Furcht968: ページの作成:「-- This module follows User:Ganaram inukshuk/Provisional style guide for Lua local getArgs = require("Module:Arguments").getArgs local med = require("Module:Mediants") local rat = require("Module:Rational") local tip = require("Module:Template input parse") local utils = require("Module:Utils") local yesno = require("Module:Yesno") local p = {} -- Template for handling multiple entry of JI ratios into a template, and for -- searching for JI ratios if automatic…」

2026-04-01T18:54:24Z

ページの作成:「-- This module follows User:Ganaram inukshuk/Provisional style guide for Lua local getArgs = require("Module:Arguments").getArgs local med = require("Module:Mediants") local rat = require("Module:Rational") local tip = require("Module:Template input parse") local utils = require("Module:Utils") local yesno = require("Module:Yesno") local p = {} -- Template for handling multiple entry of JI ratios into a template, and for -- searching for JI ratios if automatic…」

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-- This module follows [[User:Ganaram inukshuk/Provisional style guide for Lua]]
local getArgs = require("Module:Arguments").getArgs
local med = require("Module:Mediants")
local rat = require("Module:Rational")
local tip = require("Module:Template input parse")
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")

local 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.

-- TODO: Refactor code such that:
-- - For int-limit search, int limit is the first arg, and equave and min/max
-- cents default to 2/1, 0c, and 1200c respectively.
-- (int_limit, equave)
-- (int_limit, min_cents, max_cents)
-- - For odd-limit search, odd limit is the first arg, int limit defaults to
-- twice the odd limit, and equave and min/max cents default to 2/1, 0c, and
-- 1200c respectively.
-- (odd_limit, int_limit, equave)
-- (odd_limit, int_limit, min_cents, max_cents)
-- - For prime-limit search, prime-limit is the first arg, int limit defaults to
-- twice the largest prime, and equave and min/max cents default to 2/1, 0c,
-- and 1200c respectively.
-- (prime_limit, int_limit, equave)
-- (prime_limit, int_limit, min_cents, max_cents)
-- - For subgroup search, subgroup is the first arg, there's no default value
-- for int limit (due to complexity of subgroups), and equave and min/max
-- cents default to 2/1, 0c, and 1200c respectively.
-- (subgroup, int_limit, equave)
-- (subgroup, int_limit, min_cents, max_cents)
-- - Filter ratios function is split into two:
-- - Filter ratios by complement removes ratios from a table if its complement
-- is missing. Complements are octave-complements by default.
-- - Filter ratios by tenney height removes ratios from a table if its tenney
-- height exceeds a passed-in value.

-- TODO: write filter function for cent range

-- Module searches for ratios that are, at the minimum, up to an equave and are
-- up to some integer limit. Search hierarchy is as follows:
-- - Search by subgroup (subgroup elements may be nonprime or rational)
-- - Then search by prime limit
-- - Then search by odd limit
-- - Then search by int limit

-- Optional args omit ratios that don't meet certain conditions, and are used
-- to further limit the number of ratios found. Current options include:
-- - Tenney Height: omits ratios that exceed some max Tenney height. Has no
-- effect if no Tenney height is passed in.
-- - Complements Only: omits ratios and their equave complements if either would
-- be omitted by Tenney height, or if no Tenney height is entered, omits
-- ratios whose complements are missing.

local DEFAULT_EQUAVE = rat.new(2)
local DEFAULT_INT_LIMIT = 30

--------------------------------------------------------------------------------
------------------------------- FILTER FUNCTIONS -------------------------------
--------------------------------------------------------------------------------

-- Filter function removes certain ratios that don't meet some requirement.
-- Filters currently include:
-- - Removing ratios that exceed a max Tenney height.
-- - Removing ratios whose complement would exceed a max Tenney height or int limit
function p.filter_ratios(ratios, equave, int_limit, tenney_height, complements_only)

local filtered_ratios = {}
for i = 1, #ratios do
local complement = rat.mul(rat.inv(ratios[i]), equave)
local ratio_th = rat.tenney_height(ratios[i])
local compl_th = rat.tenney_height(complement)

-- Are the ratios within the Tenney height?
-- Has no effect (defaults to TRUE) if Tenney height is infinity.
local ratio_within_th = ratio_th <= tenney_height
local compl_within_th = compl_th <= tenney_height

-- Is the ratio's complement within the int limit?
local compl_within_int_limit = rat.is_within_int_limit(complement, int_limit)

if complements_only then
if ratio_within_th and compl_within_th and compl_within_int_limit then
table.insert(filtered_ratios, ratios[i])
end
else
if ratio_within_th then
table.insert(filtered_ratios, ratios[i])
end
end
end

return filtered_ratios
end

-- Filters ratios from a table of ratios, returning an array of ratios within
-- the cent range and preserving the original table. Meant for searching for
-- multiple ranges. TODO: write
function p.filter_ratios_within_cent_range(ratios, min_cents, max_cents)

end

--------------------------------------------------------------------------------
-------------------------- INT-LIMIT SEARCH FUNCTION ---------------------------
--------------------------------------------------------------------------------

-- Int limit search finds ratios from 1/1 to an equave, where each ratio's
-- numerator or denominator don't exceed the int limit.
function p.search_by_int_limit(equave, int_limit)
return p.search_by_int_limit_within_cents(0, rat.cents(equave), int_limit)
end

-- Cent range search finds ratios within a cent range. Meant for searching for
-- ratios within a single interval range. If searching for ratios within many
-- interval ranges, then try a broad search first.
function p.search_by_int_limit_within_cents(min_cents, max_cents, int_limit)

local init_ratios = {{1,1}, {1,0}}
local ratios = med.find_only_mediants(init_ratios, 2)
for i = 3, int_limit do
ratios = med.find_mediants_by_int_limit(ratios, i)

-- Purge ratios from the beginning.
-- If the first and second ratio are smaller than min_cents, and smaller
-- than max_cents, then remove the first ratio. Keeping the first ratio
-- would add mediants outside the cent range.
local cents_1 = utils.log2(ratios[1][1] / ratios[1][2]) * 1200
local cents_2 = utils.log2(ratios[2][1] / ratios[2][2]) * 1200
if cents_1 < min_cents and cents_2 <= min_cents and cents_1 < max_cents and cents_2 < max_cents then
table.remove(ratios, 1)
end

-- Purge ratios from the end.
-- If the 2nd-last ratio and last ratio are greater than max_cents, and
-- larger than min_cents, then remove the last ratio. Keeping the last
-- ratio would add mediants outside the cent range.
local cents_3 = utils.log2(ratios[#ratios-1][1] / ratios[#ratios-1][2]) * 1200
local cents_4 = utils.log2(ratios[#ratios ][1] / ratios[#ratios ][2]) * 1200
if cents_3 > max_cents and cents_4 >= max_cents and cents_3 > min_cents and cents_4 > min_cents then
table.remove(ratios, #ratios)
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

-- Remove any remaining ratios that fall outside the cent range.
while rat.cents(ratios[1]) < min_cents do
table.remove(ratios, 1)
end
while rat.cents(ratios[#ratios]) > max_cents do
table.remove(ratios, #ratios)
end

return ratios
end

--------------------------------------------------------------------------------
-------------------------- ODD-LIMIT SEARCH FUNCTION ---------------------------
--------------------------------------------------------------------------------

-- Convert odd limit into equivalent subgroup.
-- EG, 11-odd-limit becomes 2.3.5.7.9.11
-- 2 is part of the subgroup by definition.
function p.odd_limit_to_subgroup(odd_limit)
local subgroup = { rat.new(2) }
for i = 3, odd_limit, 2 do
table.insert(subgroup, rat.new(i))
end
return subgroup
end

function p.search_by_odd_limit(equave, int_limit, odd_limit)
local subgroup = p.odd_limit_to_subgroup(odd_limit)
return p.search_by_subgroup_within_cents(0, rat.cents(equave), int_limit, subgroup)
end

function p.search_by_odd_limit_within_cents(min_cents, max_cents, odd_limit)
local subgroup = p.odd_limit_to_subgroup(odd_limit)
return p.search_by_subgroup_within_cents(min_cents, max_cents, int_limit, subgroup)
end

--------------------------------------------------------------------------------
------------------------- PRIME-LIMIT SEARCH FUNCTION --------------------------
--------------------------------------------------------------------------------

-- Convert prime limit into equivalent subgroup.
-- EG, 11-prime-limit becomes 2.3.5.7.11
function p.prime_limit_to_subgroup(prime_limit)
local subgroup = {}
for i = 3, 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(subgroup, rat.new(i))
end
end
return subgroup
end

-- Prime limit search finds ratios with prime factors that don't exceed some
-- prime limit.
-- Upper bounds for searching is the equave and int limit.
function p.search_by_prime_limit(equave, int_limit, prime_limit)
local subgroup = p.prime_limit_to_subgroup(prime_limit)
return p.search_by_subgroup_within_cents(0, rat.cents(equave), int_limit, subgroup)
end

-- Prime limit search finds ratios with prime factors that don't exceed some
-- prime limit. Searches within a cent range.
function p.search_by_prime_limit_within_cents(min_cents, max_cents, int_limit, prime_limit)
local subgroup = p.prime_limit_to_subgroup(prime_limit)
local ratios = p.search_by_subgroup_within_cents(min_cents, max_cents, int_limit, subgroup)
while rat.cents(ratios[1]) < min_cents do
table.remove(ratios, 1)
end
return ratios
end

--------------------------------------------------------------------------------
---------------------------- SUBGROUP SEARCH FUNCTION --------------------------
--------------------------------------------------------------------------------

-- Subgroup search find ratios that are products of at least two non-unique
-- elements from the subgroup.
function p.search_by_subgroup(equave, int_limit, subgroup)
local ratios = p.search_by_subgroup_within_cents(0, rat.cents(equave), int_limit, subgroup)
return ratios
end

function p.search_by_subgroup_within_cents(min_cents, max_cents, int_limit, subgroup)
--local equave = equave or rat.new(2,1) -- Defualt equave is 2/1.
--local int_limit = int_limit or 50 -- Default is 50
--local subgroup = subgroup or {rat.new(2), rat.new(3), rat.new(7)} -- Default is 2.3.7 subgroup

-- Find all possible ways to multiply subgroup elements with one another
-- using breadth-first-search. Products found this way should not exceed the
-- int limit, and if a subgroup element is rational, neither its numerator
-- nor denominator should exceed the int limit.
local products = { rat.new(1) }
local i = 1
while i <= #products do
-- Multiply each subgroup element by the current ratio. The table of
-- product ratios created this way is merged with the running table of
-- ratios. This is the Cartesian product of the single ratio as a set,
-- with the subgroup elements as a set, or {p/q} X subgroup.
local new_products = {}
for j = 1, #subgroup do
local new_ratio = rat.mul(products[i], subgroup[j])
if rat.is_within_int_limit(new_ratio, int_limit) and not p.find_ratio_in_table(new_products, new_ratio) then
table.insert(new_products, new_ratio)
end
end

-- Merge new products with the table of products, omitting duplicates.
p.merge_tables(products, new_products)
i = i + 1
end

-- Sort for next step
table.sort(products, rat.lt)

-- Use the products found to find all ratios between 1 and the equave.
-- For each ratio in the table of products, create a set of new ratios by
-- having that ratio be the numerator and all successive ratios be possible
-- denominators. Store these new ratios in a table, and repeat with all
-- successive products, omitting duplicats. From earlier testing, this is
-- faster than performing BFS on each ratio, and yields the same results.
local ratios = {}
for i = 1, #products do
local new_ratios = {}
for j = i, #products do
local new_ratio = rat.div(products[j], products[i])
if rat.cents(new_ratio) > max_cents then break end

if not p.find_ratio_in_table(new_ratios, new_ratio) and rat.is_within_int_limit(new_ratio, int_limit) then
table.insert(new_ratios, new_ratio)
end
end

-- Merge new ratios with the table of ratios, omitting duplicates.
p.merge_tables(ratios, new_ratios)
end

-- Sort
table.sort(ratios, rat.lt)

-- Remove ratios less than minimum
while rat.cents(ratios[1]) < min_cents do
table.remove(ratios, 1)
end

return ratios
end

--------------------------------------------------------------------------------
------------------------------- HELPER FUNCTIONS -------------------------------
--------------------------------------------------------------------------------

-- Heleper function; merges elements from source table with destination table
-- while disallowing duplicates.
function p.merge_tables(dest_table, source_table)
for i = 1, #source_table do
if not p.find_ratio_in_table(dest_table, source_table[i]) then
table.insert(dest_table, source_table[i])
end
end
end

-- Helper function for merge function.
function p.find_ratio_in_table(table_, ratio)
local found = false
for i = 1, #table_ do
if rat.as_float(table_[i]) == rat.as_float(ratio) then
found = true
break
end
end
return found
end

--------------------------------------------------------------------------------
---------------------------- RATIO STRING FUNCTIONS ----------------------------
--------------------------------------------------------------------------------

-- Convert a table of ratios into a string, with options for links and delimiter
function p.ratios_as_string(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 jagged array of ratios into an array of strings
function p.ratios_as_strings(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_string(ratios[i], add_links, delimiter)
table.insert(texts, text)
end
return texts
end

--------------------------------------------------------------------------------
---------------------------- ARG-PARSING FUNCTION ------------------------------
--------------------------------------------------------------------------------

-- Parse search args if entered as one string. Use is to be determined.
function p.parse_args(search_args)
local parsed = tip.parse_kv_pairs(search_args)

if parsed["Equave"] ~= nil then
parsed["Equave"] = rat.parse(parsed["Equave"])
end

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

if parsed["Subgroup"] ~= nil then
local subgroup_elements = tip.parse_numeric_pairs(parsed["Subgroup"], ".", "/", true)
for i = 1, #subgroup_elements do
subgroup_elements[i] = rat.new(subgroup_elements[i][1], subgroup_elements[i][2])
end
parsed["Subgroup"] = subgroup_elements
end

if parsed["Complements Only"] ~= nil then
parsed["Complements Only"] = yesno(parsed["Complements Only"])
end

return parsed
end

--------------------------------------------------------------------------------
----------------------------- INVOKABLE FUNCTIONS ------------------------------
--------------------------------------------------------------------------------

-- Function callable by other modules
-- Ratios are returned as a table, for use with other modules.
function p._ji_ratios(args)
-- Args for ease of access
equave = args["Equave" ] or DEFAULT_EQUAVE
int_limit = args["Int Limit" ] or DEFAULT_INT_LIMIT
odd_limit = args["Odd Limit" ]
prime_limit = args["Prime Limit"]
subgroup = args["Subgroup" ]

-- Filtering args
tenney_height = args["Tenney Height" ] or 1/0 -- Default Tenney height is infinity
complements_only = args["Complements Only"] or false -- Default is to include all ratios

local ratios = {}
if subgroup ~= nil then
ratios = p.search_by_subgroup(equave, int_limit, subgroup)
elseif prime_limit ~= nil then
ratios = p.search_by_prime_limit(equave, int_limit, prime_limit)
elseif int_limit ~= nil then
ratios = p.search_by_int_limit(equave, int_limit)
end

-- Filter ratios
ratios = p.filter_ratios(ratios, equave, int_limit, tenney_height, complements_only)

return ratios
end

-- Invokable function; for templates
-- Ratios are returned as a comma-delimited list. For finer control, it's
-- necessary to call the "main" function, then further process the results.
function p.ji_ratios(frame)
args = getArgs(frame)

-- Preprocess equave
-- Ratios are searched from 1/1 to some equave (default 2/1), so an equave
-- must be passed in.
args["Equave"] = args["Equave"] ~= nil and rat.parse(args["Equave"])

-- Preprocess int limit
-- Ratios are searched up to some int limit (default 50), so an int limit
-- must be passed in.
args["Int Limit"] = args["Int Limit"] ~= nil and tonumber(args["Int Limit"])

-- Preprocess Tenney height
if args["Tenney Height"] ~= nil then
args["Tenney Height"] = tonumber(args["Tenney Height"])
end

-- Preprocess prime limit
if args["Prime Limit"] ~= nil then
args["Prime Limit"] = tonumber(args["Prime Limit"])
end

-- Preprocess subgroup
if args["Subgroup"] ~= nil then
local subgroup_elements = tip.parse_numeric_pairs(args["Subgroup"], ".", "/", true)
for i = 1, #subgroup_elements do
subgroup_elements[i] = rat.new(subgroup_elements[i][1], subgroup_elements[i][2])
end
args["Subgroup"] = subgroup_elements
end

if args["Complements Only"] ~= nil then
args["Complements Only"] = yesno(args["Complements Only"], false)
end

-- Find and return ratios
local result = p.ratios_as_string(p._ji_ratios(args))
local debugg = yesno(frame.args["debug"])

if debugg == true then
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end

return frame:preprocess(result)

end

function p.tester()
--return p.ratios_as_string(p._ji_ratios(p.parse_args("Int Limit: 16; Equave: 3/1; Complements Only: 0")))
--return p.ratios_as_string(p.search_by_prime_limit_within_cents(372, 440, 17, 30))
return p.ratios_as_string(p.search_by_odd_limit(rat.new(2), 15, 15*2))
end

--------------------------------------------------------------------------------
---------------------------- FUNCTIONS TO BE MOVED -----------------------------
--------------------------------------------------------------------------------

-- 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

-- Sorts ratios by closeness to cent values. Move to new module?
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

return p

モジュール:JI ratios - 版の履歴