Module:MOS

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This module primarily serves as a library for other modules and has no corresponding template.

This module provides functions for working with MOS scales in Lua code.

Introspection summary for Module:MOS
Functions provided (6) Line Function Params 7 new (nL, ns, equave) 20 parse (unparsed) 33 as_string (mos) 43 brightest_mode (mos) 74 bright_gen (mos) 111 et_tuning_by_hardness (mos, hardness)	Lua modules required (3) Variable Module Functions used et Module:ET new rat Module:Rational parse eq as_ratio gcd as_pair seq Module:Sequence dependency not used

No function descriptions were provided. The Lua code may have further information.

---

local rat = require('Module:Rational')
local seq = require('Module:Sequence')
local et = require('Module:ET')
local p = {}

-- create a MOS structure (nL)L (ns)s <equave>
function p.new(nL, ns, equave)
	local nL = nL or 5
	local ns = ns or 2
	local equave = equave or 2
	return { nL = nL, ns = ns, equave = equave }
end

function round(num, numDecimalPlaces)
  local mult = 10^(numDecimalPlaces or 0)
  return math.floor(num * mult + 0.5) / mult
end

-- parse a MOS structure
function p.parse(unparsed)
	local nL, ns, equave = unparsed:match('^(%d+)[Ll]%s*(%d+)[Ss]%s*(.*)$')
	nL = tonumber(nL)
	ns = tonumber(ns)
	equave = equave:match('^%((.*)-equivalent%)$') or equave:match('^<(.*)>$') or '2/1' -- Assumes this is a rational ratio written a/b
	equave = rat.parse(equave)
	if nL == nil or ns == nil or equave == nil then
		return nil
	end
	return p.new(nL, ns, equave)
end

-- construct a string representation for a MOS structure
function p.as_string(mos)
	local suffix = ''
	if not rat.eq(mos.equave, 2) then
		suffix = '<' .. rat.as_ratio(mos.equave):lower() .. '>'
	end
	return '' .. mos.nL .. 'L ' .. mos.ns .. 's' .. suffix
end

-- Find the brightest mode of a mos.
-- We go back to the root of the scale tree, then progressively construct descendants.
function p.brightest_mode(mos)
	local nL = mos.nL
	local ns = mos.ns
	local d = rat.gcd(nL, ns)
	if d > 1 then -- use single period mos, with period as new equave
		nL = round(nL/d)
		ns = round(ns/d)
	end
	current_nL, current_ns = nL, ns
	local path_to_root = {}
	while current_nL > 1 or current_ns > 1 do -- while current mos is not 1L 1s<equave>, record current mos and go up to parent
		assert(current_nL ~= current_ns, "current_nL == current_ns")
		table.insert(path_to_root, {[1] = current_nL, [2] = current_ns})
		current_nL, current_ns = math.min(current_nL, current_ns), math.max(current_nL, current_ns)-math.min(current_nL, current_ns) -- parent's nL and ns
	end
	assert(current_nL == 1 and current_ns == 1, "Did not reach root successfully")
	local len_of_path = table.getn(path_to_root)
	assert(len_of_path >= 0)
	local result = 'Ls'
	for j = len_of_path, 1, -1 do
		local child_nL, child_ns = path_to_root[j][1], path_to_root[j][2]
		if child_nL > child_ns then -- this will give darkest mode, reverse for brightest mode
			result = string.gsub(result, '[Ls]', {['L'] = 'sL', ['s'] = 'L'})
			result = string.reverse(result)
		else
			result = string.gsub(result, '[Ls]', {['L'] = 'Ls', ['s'] = 's'})
		end
	end
	return string.rep(result, d)
end

function p.bright_gen(mos) -- Compute the abstract, equave-agnostic bright generator as a "vector" of L and s steps.
	local nL = mos.nL
	local ns = mos.ns
	local d = rat.gcd(nL, ns)
	if d > 1 then -- use single period mos, with period as new equave
		nL = round(nL/d)
		ns = round(ns/d)
	end
	current_nL, current_ns = nL, ns
	local path_to_root = {}
	while current_nL > 1 or current_ns > 1 do -- while current mos is not 1L 1s, record current mos and go up to parent
		assert(current_nL ~= current_ns, "current_nL == current_ns")
		table.insert(path_to_root, {[1] = current_nL, [2] = current_ns})
		current_nL, current_ns = math.min(current_nL, current_ns), math.max(current_nL, current_ns)-math.min(current_nL, current_ns)
	end
	local len_of_path = table.getn(path_to_root)
	local result = {['L'] = 1, ['s'] = 0} -- Record the previous bright gen; the bright gen of 1L 1s is 1L + 0s.
	for j = len_of_path, 1, -1 do
		local child_nL, child_ns = path_to_root[j][1], path_to_root[j][2]
		if child_nL > child_ns then 
			-- The old bright gen will now be the dark gen, take equave complement for the new bright gen.
			-- new L = old s.
			-- The # of new L's in (now dark) generator is # of old L's + # of old s's;
			-- the # of new s's in it is the # of old L's.
			result = {['L'] = child_nL - (result['L'] + result['s']), ['s'] = child_ns - result['L']}
		else -- The old bright gen will stay bright.
			-- new s = old s.
			-- The # of new L's in the generator is # of old L's;
			-- the # of new s's in it is # of old L's + # of new s's.
			result = {['L'] = result['L'], ['s'] = result['L'] + result['s']}
		end
	end
	return result
end

-- Given mos a MOS structure, hardness = L/s a rational number,
-- return the corresponding et tuning and the bright MOS generator for the hardness.
function p.et_tuning_by_hardness(mos, hardness)
	local nL, ns, equave = mos.nL, mos.ns, mos.equave
	hardness = rat.parse(hardness) or hardness
	if nL == nil or ns == nil or equave == nil or hardness == nil then
		return nil
	end
	L_in_et_steps, s_in_et_steps = rat.as_pair(hardness)
	local et = et.new(nL*L_in_et_steps + ns*s_in_et_steps, equave)
	local gen = p.bright_gen(mos)
	local gen_steps = gen['L']*L_in_et_steps + gen['s']*s_in_et_steps
	return et, gen_steps
end
return p