Module:JI ratios in ED

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This module should not be invoked directly; use its corresponding template instead: Template:JI ratios in ED.

Module:JI ratios in ED is deprecated and has no replacement. Further use of this module is not advised. This module is kept for historical purposes and should not be deleted.

Introspection summary for Module:JI ratios in ED

Functions provided (6) Line Function Params 15 primes_within_prime_limit (prime_limit) 29 subgroup_as_text (primes) 45 ji_ratio_in_ed_content_cells (steps, equave, candidate_ratios, primes, tolerance) 100 ji_ratios_in_ed_by_prime_limit (input_et, int_limit, prime_limit, tenney_height, threshold) 154 ji_ratios_in_ed_by_prime_subgroup (input_et, int_limit, primes, tenney_height, threshold) 208 ji_ratios_in_ed_frame (invokable) (frame)

Lua modules required (6) Variable Module Functions used et Module:ET parse as_string jiraf Module:JI ratio finder filter_ratios_by_range filter_ratios_by_prime_limit filter_ratios_by_harmonic_class ratios_to_text find_candidate_ratios_within_prime_limit filter_ratios_by_equave_complement_int_limit filter_ratios_by_no_equave_factors_tenney_height find_candidate_ratios_within_subgroup rat Module:Rational new cents tip Module:Template input parse parse_numeric_entries utils Module:Utils is_prime yesno Module:Yesno yesno

No function descriptions were provided. The Lua code may have further information.

---

local p = {}

local et = require("Module:ET")
--local interval = require('Module:Harmonic entropy')
local jiraf = require("Module:JI ratio finder")
local rat = require("Module:Rational")
local tip = require("Module:Template input parse")
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")

-- Helper function
-- Given a prime limit, return an array of all primes between (and including) 2
-- and that limit
-- EG, 7-limit becomes { 2, 3, 5, 7 }
function p.primes_within_prime_limit(prime_limit)
	local prime_limit = prime_limit or 7
	
	local primes = {}
	for i = 2, prime_limit do
		if utils.is_prime(i) then
			table.insert(primes, i)
		end
	end
	return primes
end

-- Helper function
-- Converts a set of primes (typically a prime subgroup) into text
function p.subgroup_as_text(primes)
	local primes = primes or { 2, 3, 5, 7 }
	
	local subgroup = ""
	for i = 1, #primes do
		if i ~= #primes then
			subgroup = subgroup .. string.format("%d.", primes[i])
		else
			subgroup = subgroup .. primes[i]
		end
	end
	return subgroup
end

-- Helper function
-- Creates the non-header cells in the table
function p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
	local steps = steps or 12
	local equave = equave or rat.new(2)
	local candidate_ratios = candidate_ratios or { rat.new(1), rat.new(2), rat.new(3, 2), rat.new(4, 3), rat.new (5, 4), rat.new (9, 7)}
	local primes = primes or { 2, 3, 7 }
	local tolerance = tolerance or 20
	
	-- Calculate equave
	local equave_in_cents = rat.cents(equave)
	
	-- Build the rows for each step, showing ratios by limit
	local result = ""
	for i = 1, steps + 1 do
		local step = i - 1
		
		-- Table headers
		local step_in_cents = (step / steps) * rat.cents(equave)
		result = result .. string.format("| %d\n", step)
		result = result .. string.format("| %.3f\n", step_in_cents)
		
		-- If this is the first or last step, only use the unison or equave
		-- respectively; otherwise, filter ratios by whether they're within the
		-- current step
		local filtered_ratios = {}
		if step == 0 then
			filtered_ratios = { rat.new(1) }
		elseif step == steps then
			filtered_ratios = { equave }
		else 
			filtered_ratios = jiraf.filter_ratios_by_range(candidate_ratios, step_in_cents - tolerance, step_in_cents + tolerance)
		end
		
		-- Add ratios according to harmonic class
		for j = 1, #primes do
			local current_prime = primes[j]
			
			-- For each prime, filter by harmonic class
			-- For the first column, filter by prime limit instead
			local prime_filtered_ratios = {}
			if j == 1 then
				prime_filtered_ratios = jiraf.filter_ratios_by_prime_limit(filtered_ratios, primes[j])
			else
				prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class(filtered_ratios, primes[j])	
			end

			local ratios_as_text = jiraf.ratios_to_text(prime_filtered_ratios, "<br>", true)
			result = result .. string.format("| %s\n", ratios_as_text)
		end
		
		result = result .. string.format("|-\n")
	end
	return result	
end

-- Main function variant for prime limit
function p.ji_ratios_in_ed_by_prime_limit(input_et, int_limit, prime_limit, tenney_height, threshold)
	local input_et = input_et or et.parse("12edo")
	local prime_limit = prime_limit or 7
	local tenney_height = tenney_height or 10
	local int_limit = int_limit or 99
	local threshold = threshold or 0.3
	
	-- Get the number of divisions, equave, and et as text (eg edo, edt, etc)
	local steps = input_et["size"]
	local equave = input_et["equave"]
	if tonumber(equave) ~= nil then
		equave = rat.new(equave)
	end
	local et_as_string = et.as_string(input_et)
	
	-- Calculate equave and tolerance
	-- Tolerance is a percentage (threshold) of the step size
	local equave_in_cents = rat.cents(equave)
	local tolerance = equave_in_cents / steps * threshold

	-- Calculate candidate ratios
	-- Then filter based on whether their complements exceed the int limit
	-- Then filter candidate ratios by tenney height (excludes equave factors)
	local candidate_ratios = jiraf.find_candidate_ratios_within_prime_limit(equave_in_cents, int_limit, prime_limit)
	candidate_ratios = jiraf.filter_ratios_by_equave_complement_int_limit(candidate_ratios, int_limit, equave)
	candidate_ratios = jiraf.filter_ratios_by_no_equave_factors_tenney_height(candidate_ratios, tenney_height, equave)
	
	-- Get the primes
	local primes = p.primes_within_prime_limit(prime_limit)
	
	-- Build table headers
	local result = "{| class=\"wikitable center-all\"\n"
		.. "|+ style=\"font-size: 105%;\" | "
		.. string.format("Intervals of %s (as a %d-limit temperament)\n", et_as_string, prime_limit)
		.. "|-\n"
		.. "! rowspan=\"2\" | [[Degree]]\n"
		.. "! rowspan=\"2\" | [[Cent]]s\n"
		.. string.format("! colspan=\"%d\" | Approximated [[JI]] intervals\n", #primes)
		.. "|-\n"
	
	-- Build header cells for each prime limit
	for i = 1, #primes do
		result = result .. string.format("! [[%d-limit]]\n", primes[i])
	end
	result = result .. string.format("|-\n")
	
	-- Add rest of table
	result = result .. p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
	
	result = result .. string.format("|}\n")
	return result
end

-- Main function variant for prime subgroup
function p.ji_ratios_in_ed_by_prime_subgroup(input_et, int_limit, primes, tenney_height, threshold)
	local input_et = input_et or et.parse("12edo")
	local primes = primes or { 2, 3, 5, 11 }
	local tenney_height = tenney_height or 10
	local int_limit = int_limit or 99
	local threshold = threshold or 0.3
	
	-- Get the number of divisions, equave, and et as text (eg edo, edt, etc)
	local steps = input_et["size"]
	local equave = input_et["equave"]
	if tonumber(equave) ~= nil then
		equave = rat.new(equave)
	end
	local et_as_string = et.as_string(input_et)
	
	-- Calculate equave and tolerance
	-- Tolerance is a percentage (threshold) of the step size
	local equave_in_cents = rat.cents(equave)
	local tolerance = equave_in_cents / steps * threshold
	
	-- Calculate candidate ratios
	-- Then filter based on whether their complements exceed the int limit
	-- Then filter candidate ratios by tenney height (excludes equave factors)
	local candidate_ratios = jiraf.find_candidate_ratios_within_subgroup(equave_in_cents, int_limit, primes)
	candidate_ratios = jiraf.filter_ratios_by_equave_complement_int_limit(candidate_ratios, int_limit, equave)
	candidate_ratios = jiraf.filter_ratios_by_no_equave_factors_tenney_height(candidate_ratios, tenney_height, equave)
	
	-- Get subgroup as text
	local subgroup_as_text = p.subgroup_as_text(primes)
	
	-- Build table headers
	local result = "{| class=\"wikitable center-all\"\n"
		.. "|+ style=\"font-size: 105%;\" | "
		.. string.format("Intervals of %s (as a %s subgroup temperament)\n", et_as_string, subgroup_as_text)
		.. "|-\n"
		.. "! rowspan=\"2\" | [[Degree]]\n"
		.. "! rowspan=\"2\" | [[Cent]]s\n"
		.. string.format("! colspan=\"%d\" | Approximated [[JI]] intervals\n", #primes)
		.. "|-\n"
	
	-- Build header cells for each prime limit
	for i = 1, #primes do
		result = result .. string.format("! [[%d-limit]]\n", primes[i])
	end
	result = result .. "|-\n"
	
	-- Add rest of table
	result = result .. p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
	
	result = result .. string.format("|}\n")
	return result
end

-- Wrapper function for primary function; to be called by template
function p.ji_ratios_in_ed_frame(frame)
	-- Parse the ed; if it's just a number, interpret it as an edo
	local input_et_unparsed = frame.args["ED"] or 12
	if tonumber(input_et_unparsed) ~= nil then
		input_et_unparsed = input_et_unparsed .. "edo"
	end
	local input_et = et.parse(input_et_unparsed)
	
	local tenney_height = tonumber(frame.args["Tenney Height"]) or 10
	local int_limit = tonumber(frame.args["Integer Limit"]) or 99
	local threshold = tonumber(frame.args["Threshold"]) or 0.3

	local primes = tonumber(frame.args["Prime Limit"]) or 5
	local temperament_type = "Prime Limit"
	if string.len(frame.args["Subgroup"]) > 0 then 
		primes = tip.parse_numeric_entries(frame.args["Subgroup"], ".") or tip.parse_numeric_entries(frame.args["Subgroup"], ",")
		temperament_type = "Subgroup"
	end
	
	local result = ""
	if temperament_type == "Subgroup" then
		result = p.ji_ratios_in_ed_by_prime_subgroup(input_et, int_limit, primes, tenney_height, threshold)
	elseif temperament_type == "Prime Limit" then
		result = p.ji_ratios_in_ed_by_prime_limit(input_et, int_limit, primes, tenney_height, threshold)
	end
	
	local debugg = yesno(frame.args["debug"])
	if debugg == true then
		result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
	end
	
	return frame:preprocess(result)
end

return p