local rat = require("Module:Rational")
local utils = require("Module:Utils")
local tip = require("Module:Template input parse")
local m = require("Module:Mediants")
p = {}
-- TODO:
-- Adopt mediants module
-- Template for handling multiple entry of JI ratios into a template, and for
-- searching for JI ratios if automatic entry is desired.
-- This is a successor/replacement for JI ratio finder.
-- JI ratios are searched by the following params in a hierarchy:
-- - The absolute minimum for ratio search int limit, which limits the maximum
-- size of the numerator and denominator.
-- - If subgroup is present, ratios are searched by subgroup within an int
-- limit. Subgroup takes precedence over prime limit, as subgroup is
-- (typically) a subset of prime limit, so prime limit is ignored. (Nonprime
-- subgroups take precedence over prime subgroups.)
-- - If prime limit is present, ratios are searched by prime limit within an int
-- limit.
-- NOTES:
-- - Prime limits are infinite sets, so int limit is used to restrain the set
-- to a finite size. The same is true for subgroup.
-- - Tenney height is used for further filtering of ratios, and is considered
-- optional.
-- INT_LIMIT_MAX is hardcoded to limit the size of output.
-- 400 -> ~24000 ratios
-- 300 -> ~14000 ratios
-- 250 -> ~9500 ratios
-- 200 -> ~6000 ratios
-- 150 -> ~3400 ratios
-- 128 -> ~2500 ratios
-- 100 -> ~1500 ratios
local INT_LIMIT_MAX = 200
local DEFAULT_INT_LIMIT = 50
--------------------------------------------------------------------------------
----------------------- INT-LIMIT-BASED SEARCH FUNCTION ------------------------
--------------------------------------------------------------------------------
-- Find JI ratios up to an integer limit within the octave by finding mediants.
-- A cent value can be passed in to either exclude ratios that are above an
-- interval below the octave or include ratios above the octave.
function p.search_by_int_limit(integer_limit, max_cents)
local max_cents = max_cents or 1200
local integer_limit = integer_limit or DEFAULT_INT_LIMIT
integer_limit = math.max(0, math.min(INT_LIMIT_MAX, integer_limit))
local init_ratios = {{1,1}, {2,1}}
local func = m.int_limit_search
local args = integer_limit
local ratios = m.find_mediants_by_search_func(init_ratios, func, args)
-- If the max cents is greater than the octave, duplicate all existing
-- ratios and raise them by the required number of octaves.
if max_cents > 1200 then
local new_ratios = {}
local num_octaves_up = math.ceil(max_cents / 1200)
for j = 1, num_octaves_up do
for i = 2, #ratios do
local num = ratios[i][1] * math.pow(2, j)
local den = ratios[i][2]
local gcd = utils._gcd(num, den)
num = num / gcd
den = den / gcd
if math.max(num, den) <= integer_limit then
table.insert(new_ratios, {num, den})
end
end
end
for i = 1, #new_ratios do
table.insert(ratios, new_ratios[i])
end
end
-- Remove any ratios that exceed the max cents
-- Convert to ratios that Module:Rational can work with
for i = 1, #ratios do
ratios[i] = rat.new(ratios[i][1], ratios[i][2])
end
return ratios
end
--------------------------------------------------------------------------------
------------------------ SUBGROUP-BASED SEARCH FUNCTION ------------------------
--------------------------------------------------------------------------------
-- Subgroup-based search
-- Can support higher int limits than int-limit search can, provided the sub-
-- group is sufficiently small (about 10 members)
function p.search_by_subgroup(subgroup, int_limit, equave)
local subgroup = subgroup or { 2, 3, 7, 11 }
local int_limit = int_limit or 50
local equave = equave or {2,1}
local possible_values = p.find_products(subgroup, int_limit)
local ratios = p.find_ratios_using_values(possible_values, equave)
-- Convert to ratios that Module:Rational can work with
for i = 1, #ratios do
ratios[i] = rat.new(ratios[i][1], ratios[i][2])
end
return ratios
end
-- Helper function
-- Finds all eligible values for the numerator and denominator
function p.find_products(factors, max_product)
local factors = factors or { 2, 3, 7, 11 }
local max_product = max_product or 50
-- Perform a breadth-first-search.
-- Starting with the number 1 at the root node of a (simulated) search tree,
-- explore the possible products (child nodes) of multiplying that number
-- with exactly one each of the given factors. Any products that are less
-- than the max product are added to the search tree, and the search
-- recurses for each child node by finding its children produced by multi-
-- plying by one of each factor. The search on any one branch stops if the
-- resulting products exceed that of the max product.
-- Products are stored as a jagged array, where the index of each inner
-- array is the search depth. Duplicate products are excluded.
-- NOTE: the search starts with the number 1 for this operation to work. To
-- make sense of this, this operation can be thought of a BFS for powers
-- pi raising factors fi (f1^p1 * f2^p2 * ... * fn^pn), so 1 is where each
-- factor fi is raised by zero, thus BFS increases the exponents by 1.
local products = {{1}}
local new_products_found = true
while new_products_found do
local new_products = {}
for i = 1, #factors do
for j = 1, #products[#products] do
local new_product = products[#products][j] * factors[i]
if new_product <= max_product then
local product_already_added = false
for k = 1, #new_products do
product_already_added = product_already_added or new_product == new_products[k]
if product_already_added then break end
end
if not product_already_added then
table.insert(new_products, new_product)
end
end
end
end
if #new_products == 0 then
new_products_found = false
else
table.insert(products, new_products)
end
end
-- Consolidate and sort products
local consolidated_products = {}
for i = 1, #products do
for j = 1, #products[i] do
table.insert(consolidated_products, products[i][j])
end
end
products = consolidated_products
table.sort(products)
return products
end
-- Finds all potential ratios whose numerator and denominator is from the list
-- of given values, and whose value, as a float, is between 1 and a given
-- equave.
function p.find_ratios_using_values(values, equave)
local values = values or p.find_products()
local equave = equave or { 2, 1 }
local equave_as_float = equave[1]/equave[2]
local ratios = {}
for i = 1, #values do
local denominator = values[i]
for j = i, #values do
local numerator = values[j]
local gcd = utils._gcd(numerator, denominator)
if gcd == 1 then
local within_equave = numerator / denominator <= equave_as_float
if within_equave then
table.insert(ratios, {numerator, denominator})
else
break
end
end
end
end
return ratios
end
--------------------------------------------------------------------------------
------------------------- PARAM-BASED SEARCH FUNCTIONS -------------------------
--------------------------------------------------------------------------------
-- Search for ratios based on params passed in. Each param is its own
-- function call. Params must be parsed first.
function p.search_by_params(params, max_cents)
local max_cents = max_cents or 1200
-- First get ratios up to an int limit. If no int limit was passed in, it
-- will default to the hardcoded default value.
local ratios = {}
if params["Int Limit"] ~= nil then
ratios = p.search_by_int_limit(params["Int Limit"], max_cents)
end
if params["Prime Limit"] ~= nil then
ratios = p.filter_by_prime_limit(ratios, params["Prime Limit"])
end
if params["Tenney Height"] ~= nil then
ratios = p.filter_by_tenney_height(ratios, params["Tenney Height"])
end
return ratios
end
-- Parse search params.
function p.parse_search_params(search_params)
local parsed = tip.parse_kv_pairs(search_params)
if parsed["Int Limit"] ~= nil then
parsed["Int Limit"] = tonumber(parsed["Int Limit"])
end
if parsed["Tenney Height"] ~= nil then
parsed["Tenney Height"] = tonumber(parsed["Tenney Height"])
end
if parsed["Prime Limit"] ~= nil then
parsed["Prime Limit"] = tonumber(parsed["Prime Limit"])
end
return parsed
end
function p.search_param_footnotes(search_params)
local result = "Not all notable ratios may be shown, and other interpretations are possible."
if search_params["Prime Limit"] ~= nil then
result = string.format("Ratios shown are within the [[%s-limit]]. %s", search_params["Prime Limit"], result)
elseif search_params["Int Limit"] ~= nil then
result = string.format("Ratios shown are %s-[[integer-limit|integer limit]]. %s", search_params["Int Limit"], result)
end
return result
end
--------------------------------------------------------------------------------
---------------------------- RATIO FILTER FUNCTIONS ----------------------------
--------------------------------------------------------------------------------
-- Filter ratios by Tenney height.
function p.filter_by_tenney_height(ratios, tenney_height)
local tenney_height = tenney_height or 10
local filtered_ratios = {}
for i = 1, #ratios do
local curr_tenney_height = rat.tenney_height(ratios[i])
if curr_tenney_height <= tenney_height then
table.insert(filtered_ratios, ratios[i])
end
end
return filtered_ratios
end
-- Filter ratios by prime limit.
function p.filter_by_prime_limit(ratios, prime_limit)
local prime_limit = prime_limit or 41
local filtered_ratios = {}
for i = 1, #ratios do
local curr_max_prime = rat.max_prime(ratios[i])
if curr_max_prime <= prime_limit then
table.insert(filtered_ratios, ratios[i])
end
end
return filtered_ratios
end
-- Filter ratios by (prime) subgroup. EG: 2.3.5.7
function p.filter_by_subgroup(ratios, subgroup)
end
-- Filter ratios by rational/nonprime subgroup. EG, 2.7/2.11/2, or 2.5.7.9
-- Does not support irrational subgroups.
function p.filter_by_nonprime_subgroup(ratios, subgroup)
end
--------------------------------------------------------------------------------
--------------------------- RATIO SORTING FUNCTIONS ----------------------------
--------------------------------------------------------------------------------
-- Sorts ratios by closeness to cent values.
function p.sort_by_closeness_to_cent_values(ratios, cent_values, tolerance)
local tolerance = tolerance or 30
local sorted_ratios = {}
local curr_index = 1 -- Index of current_ratio
for i = 1, #cent_values do
local lower_bound = cent_values[i] - tolerance
local upper_bound = cent_values[i] + tolerance
local cents_within_range = true
local curr_ratios = {}
for j = curr_index, #ratios do
local curr_ratio = ratios[j]
local curr_cents = rat.cents(curr_ratio)
if lower_bound < curr_cents and curr_cents < upper_bound then
table.insert(curr_ratios, curr_ratio)
--elseif curr_cents > upper_bound then
-- curr_index = j
-- break
end
end
table.insert(sorted_ratios, curr_ratios)
end
return sorted_ratios
end
--------------------------------------------------------------------------------
------------------------ RATIO PARSING/INPUT FUNCTIONS -------------------------
--------------------------------------------------------------------------------
-- Parse a list of ratios from a string. String is formatted as follows:
-- "a/b; c/d; e/f; g/h"
function p.parse_ratios(unparsed)
local parsed = tip.parse_numeric_pairs(unparsed)
for i = 1, #parsed do
parsed[i] = rat.new(parsed[i][1], parsed[i][2])
end
return parsed
end
--------------------------------------------------------------------------------
---------------------------- RATIO STRING FUNCTIONS ----------------------------
--------------------------------------------------------------------------------
-- Convert a table of ratios into a string, with options for links and delimiter
function p.ratios_as_text(ratios, add_links, delimiter)
local add_links = add_links == true
local delimiter = delimiter or ", "
local text = ""
if #ratios ~= 0 then
text = add_links and string.format("[[%s]]", rat.as_ratio(ratios[1])) or rat.as_ratio(ratios[1])
for i = 2, #ratios do
text = text .. (add_links and string.format("%s[[%s]]", delimiter, rat.as_ratio(ratios[i])) or string.format("%s%s", delimiter, rat.as_ratio(ratios[i])))
end
end
return text
end
-- Convert a table of tables into a table of text
function p.ratios_as_texts(ratios, add_links, delimiter)
local add_links = add_links == true
local delimiter = delimiter or ", "
local texts = {}
for i = 1, #ratios do
local text = p.ratios_as_text(ratios[i], add_links, delimiter)
table.insert(texts, text)
end
return texts
end
function p.tester()
local params = p.parse_search_params("Int Limit: 30; Prime Limit: 17")
--ratios = p.search_by_params(params)
--ratios = p.sort_by_closeness_to_cent_values(ratios, {0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200}, 15)
--return p.ratios_as_texts(ratios)
--local ratios = p.search_by_int_limit(250)
--return p.ratios_as_text(ratios) .. " " .. #ratios
-- Using these params with the naive search algorithm (iterating through
-- every number from to to the int limit and checking whether its factors
-- are present in the subgroup) takes several seconds to return only 1563
-- results using these params: factors 2, 3, 7, 11; max product: 10 million.
local factors = { 2, 3 }
local max_product = 5000
return p.ratios_as_text(p.search_by_subgroup(factors, max_product, {3,1}))
--return p.find_products(factors, max_product)
end
return p
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