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 = {}

-- 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.moses_in_edo(edo, number_of_periods, show_subsets, temperaments)
	local edo = edo or 12
	local number_of_periods = number_of_periods or 1
	local show_subsets = show_subsets == 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
	
	-- 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)
		if gcd ~= 1 and not show_subsets then
			local subset_edo = edo / gcd;
			local subset_gen = gen / gcd;
			local subset_comp = comp / gcd;
			result = result .. string.format('Generators form a subset scale in [[%iedo]] with the generators %i\\%i and %i\\%i.\n', subset_edo, subset_gen, subset_edo, subset_comp, subset_edo)
		else
			-- 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(edo, i, verified_number_of_periods, temperaments[temperament_index])
			else
				result = result .. mosinedo.mos_in_edo(edo, i, verified_number_of_periods)
			end
		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 show_subsets = frame.args["Show Subsets"] == "1"
	
	local result = p.moses_in_edo(edo, number_of_periods, show_subsets, temperaments)
	
	return result
	
end

return p