filter_ratios_by_odd_limit(ratios, odd_limit)
	local ratios = ratios or { rat.new(5, 4), rat.new(81, 64), rat.new(9, 7) }
	local odd_limit = odd_limit or 5
	
	local filtered_ratios = {}
	for i = 1, #ratios do
		if rat.odd_limit(ratios[i]) <= odd_limit then
			table.insert(filtered_ratios, ratios[i])
		end
	end
	
	return filtered_ratios
end

-- Filters ratios by harmonic class
-- Filters out ratios whose largest prime is larger than the given prime; only
-- ratios whose largest prime is the given harmonic class are kept
function p.filter_ratios_by_harmonic_class(ratios, harmonic_class)
	local ratios = ratios or { rat.new(5, 4), rat.new(81, 64), rat.new(9, 7) }
	local harmonic_class = harmonic_class or 5
	
	local filtered_ratios = {}
	for i = 1, #ratios do
		if rat.max_prime(ratios[i]) == harmonic_class then
			table.insert(filtered_ratios, ratios[i])
		end
	end
	
	return filtered_ratios
end

-- Filters ratios by Tenney height
-- Filters ratios where lg(numerator) + lg(denominator) does not exceed the
-- given height, where lg is log-base-2
function p.filter_ratios_by_tenney_height(ratios, tenney_height)
	local ratios = ratios or { rat.new(5, 4), rat.new(81, 64), rat.new(9, 7) }
	local tenney_height = tenney_height or 5.0
	
	local filtered_ratios = {}
	for i = 1, #ratios do
		if rat.tenney_height(ratios[i]) <= tenney_height then
			table.insert(filtered_ratios, ratios[i])
		end
	end
	
	return filtered_ratios
end

-- Finds approximated JI ratios for a cent value for a prime and odd limit
-- Meant to find ratios within the range of a single cent value
-- TODO: use integer limit instead of odd limit
function p.find_ratios_for_cents(cents, tolerance, prime_limit, odd_limit)
	local cents = cents or 700
	local tolerance = tolerance or 20
	local prime_limit = prime_limit or 5
	local odd_limit = odd_limit or 49
	
	local num = 1
	local den = 1
	
	local within_min_tolerance = true
	local within_max_tolerance = true
	local within_odd_limit = true
	local within_prime_limit = true
	local is_simplified = true
	
	local found_ratios = {}
	
	-- Algorithm is as follows:
	-- Start with a unison p/q, where p=q and check whether it's within the
	-- range of the target ratio. If so, record it. Increment p by 1 and repeat
	-- until p/q exceeds the target range.
	-- Once p/q exceeds the range of the target ratio, increment q and repeat
	-- the process described above. End this process once p or q exceed a
	-- specified limit (the odd limit, in this case).
	repeat
		repeat
			local current_ratio = rat.new(num, den)
			local ratio_in_cents = rat.cents(current_ratio)
			
			-- Check conditions
			within_min_tolerance = ratio_in_cents > cents - tolerance
			within_max_tolerance = ratio_in_cents < cents + tolerance
			within_odd_limit = rat.odd_limit(current_ratio) <= odd_limit
			within_prime_limit = rat.max_prime(current_ratio) <= prime_limit
			is_simplified = utils._gcd(num, den) == 1
			
			if within_min_tolerance and is_simplified and within_prime_limit and within_max_tolerance and within_odd_limit then
				table.insert(found_ratios, current_ratio)
			end
			
			-- Increment numerator
			num = num + 1

		until not within_max_tolerance
		
		den = den + 1
		num = den
		
	until not within_odd_limit
	
	return found_ratios
end

-- Converts ratios to text, with delimiter
-- Default delimiter is a comma followed by a space
function p.ratios_to_text(ratios, delimiter)
	local ratios = ratios or { rat.new(5, 4), rat.new (81, 64) }
	local delimiter = delimiter or ", "

	local text = ""
	for i = 1, #ratios do
		text = text .. rat.as_ratio(ratios[i])
		if i ~= #ratios then
			text = text .. delimiter
		end
	end
	return text
end

return p