local rat = require("Module:Rational")
local utils = require("Module:Utils")
local tip = require("Module:Template input parse")
local med = require("Module:Mediants")
p = {}
-- 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:
-- - Search by prime limit. Int limit is used to limit the num/den of ratios.
-- Prime limit takes precedence over subgroup.
-- - Search by subgroup. (Subgroup may contain nonprime numbers, but ratios are
-- currently not supported.) Int limit is used to limit the num/den of ratios.
-- - If neither prime limit or subgroup is present, search by int limit. This
-- is considered the absolute minimum requirement for ratio searching.
-- 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. If omitted, tenney height defaults to infinity.
-- INT_LIMIT_MAX is hardcoded to limit the size of output. This only applies to
-- int limit search, as other search functions (subgroup, prime-limit) may allow
-- higher search maxima. For reference, searching within the octave yields this
-- many ratios:
-- 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 ------------------------
--------------------------------------------------------------------------------
-- Int-limit-based search; finds ratios between 1/1 and an equave, within an int
-- limit. An optional tenney height can be passed in.
-- Int limit is hardcoded to a max size to restrict the size of output, to avoid
-- risk of out-of-memory operations or the like.
function p.search_by_int_limit_within_equave(equave, int_limit, tenney_height)
local int_limit = int_limit or DEFAULT_INT_LIMIT
local equave = equave or rat.new(2,1) -- Defualt equave is 2/1.
local tenney_height = tenney_height or 1/0 -- Defualt tenney height is infinity.
int_limit = math.max(0, math.min(INT_LIMIT_MAX, int_limit))
local init_ratios = {{1,1}, {1,0} }
local search_func = p.int_limit_mediant_search
local search_args = { ["equave"] = equave, ["int_limit"] = int_limit, ["tenney_height"] = tenney_height }
local ratios = med.find_only_mediants_by_search_func(init_ratios, search_func, search_args)
-- 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
-- Remove ratios that exceed the equave.
-- Note that mediant search results in sorted ratios, so remove them from
-- the end until there's no more to remove.
while rat.gt(ratios[#ratios], equave) do
table.remove(ratios, #ratios)
end
return ratios
end
-- Int limit search function, with equave and tenney height cutoffs.
-- If nil is passed in for the tenney height, it will defualt to infinity.
-- To be passed into mediant-search function, as part of int-limit-search
-- function call.
function p.int_limit_mediant_search(mediant_data, search_args)
local mediant = mediant_data["mediant"]
local ratio_1 = mediant_data["ratio_1"]
local equave = search_args["equave"]
local int_limit = search_args["int_limit"]
local tenney_height = search_args["tenney_height"]
local equave_as_float = rat.as_float(equave)
local rat_1_as_float = ratio_1[1] / ratio_1[2]
local mediant_th = math.log(mediant[1] * mediant[2]) / math.log(2)
return math.max(mediant[1], mediant[2]) <= int_limit and rat_1_as_float < equave_as_float and mediant_th <= tenney_height
end
--------------------------------------------------------------------------------
------------------------ SUBGROUP-BASED SEARCH FUNCTION ------------------------
--------------------------------------------------------------------------------
-- Subgroup-based search; finds ratios between 1/1 and an equave, within a sub-
-- group. An int limit is passed in to limit the size of output, since subgroups
-- are infinite sets. An optional tenney height can be passed in to further
-- limit output.
-- Unlike int limit search, subgroup search can allow for very high int limits,
-- as long as the subgroup is reasonably small and has reasonably small terms.
-- Note that members in a subgroup need not be prime, as long as the terms are,
-- for the most part, relatively prime.
function p.search_by_subgroup_within_equave(equave, subgroup, int_limit, tenney_height)
local subgroup = subgroup or { 2, 3, 7 }
local int_limit = int_limit or 50
local equave = equave or rat.new(2,1) -- Defualt equave is 2/1.
local tenney_height = tenney_height or 1/0 -- Defualt tenney height is infinity.
-- Be absolutely sure the subgroup's members are sorted!
table.sort(subgroup)
-- Find all possible products given the factors in the subgroup.
-- These will be used to find all possible ratios.
local products = {{1}}
local new_products_found = true
while new_products_found do
local new_products = {}
for i = 1, #subgroup do
for j = 1, #products[#products] do
local new_product = products[#products][j] * subgroup[i]
if new_product <= int_limit 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)
-- Using the products produced earlier, combine them to make all possible
-- ratios from 1/1 to the equave. Ratios with non-coprime numerator and
-- denominator, or exceed the tenney height, are omitted.
local ratios = {}
local equave_as_float = rat.as_float(equave)
for i = 1, #products do
local denominator = products[i]
for j = i, #products do
local numerator = products[j]
local gcd = utils._gcd(numerator, denominator)
if gcd == 1 then
local within_equave = numerator / denominator <= equave_as_float
local within_tenney_height = math.log(numerator * denominator) / math.log(2) <= tenney_height
if within_equave and within_tenney_height then
table.insert(ratios, {numerator, denominator})
else
break
end
end
end
end
-- 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
--------------------------------------------------------------------------------
---------------------- PRIME-LIMIT-BASED SEARCH FUNCTION -----------------------
--------------------------------------------------------------------------------
-- Int-limit-based search; finds ratios between 1/1 and an equave, within a
-- prime limit. An int limit is passed in to limit the size of output, since
-- prime limits are inifinite sets. An optional tenney height can be passed in
-- to further limit output.
-- Like subgroup search, prime limit search can also allow for very high int
-- limits, as long as the prime is reasonably small.
function p.search_by_prime_limit_within_equave(equave, prime_limit, int_limit, tenney_height)
local prime_limit = prime_limit or 5
local int_limit = int_limit or 1000
local equave = equave or rat.new(2,1) -- Defualt equave is 2/1.
local tenney_height = tenney_height or 1/0 -- Defualt tenney height is infinity.
-- Find all primes up to the prime limit.
local primes = {}
for i = 2, prime_limit do
local is_prime = true
for j = 2, math.floor(math.sqrt(i)) do
if i % j == 0 then
is_prime = false
break
end
end
if is_prime then
table.insert(primes, i)
end
end
-- Perform subgroup search on the primes found, as subgroup-search code can
-- be reused for prime-limit search.
return p.search_by_subgroup_within_equave(equave, primes, int_limit, tenney_height)
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, equave)
local equave = equave or rat.new(2,1)
-- 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_within_equave(equave, params["Int Limit"], 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
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["Int Limit"] ~= nil then
local tenney_height_text = string.format("Ratios shown are within the %s-integer limit", search_params["Int Limit"])
local int_limit_text = search_params["Tenney Height"] ~= nil and string.format(", capped at a Tenney height of %.1f.", search_params["Tenney Height"]) or "."
result = tenney_height_text .. ". " .. result
end
return result
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 ratios (tables, as defined by rational module) into a
-- line of text, with options for delimiters.
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 primes = { 2, 3, 5, 7, 11, 13, 17, 19 }
local ratios = p.search_by_subgroup_within_equave(nil, primes, 4000, nil)
return p.ratios_as_text(ratios)
end
return p
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