local mos = require("Module:MOS") -- For testing
local utils = require("Module:Utils") -- For testing
local p = {}
-- Module for finding mediants, either by search depth or by search function.
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------------------------------- SEARCH FUNCTIONS -------------------------------
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-- 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,
-- its search depth, or both.
-- 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 search function has two params: a table containing the mediant and the
-- depth it was found at, and a search param (which can be a table of search
-- params, for finer control).
-- Int limit search determines whether a ratio is within an int limit. Does not
-- use depth.
function p.int_limit_search(mediant_data, int_limit)
local mediant = mediant_data["mediant"]
return math.max(mediant[1], mediant[2]) <= int_limit
end
-- Depth search determines whether a ratio is within a target depth. Does not
-- use the mediant itself.
function p.depth_search(mediant_data, search_depth)
local depth = mediant_data["depth"]
return depth <= search_depth
end
-- Tenney height search determines whether a ratio is within a target Tenney
-- height. Does not use depth.
function p.tenney_height_search(mediant_data, tenney_height)
local mediant = mediant_data["mediant"]
return math.log(mediant[1] * mediant[2]) / math.log(2) <= tenney_height
end
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---------------------------- GENERAL SEARCH FUNCTION ---------------------------
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-- General search function searches for mediants using a filter function. A
-- custom filter function can be passed in to "filter" out mediants. Ratios
-- are added using a while loop, which exits if a loop iteration adds no new
-- ratios.
-- Find mediants by filter, where the filter function and its args are passed in
-- as part of the function call.
function p.find_mediants_by_search_func(init_ratios, search_func, search_args)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local ratios = {}
local depths = {}
for i = 1, #init_ratios do
table.insert(ratios, init_ratios[i])
table.insert(depths, 0)
end
local new_ratios_added = true
while new_ratios_added do
new_ratios_added = false
local new_ratios = {}
local new_depths = {}
for i = 1, #ratios-1 do
local ratio_1 = ratios[i]
local ratio_2 = ratios[i+1]
local mediant = { ratio_1[1] + ratio_2[1], ratio_1[2] + ratio_2[2] }
table.insert(new_ratios, ratio_1)
local depth_1 = depths[i]
local depth_2 = depths[i+1]
local new_depth = math.max(depth_1, depth_2) + 1
table.insert(new_depths, depth_1)
local mediant_data = { ["mediant"] = mediant, ["depth"] = new_depth }
if search_func(mediant_data, search_args) then
table.insert(new_ratios, mediant)
table.insert(new_depths, new_depth)
new_ratios_added = true
end
end
table.insert(new_ratios, ratios[#ratios])
table.insert(new_depths, depths[#depths])
ratios = new_ratios
depths = new_depths
end
return ratios, depths
end
-- 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.
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 ratios, depths
ratios, depths = p.find_mediants_by_search_func(init_ratios, search_func, search_args)
return ratios
end
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------------------------- DEPTH-BASED SEARCH FUNCTION --------------------------
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-- 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
-- depth-based search is a common enough operation (EG, JI ratio search, tuning
-- spectrum step ratio search).
-- Find mediants by depth, how many times mediants are found in a set of ratios.
function p.find_mediants(init_ratios, depth)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local depth = depth or 5
local ratios, depths
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.depth_search, depth)
return ratios, depths
end
-- Find mediants by depth, how many times mediants are found in a set of ratios.
-- Does not return depths.
function p.find_only_mediants(init_ratios, depth)
local init_ratios = init_ratios or {{1,1}, {1,0}}
local depth = depth or 5
local ratios, depths
ratios, depths = p.find_mediants_by_search_func(init_ratios, p.depth_search, depth)
return ratios
end
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----------------------------------- TESTER -------------------------------------
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function p.tester()
local func = p.int_limit_search
local ratios, depths = p.find_mediants_by_search_func({{1,1}, {1,0}}, func, 50)
--ratios, depths = p.find_mediants({{1,1}, {1,0}}, 7)
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%s\t%sedo\t%.3f", ratios[i][1]/gcd, ratios[i][2]/gcd, depths[i], edo, gen)
local new_string = string.format("%s/%s\t%s", ratios[i][1]/gcd, ratios[i][2]/gcd, depths[i])
table.insert(generators, new_string)
end
return generators
end
return p
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