Module:MOS in EDO allperiods

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Note: Do not invoke this module directly; use the corresponding template instead: Template:MOS in EDO allperiods.

This module depends on the following other modules: Module: MOS Module: MOS in EDO Module: Rational Module: Utils Module: Yesno

This module calls Template:MOS in EDO allgens repeatedly to list every MOS scale in a particular equal temperament tuning over all possible periods.

---

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
function p.moses_in_edo(edo, number_of_periods, temperaments)
	local edo = edo or 12
	local number_of_periods = number_of_periods or 1
	local temperaments = temperaments --or { "slender", "valentine", "miracle", "nusecond", "hemithirds", "mothra", "orwell", "myna", "mohajira", "würschmidt", "squares", "semisept", "meantone", "casablanca", "tritonic" }
	
	-- 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
	
	-- 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 / verified_number_of_periods / 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)
	
	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 generator %d\\%d and %d\\%d ===\n", gen, edo, comp, edo)
		
		local temperament_index = 1 + i - starting_generator
		if show_temperament then
			result = result .. mosinedo.mos_in_edo(edo, i, verified_number_of_periods, temperaments[temperament_index])
		else
			result = result .. mosinedo.mos_in_edo(edo, i, verified_number_of_periods)
		end
	end
	
	return result
	
end

function p.moses_in_edo_frame(frame)
	
	local edo = tonumber(frame.args["EDO"])
	local temperaments = p.parse_entries(frame.args["Temperaments"])
	local number_of_periods = tonumber(frame.args["Number of Periods"])
	
	local result = p.moses_in_edo(edo, number_of_periods, temperaments)
	
	return result
	
end

return p