Xenharmonic Wiki

Module:JI ratios: Difference between revisions

← Older edit
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
m Rename functions
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
m comments
 
(68 intermediate revisions by 2 users not shown)
Line 1: Line 1:
-- 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 rat = require("Module:Rational")
local tip = require("Module:Template input parse")
local utils = require("Module:Utils")
local utils = require("Module:Utils")
local tip = require("Module:Template input parse")
local yesno = require("Module:Yesno")
local med = require("Module:Mediants")
 
p = {}
local p = {}


-- Template for handling multiple entry of JI ratios into a template, and for
-- Template for handling multiple entry of JI ratios into a template, and for
Line 9: Line 13:
-- This is a successor/replacement for JI ratio finder.
-- This is a successor/replacement for JI ratio finder.


-- JI ratios are searched by the following params in a hierarchy:
-- TODO: Refactor code such that:
-- - Search by prime limit. Int limit is used to limit the num/den of ratios.
-- - For int-limit search, int limit is the first arg, and equave and min/max
--  Prime limit takes precedence over subgroup.
--  cents default to 2/1, 0c, and 1200c respectively.
-- - Search by subgroup. (Subgroup may contain nonprime numbers, but ratios are
--   (int_limit, equave)
--  currently not supported.) Int limit is used to limit the num/den of ratios.
--  (int_limit, min_cents, max_cents)
-- - If neither prime limit or subgroup is present, search by int limit. This
-- - For odd-limit search, odd limit is the first arg, int limit defaults to
--  is considered the absolute minimum requirement for ratio searching.
--  twice the odd limit, and equave and min/max cents default to 2/1, 0c, and
-- NOTES:
--  1200c respectively.
-- - Prime limits are infinite sets, so int limit is used to restrain the set
--  (odd_limit, int_limit, equave)
--   to a finite size. The same is true for subgroup.
--  (odd_limit, int_limit, min_cents, max_cents)
-- - Tenney height is used for further filtering of ratios, and is considered
-- - For prime-limit search, prime-limit is the first arg, int limit defaults to
--  optional. If omitted, tenney height defaults to infinity.
--  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.


-- INT_LIMIT_MAX is hardcoded to limit the size of output. This only applies to
local DEFAULT_EQUAVE = rat.new(2)
-- int limit search, as other search functions (subgroup, prime-limit) may allow
local DEFAULT_INT_LIMIT = 30
-- 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 ------------------------
------------------------------- FILTER FUNCTIONS -------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Int-limit-based search; finds ratios between 1/1 and an equave, within an int
-- Filter function removes certain ratios that don't meet some requirement.
-- limit. An optional tenney height can be passed in.
-- Filters currently include:
-- Int limit is hardcoded to a max size to restrict the size of output, to avoid
-- - Removing ratios that exceed a max Tenney height.
-- risk of out-of-memory operations or the like.
-- - Removing ratios whose complement would exceed a max Tenney height or int limit
function p.search_within_equave(equave, int_limit, tenney_height)
function p.filter_ratios(ratios, equave, int_limit, tenney_height, complements_only)
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 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 init_ratios = {{1,1}, {1,0}}
local search_func = p.int_limit_mediant_search
local ratios = med.find_only_mediants(init_ratios, 2)
local search_args = { ["equave"] = equave, ["int_limit"] = int_limit, ["tenney_height"] = tenney_height }
for i = 3, int_limit do
local ratios = med.find_only_mediants_by_search_func(init_ratios, search_func, search_args)
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
-- Convert to ratios that Module:Rational can work with
Line 61: Line 150:
end
end
-- Remove ratios that exceed the equave.
-- Remove any remaining ratios that fall outside the cent range.
-- Note that mediant search results in sorted ratios, so remove them from
while rat.cents(ratios[1]) < min_cents do
-- the end until there's no more to remove.
table.remove(ratios, 1)
while rat.gt(ratios[#ratios], equave) do
end
while rat.cents(ratios[#ratios]) > max_cents do
table.remove(ratios, #ratios)
table.remove(ratios, #ratios)
end
end
Line 71: Line 161:
end
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.
-------------------------- ODD-LIMIT SEARCH FUNCTION ---------------------------
-- 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)
-- Convert odd limit into equivalent subgroup.
local mediant  = mediant_data["mediant"]
-- EG, 11-odd-limit becomes 2.3.5.7.9.11
local ratio_1  = mediant_data["ratio_1"]
-- 2 is part of the subgroup by definition.
local equave        = search_args["equave"]
function p.odd_limit_to_subgroup(odd_limit)
local int_limit    = search_args["int_limit"]
local subgroup = { rat.new(2) }
local tenney_height = search_args["tenney_height"]
for i = 3, odd_limit, 2 do
table.insert(subgroup, rat.new(i))
local equave_as_float = rat.as_float(equave)
end
local rat_1_as_float = ratio_1[1] / ratio_1[2]
return subgroup
local mediant_th = math.log(mediant[1] * mediant[2]) / math.log(2)
end
 
return math.max(mediant[1], mediant[2]) <= int_limit and rat_1_as_float < equave_as_float and mediant_th <= tenney_height
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
end


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
------------------------ SUBGROUP-BASED SEARCH FUNCTION ------------------------
------------------------- PRIME-LIMIT SEARCH FUNCTION --------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Subgroup-based search; finds ratios between 1/1 and an equave, within a sub-
-- Convert prime limit into equivalent subgroup.
-- group. An int limit is passed in to limit the size of output, since subgroups
-- EG, 11-prime-limit becomes 2.3.5.7.11
-- are infinite sets. An optional tenney height can be passed in to further
function p.prime_limit_to_subgroup(prime_limit)
-- limit output.
local subgroup = {}
-- Unlike int limit search, subgroup search can allow for very high int limits,
for i = 3, prime_limit do
-- as long as the subgroup is reasonably small and has reasonably small terms.
local is_prime = true
-- Note that members in a subgroup need not be prime, as long as the terms are,
for j = 2, math.floor(math.sqrt(i)) do
-- for the most part, relatively prime.
if i % j == 0 then
function p.search_by_subgroup_within_equave(subgroup, equave, int_limit, tenney_height)
is_prime = false
local subgroup = subgroup or { 2, 3, 7 }
break
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
end
end
if #new_products == 0 then
if is_prime then
new_products_found = false
table.insert(subgroup, rat.new(i))
else
table.insert(products, new_products)
end
end
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
-- Consolidate and sort products
-- Find all possible ways to multiply subgroup elements with one another
local consolidated_products = {}
-- using breadth-first-search. Products found this way should not exceed the
for i = 1, #products do
-- int limit, and if a subgroup element is rational, neither its numerator
for j = 1, #products[i] do
-- nor denominator should exceed the int limit.
table.insert(consolidated_products, products[i][j])
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
end
-- Merge new products with the table of products, omitting duplicates.
p.merge_tables(products, new_products)
i = i + 1
end
end
products = consolidated_products
table.sort(products)
-- Sort for next step
 
table.sort(products, rat.lt)
-- Using the products produced earlier, combine them to make all possible
-- ratios from 1/1 to the equave. Ratios with non-coprime numerator and
-- Use the products found to find all ratios between 1 and the equave.
-- denominator, or exceed the tenney height, are omitted.
-- 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 = {}
local ratios = {}
local equave_as_float = rat.as_float(equave)
for i = 1, #products do
for i = 1, #products do
local denominator = products[i]
local new_ratios = {}
for j = i, #products do
for j = i, #products do
local numerator = products[j]
local new_ratio = rat.div(products[j], products[i])
local gcd = utils._gcd(numerator, denominator)
if rat.cents(new_ratio) > max_cents then break end
if gcd == 1 then
local within_equave = numerator / denominator <= equave_as_float
if not p.find_ratio_in_table(new_ratios, new_ratio) and rat.is_within_int_limit(new_ratio, int_limit) then
local within_tenney_height = math.log(numerator * denominator) / math.log(2) <= tenney_height
table.insert(new_ratios, new_ratio)
if within_equave and within_tenney_height then
table.insert(ratios, {numerator, denominator})
else
break
end
end
end
end
end
-- Merge new ratios with the table of ratios, omitting duplicates.
p.merge_tables(ratios, new_ratios)
end
end
 
-- Convert to ratios that Module:Rational can work with
-- Sort
for i = 1, #ratios do
table.sort(ratios, rat.lt)
ratios[i] = rat.new(ratios[i][1], ratios[i][2])
-- Remove ratios less than minimum
while rat.cents(ratios[1]) < min_cents do
table.remove(ratios, 1)
end
end
Line 179: Line 305:


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
---------------------- PRIME-LIMIT-BASED SEARCH FUNCTION -----------------------
------------------------------- HELPER FUNCTIONS -------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Int-limit-based search; finds ratios between 1/1 and an equave, within a
-- Heleper function; merges elements from source table with destination table
-- prime limit. An int limit is passed in to limit the size of output, since
-- while disallowing duplicates.
-- prime limits are inifinite sets. An optional tenney height can be passed in
function p.merge_tables(dest_table, source_table)
-- to further limit output.
for i = 1, #source_table do
-- Like subgroup search, prime limit search can also allow for very high int
if not p.find_ratio_in_table(dest_table, source_table[i]) then
-- limits, as long as the prime is reasonably small.
table.insert(dest_table, source_table[i])
function p.search_by_prime_limit_within_equave(prime_limit, equave, 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
end
if is_prime then
end
table.insert(primes, i)
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
end
end
return found
-- 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(primes, equave, int_limit, tenney_height)
end
end


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
------------------------- PARAM-BASED SEARCH FUNCTIONS -------------------------
---------------------------- RATIO STRING FUNCTIONS ----------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Search for ratios based on params passed in. Each param is its own
-- Convert a table of ratios into a string, with options for links and delimiter
-- function call. Params must be parsed first.
function p.ratios_as_string(ratios, add_links, delimiter)
function p.search_by_params(params, equave)
local add_links = add_links == true
local equave = equave or rat.new(2,1)
local delimiter = delimiter or ", "
-- First get ratios up to an int limit. If no int limit was passed in, it
local text = ""
-- will default to the hardcoded default value.
if #ratios ~= 0 then
local ratios = {}
text = add_links and string.format("[[%s]]", rat.as_ratio(ratios[1])) or rat.as_ratio(ratios[1])
if params["Int Limit"] ~= nil then
for i = 2, #ratios do
ratios = p.search_within_equave(equave, params["Int Limit"], params["Tenney Height"])
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
end
return ratios
return texts
end
end


-- Parse search params.
--------------------------------------------------------------------------------
function p.parse_search_params(search_params)
---------------------------- ARG-PARSING FUNCTION ------------------------------
local parsed = tip.parse_kv_pairs(search_params)
--------------------------------------------------------------------------------
 
-- 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
if parsed["Int Limit"] ~= nil then
Line 242: Line 380:
if parsed["Tenney Height"] ~= nil then
if parsed["Tenney Height"] ~= nil then
parsed["Tenney Height"] = tonumber(parsed["Tenney Height"])
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
end
Line 247: Line 401:
end
end


function p.search_param_footnotes(search_params)
--------------------------------------------------------------------------------
local result = "Not all notable ratios may be shown, and other interpretations are possible."
----------------------------- 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
if search_params["Int Limit"] ~= nil then
-- Preprocess prime limit
local tenney_height_text = string.format("Ratios shown are within the %s-integer limit", search_params["Int Limit"])
if args["Prime Limit"] ~= nil then
local int_limit_text = search_params["Tenney Height"] ~= nil and string.format(", capped at a Tenney height of %.1f.", search_params["Tenney Height"]) or "."
args["Prime Limit"] = tonumber(args["Prime Limit"])
result = tenney_height_text .. ". " .. result
end
end
return result
-- 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
end


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
--------------------------- RATIO SORTING FUNCTIONS ----------------------------
---------------------------- FUNCTIONS TO BE MOVED -----------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Sorts ratios by closeness to cent values.
-- 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)
function p.sort_by_closeness_to_cent_values(ratios, cent_values, tolerance)
local tolerance = tolerance or 30
local tolerance = tolerance or 30
Line 290: Line 533:
return sorted_ratios
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
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:JI_ratios"