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 (5) Line Function Params 13 primes_within_prime_limit (prime_limit) 27 primes_as_subgroup (primes) 48 primes_as_temperament_interpretation (primes) 63 find_ratios_in_ed (input_et, primes, tenney_height, int_limit) 153 ji_ratios_in_ed_frame (invokable) (frame)

Lua modules required (6) Variable Module Functions used et Module:ET parse as_string 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_equave_complement_int_limit filter_ratios_by_no_equave_factors_tenney_height ratios_to_text_with_error rat Module:Rational new cents 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
-- 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 into a subgroup
function p.primes_as_subgroup(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
-- Given a set of primes, find its temperament interpretation; IE, is it a
-- prime subgroup temperament (EG, 2.3.7) or a prime-limit temperament (EG,
-- 7-limit)?
-- If the set of primes is a prime limit, then it should contain all the primes
-- between 2 (inclusive) and the largest prime (inclusive). If it skips any
-- primes, then it's a subgroup.
function p.primes_as_temperament_interpretation(primes)
	local primes = primes or { 2, 3, 5, 7 }
	local primes_to_compare = p.primes_within_prime_limit(primes[#primes])
	
	local temperament_interpretation = ""
	if p.primes_as_subgroup(primes) == p.primes_as_subgroup(primes_to_compare) then
		temperament_interpretation = string.format("%d-limit", primes[#primes])
	else
		temperament_interpretation = p.primes_as_subgroup(primes) .. " subgroup"
	end
	
	return temperament_interpretation
end

-- Primary function
function p.find_ratios_in_ed(input_et, primes, tenney_height, int_limit)
	local input_et = input_et or et.parse("12ed5/2")
	local primes = primes or { 2, 3, 5, 7 }
	local tenney_height = tenney_height or 10
	local int_limit = int_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']
	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 +/- 40 cents or 40% of a step, whichever is smaller.
	local equave_in_cents = rat.cents(equave)
	local tolerance = math.min(equave_in_cents / steps * 0.4, 40)
	
	-- Calculate temperament interpretation
	local temperament_interpretation = p.primes_as_temperament_interpretation(primes)
		
	-- Find candidate ratios; filter later
	local max_prime = primes[#primes]
	local candidate_ratios = jiraf.find_candidate_ratios_within_subgroup(equave_in_cents, int_limit, primes)
	
	-- Build table headers
	local result = string.format('{| class="wikitable center-all"\n')
	result = result .. string.format('|+ Intervals of %s (as a %s temperament)\n', et_as_string, temperament_interpretation)
	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 = (step / steps) * rat.cents(equave)
		result = result .. string.format('| %d\n', step)
		result = result .. string.format('| %.3f\n', step_in_cents)
		
		filtered_ratios = jiraf.filter_ratios_by_range(candidate_ratios, step_in_cents - tolerance, step_in_cents + tolerance)
		
		-- Add ratios according to harmonic class
		for j = 1, #primes do
			local current_prime = primes[j]
			local prime_filtered_ratios = {}
			
			-- Override filtered ratios denpending on whether the ratio is the
			-- unison or equave
			if step == 0 and j == 1 then
				prime_filtered_ratios = { rat.new(1) }
			elseif step == 0 and j ~= 1 then
				prime_filtered_ratios = {}
			elseif step == steps then
				prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class({ equave }, current_prime)
			else
				-- Filter ratios by harmonic class, then whether the ratios'
				-- equave complement exceeds the int limit, then by
				-- no-equave-factors tenney height (nefth).
				prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class(filtered_ratios, current_prime)
				prime_filtered_ratios = jiraf.filter_ratios_by_equave_complement_int_limit(prime_filtered_ratios, int_limit, equave)
				prime_filtered_ratios = jiraf.filter_ratios_by_no_equave_factors_tenney_height(prime_filtered_ratios, tenney_height, equave)
			end
			
			-- Add ratios to cells
			-- TODO: make first column go by prime limit (this way, the unison
			-- is not excluded), with successive columns by harmonic class.
			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

-- 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"]
	if tonumber(input_et_unparsed) ~= nil then
		input_et_unparsed = input_et_unparsed .. "edo"
	end
	local input_et = et.parse(input_et_unparsed)

	local primes = { 2, 3, 5, 7 }
	if string.len(frame.args["Subgroup"]) > 0 then 
		primes = tip.parse_numeric_entries(frame.args["Subgroup"], '.') or tip.parse_numeric_entries(frame.args["Subgroup"], ',')
	end
	if string.len(frame.args["Prime Limit"]) > 0 and string.len(frame.args["Subgroup"]) == 0 then
		primes = p.primes_within_prime_limit(tonumber(frame.args["Prime Limit"]))
	end
	
	local tenney_height = tonumber(frame.args["Tenney Height"]) or 10
	local int_limit = tonumber(frame.args["Integer Limit"]) or 99
	
	local result = p.find_ratios_in_ed(input_et, primes, tenney_height, int_limit)
	
	return result
end

return p