Module:MOS in EDO allgens

---

Documentation transcluded from /doc
Note: Do not invoke this module directly; use the corresponding template instead: Template:MOS in EDO allgens.

Todo: Documentation

---

local mos = require("Module:MOS")
local rat = require("Module:Rational")
local utils = require("Module:Utils")
local mosinedo = require("Module:MOS in EDO")
local p = {}

-- Helper function
-- Parses entries from a semicolon-delimited string and returns them in an array
-- TODO: Separate this and related functions (parse_pair and parse_kv_pairs) into its own module, as they're included
-- in various modules at this point, such as: scale tree, mos mdoes
function p.parse_entries(unparsed)
	local parsed = {}
	for entry in string.gmatch(unparsed, "([^;]+)") do
		local trimmed = entry:gsub("^%s*(.-)%s*$", "%1")
		table.insert(parsed, trimmed)		-- Add to array
	end
	return parsed
end

-- Main function
-- Creates an entire page section for every mos in an edo
-- Mosses with the same period are only shown; this function must be called
-- separately for each period count if it can support multi-period mosses
-- Generators start with half the period rounded down, plus 1
-- If the edo has subset edos (such as 24edo containing 12edo and 8edo), mosses
-- for those subset edos are skipped, unless show_subsets is set to 1 (true)
function p.mos_in_edo_allgens(edo, number_of_periods, show_subsets, generation_limit, temperaments)
	local edo = edo or 12
	local number_of_periods = number_of_periods or 1
	local show_subsets = show_subsets == 1
	local generation_limit = generation_limit or edo - 1
	local temperaments = temperaments
	
	-- Check whether the number of periods divides the edo
	-- If so, the entire page section will be for multiperiod mosses
	local period_in_edosteps = edo
	local verified_number_of_periods = 1
	if edo % number_of_periods == 0 then
		period_in_edosteps = edo / number_of_periods
		verified_number_of_periods = number_of_periods
	end
	
	-- Check whether the generation limit is valid
	-- Technically, any number above the edo works with showing all generations (rows)
	-- If it's -1, then show all generations (period_in_edosteps-1)
	if generation_limit == -1 then
		generation_limit = period_in_edosteps - 1
	end
	
	-- Starting generator
	-- If the generator and its complement are the same, skip that genpair by
	-- incrementing the starting generator by 1
	local starting_generator = math.ceil(period_in_edosteps / 2)
	local complement = period_in_edosteps - starting_generator
	if starting_generator == complement then
		starting_generator = starting_generator + 1
	end
	
	-- Include temperament names?
	local show_temperament = temperaments ~= nil and #temperaments == math.floor(period_in_edosteps / verified_number_of_periods / 2)
	
	-- Temporarily disable entry of temperament names
	-- Temperament names will be entered as a set of key-value pairs instead of an array
	show_temperament = false
	
	-- Add a table for each genpair
	local result = ""
	for i = starting_generator, period_in_edosteps - 1 do
		local gen = i
		local comp = period_in_edosteps - gen
		--result = result .. string.format("MOS scales with generators %i\\%i and %i\\%i.\n", gen, edo, comp, edo)
		
		-- Skip mosses that are supported by subset edos; this happens if the
		-- gen and comp have a gcd > 1; if show_subsets is set to true, then
		-- show them anyway.
		local gcd = utils._gcd(gen, comp)
		local add_table = gcd == 1 or show_subsets
		
		-- Add table
		if add_table then
			-- TODO: Rewrite code here for entry of temperaments as a set of
			-- key-value pairs
			local temperament_index = 1 + i - starting_generator
			if show_temperament then
				result = result .. mosinedo.mos_in_edo_simplified(edo, i, verified_number_of_periods, generation_limit, temperaments[temperament_index])
			else
				result = result .. mosinedo.mos_in_edo_simplified(edo, i, verified_number_of_periods, generation_limit)
			end
		end
	end
	
	return result
end

-- Wrapper function to be called by a template
-- Args (TODO: implement):
-- - EDO: the number of divisions; this should be later set up to extract it from the page's title.
-- - Temperaments: the temperament names entered as key-value pairs, where the key is the genpair separated with a dash.
-- - Show Subsets: set to 1 to show mosses of subset edos, such as 12edo mosses for 24edo.
-- - Period Limit: the Period Limit for mosses to display; default is -1 (displays all period counts that don't produce degenerate mosses)
-- - Number of Periods: shows mosses for a particular period count
-- - Generation Limit: if set, tables will be limited to this number of generations (rows in the table)
function p.mos_in_edo_allgens_frame(frame)
	local edo = tonumber(frame.args["EDO"])
	local temperaments = p.parse_entries(frame.args["Temperaments"])
	local show_subsets = tonumber(frame.args["Show Subsets"])
	local max_periods = tonumber(frame.args["Period Limit"]) or -1
	local generation_limit = tonumber(frame.args["Generation Limit"]) or -1
	local num_periods = tonumber(frame.args["Number of Periods"]) or 1
	
	local result = ""
	result = p.mos_in_edo_allgens(edo, num_periods, show_subsets, generation_limit, temperaments)
	
	return result
end

return p