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Module:Mediants: Difference between revisions

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local mos = require("Module:MOS") -- For testing
-- This module follows [[User:Ganaram inukshuk/Provisional style guide for Lua]]
local utils = require("Module:Utils") -- For testing
local rat  = require("Module:Rational")
local utils = require("Module:Utils")
 
local p = {}
local p = {}


-- Module for finding mediants, either by search depth or by search function.
-- Mediants consists of code used to find a tree of mediants, starting from a
-- set of starting ratios (default 1/1 and 1/0). Search can be by int limit,
-- depth, or a custom search function.
-- Ratios produced this way are a table consisting of the numerator and
-- denominator, which allows for non-simplified ratios to be represented.
 
--------------------------------------------------------------------------------
------------------------------ UTILITY FUNCTIONS -------------------------------
--------------------------------------------------------------------------------
 
-- Given a table of depths, return the deepest depth
function p.deepest_depth(depths)
local deepest = nil
for _, value in ipairs(depths) do
if not deepest or value > deepest then
deepest = value
end
end
return deepest
end
 
-- Given a ratio, return its simplified form.
function p.simplify_ratio(ratio)
local gcd = utils._gcd(ratio[1], ratio[2])
return { ratio[1] / gcd, ratio[2] / gcd }
end
 
-- Sort ratios in ascending order. Comparison function is built-in.
function p.sort_ratios(ratios)
table.sort(ratios, function(ratio_1, ratio_2)
return ratio_1[1] / ratio_1[2] < ratio_2[1] / ratio_2[2]
end
)
end
 
--------------------------------------------------------------------------------
----------------------------- CONVERTER FUNCTIONS ------------------------------
--------------------------------------------------------------------------------
 
-- Converts ratios into the form defined by [[Module:Rational]], a table
-- consisting of its prime factorization.
 
-- Given a single ratio, as a table of two numbers, convert to rational and
-- return it.
function p.to_rational(ratio)
return rat.new(ratio[1], ratio[2])
end


-- TODO
-- Given a table of ratios, each a table of two numbers, return an array of
-- Make two classes of filter functions: one that returns both mediants AND
-- ratios in the form as defined by module:Rational.
-- depths, and one that returns only mediants. Filter functions therefore come
function p.to_rationals(ratios)
-- in two forms: two params (mediant, args) and three params (mediant, depth,
local rats = {}
-- args).
for i = 1, #ratios do
table.insert(rats, p.to_rational(ratios[i]))
end
return rats
end


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
------------------------------- FILTER FUNCTIONS -------------------------------
------------------------------- SEARCH FUNCTIONS -------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------


-- Filter functions determine whether a mediant meets a specific criteria for
-- Search functions determine whether a mediant meets a specific criteria for
-- being added to a set of mediants, be it based on something about the mediant,
-- being added to a set of mediants, be it based on something about the mediant,
-- its search depth, or both.
-- its search depth, the ratios that produced the mediant, or any combination
-- thereof.
-- NOTE: some search criteria, such as prime limit, are considered unsuitable,
-- since mediants not within a prime limit are used to find ratios within a
-- prime limit, it will likely prevent desired ratios from being found at all.
-- For this reason, these functions are meant for broad search, and finer
-- filtering must be done afterwards.


-- A filter function has three params: mediant, depth, and a set of args, which
-- A search function has two params: a table containing the mediant and the
-- can be a single value or a table of values.
-- depth it was found at, and a search param.
-- Mediant data is a table that contains the mediant, the search depth it was
-- found at, and the two ratios that were used to find the mediant.
-- The search params can be a single numeric value, or a table of values for
-- finer control.


-- Int limit filter determines whether a ratio is within an int limit. Does not
-- Int limit search determines whether a ratio is within an int limit. Only uses
-- use depth.
-- information about the mediant. Meant for use with searching for JI ratios.
function p.int_limit_filter(mediant, depth, int_limit)
function p.int_limit_search(mediant_data, int_limit)
local mediant = mediant_data["mediant"]
return math.max(mediant[1], mediant[2]) <= int_limit
return math.max(mediant[1], mediant[2]) <= int_limit
end
end


-- Depth filter determines whether a ratio is within a target depth. Does not
-- Depth search determines whether a ratio is within a target depth. Only uses
-- use the mediant itself.
-- the depth it was found at. Meant for use with searching for step ratios.
function p.search_depth_filter(mediant, depth, search_depth)
function p.depth_search(mediant_data, search_depth)
local depth = mediant_data["depth"]
return depth <= search_depth
return depth <= search_depth
end
-- Tenney height filter determines whether a ratio is within a target Tenney
-- height. Does not use depth.
function p.tenney_height_filter(mediant, depth, tenney_height)
return math.log(mediant[1] * mediant[2]) / math.log(2) <= tenney_height
end
end


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-- Find mediants by filter, where the filter function and its args are passed in
-- Find mediants by filter, where the filter function and its args are passed in
-- as part of the function call.
-- as part of the function call.
function p.find_mediants_by_filter(init_ratios, filter_func, filter_args)
function p.find_mediants_by_search_func(init_ratios, search_func, search_args)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local init_ratios = init_ratios or {{1,1}, {1,0}}
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table.insert(new_depths, depth_1)
table.insert(new_depths, depth_1)
if filter_func(mediant, new_depth, filter_args) then
local mediant_data = { ["mediant"] = mediant, ["depth"] = new_depth, ["ratio_1"] = ratio_1, ["ratio_2"] = ratio_2 }
if search_func(mediant_data, search_args) then
table.insert(new_ratios, mediant)
table.insert(new_ratios, mediant)
table.insert(new_depths, new_depth)
table.insert(new_depths, new_depth)
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-- Find mediants by filter, where the filter function and its args are passed in
-- Find mediants by filter, where the filter function and its args are passed in
-- as part of the function call. Only returns mediants, not depths.
-- as part of the function call. Only returns mediants, not depths.
function p.find_only_mediants_by_filter(init_ratios, filter_func, filter_args)
function p.find_only_mediants_by_search_func(init_ratios, search_func, search_args)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local init_ratios = init_ratios or {{1,1}, {1,0}}
local ratios, depths
local ratios, depths
ratios, depths = p.find_mediants_by_filter(init_ratios, filter_func, filter_args)
ratios, depths = p.find_mediants_by_search_func(init_ratios, search_func, search_args)
return ratios
return ratios
end
end
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-- Depth-based search finds mediants by building a tree of mediants up to a
-- Depth-based search finds mediants by building a tree of mediants up to a
-- specified depth. This is made a standalone function under the reasoning that
-- specified depth. This is made a standalone function under the reasoning that
-- depth-based search is a common enough operation (EG, JI ratio search, tuning
-- it's a common enough operation.
-- spectrum step ratio search).


-- Find mediants by depth, how many times mediants are found in a set of ratios.
-- Find mediants by depth of its search tree.
function p.find_mediants(init_ratios, depth)
function p.find_mediants(init_ratios, depth)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local init_ratios = init_ratios or {{1,1}, {1,0}}
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local ratios, depths
local ratios, depths
ratios, depths = p.find_mediants_by_filter(init_ratios, p.search_depth_filter, depth)
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.depth_search, depth)
return ratios, depths
return ratios, depths
end
end


-- Find mediants by depth, how many times mediants are found in a set of ratios.
-- Find mediants by depth of its search tree. Does not return depths.
-- Does not return depths.
function p.find_only_mediants(init_ratios, depth)
function p.find_only_mediants(init_ratios, depth)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local init_ratios = init_ratios or {{1,1}, {1,0}}
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local ratios, depths
local ratios, depths
ratios, depths = p.find_mediants_by_filter(init_ratios, p.search_depth_filter, depth)
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.depth_search, depth)
return ratios
end
 
--------------------------------------------------------------------------------
---------------------- INT-LIMIT-BASED SEARCH FUNCTION -------------------------
--------------------------------------------------------------------------------
 
-- Int limit search finds mediants up to an integer limit, not permitting ratios
-- whose numerator or denominator exceeds the int limit. This is made a stand-
-- alone function under the reasoning that it's a common enough operation.
 
-- Find mediants within an int limit.
function p.find_mediants_by_int_limit(init_ratios, int_limit)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local int_limit = int_limit or 50
local ratios, depths
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.int_limit_search, int_limit)
return ratios, depths
end
 
-- Find mediants within an int limit. Does not return depth.
function p.find_only_mediants_by_int_limit(init_ratios, int_limit)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local int_limit = int_limit or 50
local ratios, depths
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.int_limit_search, int_limit)
return ratios
return ratios
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function p.tester()
function p.tester()
local func = p.int_limit_filter
--return p.find_only_mediants_by_int_limit()
local ratios = {{4,3}, {5,1}, {3,2}}
local ratios, depths = p.find_mediants_by_filter({{1,1}, {1,0}}, func, 12)
p.sort_ratios(ratios)
ratios = p.find_mediants({{1,1}, {1,0}}, 6)
return p.to_rationals(ratios)
local generators = {}
for i = 1, #ratios do
local input_mos = mos.new(5,2)
local gen = mos.bright_gen_to_cents(input_mos, ratios[i])
local gcd = utils._gcd(ratios[i][1], ratios[i][2])
local edo = (ratios[i][1] * 5 + ratios[i][2] * 2)/gcd
local new_string = string.format("%s:%s\t%sedo\t%.3f", ratios[i][1]/gcd, ratios[i][2]/gcd, edo, gen)
table.insert(generators, new_string)
end
return generators
end
end


return p
return p
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