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 (4) Line Function Params 12 prime_limit_to_subgroup (prime_limit) 24 subgroup_as_string (subgroup) 38 find_ratios_in_ed (input_et, primes, tenney_height, denominator_limit) 118 ji_ratios_in_ed_frame (invokable) (frame)

Lua modules required (6) Variable Module Functions used et Module:ET parse as_string cents interval Module:Interval dependency not used jiraf Module:JI ratio finder find_candidate_ratios_within_subgroup filter_ratios_by_range filter_ratios_by_harmonic_class filter_ratios_by_complement_agnostic_tenney_height ratios_to_text_with_error rat Module:Rational cents new tip Module:Template input parse parse_numeric_entries utils Module:Utils is_prime

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

---

local utils = require('Module:Utils')
local interval = require('Module:Interval')
local rat = require('Module:Rational')
local jiraf = require('Module:JI ratio finder')
local tip = require('Module:Template input parse')
local et = require('Module:ET')
local p = {}

-- Helper function
-- Converts prime limit to subgroup
-- EG, 7-limit becomes 2.3.5.7
function p.prime_limit_to_subgroup(prime_limit)
	local prime_limit = prime_limit or 7
	
	local subgroup = {}
	for i = 2, prime_limit do
		if utils.is_prime(i) then
			table.insert(subgroup, i)
		end
	end
	return subgroup
end

function p.subgroup_as_string(subgroup)
	local subgroup = subgroup or { 2, 3, 5, 7 }
	
	local str = ""
	for i = 1, #subgroup do
		if i ~= #subgroup then
			str = str .. string.format("%d.", subgroup[i])
		else
			str = str .. subgroup[i]
		end
	end
	return str
end

function p.find_ratios_in_ed(input_et, primes, tenney_height, denominator_limit)
	local input_et = input_et or et.parse("12edo")
	local primes = primes or { 2, 3, 5, 7 }
	local tenney_height = tenney_height or 10
	local denominator_limit = denominator_limit or 99
	
	-- Get the number of divisions, equave, and et as text (eg edo, edt, etc)
	local steps = input_et['size']
	local equave = input_et['equave']
	local et_as_string = et.as_string(input_et)
	
	local equave_in_cents = rat.cents(equave)
	local tolerance = equave_in_cents / steps * 0.4
	
	-- Temperament_interpretation
	local subgroup_as_string = p.subgroup_as_string(primes)
	
	-- Find candidate ratios; filter later
	local max_prime = primes[#primes]
	local candidate_ratios = jiraf.find_candidate_ratios_within_subgroup(equave_in_cents, denominator_limit, primes)
	
	-- Build table headers
	local result = string.format('{| class="wikitable center-all"\n')
	result = result .. string.format('|+ Intervals of %s (as a %s subgroup temperament)\n', et_as_string, subgroup_as_string)
	result = result .. string.format('|-\n')
	result = result .. string.format('! rowspan="2" | [[Degree]]\n')
	result = result .. string.format('! rowspan="2" | [[Cent]]s\n')
	result = result .. string.format('! colspan="%d" | Approximated [[JI]] intervals ([[error]] in cents)\n', #primes)
	result = result .. string.format('|-\n')
	
	-- Add table headers for prime limits (technically harmonic classes)
	for i = 1, #primes do
		local current_prime = primes[i]	
		result = result .. string.format('! [[%d-limit]]\n', current_prime)
	end
	result = result .. string.format('|-\n')
	
	-- Build the rows for each step, showing ratios by limit
	for i = 1, steps + 1 do
		local step = i - 1
		
		-- Table headers
		local step_in_cents = et.cents(input_et, step)
		result = result .. string.format('| %d\n', step)
		result = result .. string.format('| %.3f\n', step_in_cents)
		
		-- Override ratios for steps for the unison and equave
		-- Otherwise, filter ratios by range
		local filtered_ratios = {}
		if i == 1 then
			filtered_ratios = { rat.new(1, 1) }
		elseif i == steps + 1 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]
			local prime_filtered_ratios = {}
			
			-- Filter ratios by harmonic class
			prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class(filtered_ratios, current_prime)
			
			-- Filter ratios by complement-agnostic tenney height
			prime_filtered_ratios = jiraf.filter_ratios_by_complement_agnostic_tenney_height(prime_filtered_ratios, tenney_height, equave)
			
			-- Add ratios to cells
			local ratios_as_text = jiraf.ratios_to_text_with_error(prime_filtered_ratios, step_in_cents, "<br>", true)
			result = result .. string.format('| %s\n', ratios_as_text)
		end
		
		result = result .. string.format('|-\n')
	end
	
	result = result .. string.format('|}\n')
	return result
end

function p.ji_ratios_in_ed_frame(frame)
	
	local input_et = et.parse(frame.args["ED"])
	if tonumber(et) ~= nil then
		input_et = input_et .. "edo"
	end

	local primes_as_text = "2.3.5.7.11.13"
	if string.len(frame.args["Primes"]) > 0 then
		primes_as_text = frame.args["Primes"]
	end
	local primes = tip.parse_numeric_entries(primes_as_text, '.') or tip.parse_numeric_entries(primes_as_text, ',')
	
	local tenney_height = tonumber(frame.args["Tenney Height"]) or 10
	local denominator_limit = tonumber(frame.args["Denominator Limit"]) or 99
	
	local result = p.find_ratios_in_ed(input_et, primes, tenney_height, denominator_limit)
	
	return result
end

return p