Module:Temperament data

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Temperament data.

This module depends on the following other modules: Module: Rational Module: Utils

Todo: add documentation

---

local rat = require('Module:Rational')
local p = {}

local function gcd(a,b)
  if type(a) == "number" and type(b) == "number" and 
        a == math.floor(a) and b == math.floor(b) then
    if b == 0 then
      return a
    else
      return gcd(b, a % b) -- tail recursion
    end
  else
    error("Invalid argument to gcd (" .. tostring(a) .. "," .. 
          tostring(b) .. ")", 2)
  end
end

-- Linear algebra and RTT functions

local function matadd(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = a[i][j] + b[i][j]
		end
	end
	return result
end

local function matsub(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = a[i][j] - b[i][j]
		end
	end
	return result
end

local function matmul(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(b[1]) do
			result[i][j] = 0
			for k = 1, #(a[1]) do
				result[i][j] = result[i][j] + (a[i][k] * b[k][j])
			end
		end
	end
	return result
end


local function scalarmatmul(a, b)
	local result = {}
	for i = 1, #a  do
		result[i] = {}
		for j = 1, #(a[1]) do
			result[i][j] = a[i][j] * b
		end
	end
	return result
end

local function matinv(a)
	local dbl_identity = {}
	for i = 1, #a do
		dbl_identity[i] = {}
		for j = 1, #a do
			if i == j then
				dbl_identity[i][j] = 2
			else
				dbl_identity[i][j] = 0
			end
		end
	end

	local xn = scalarmatmul(a, 0.000001)
	
	for i = 1, 30 do
		xn = matmul(xn, matsub(dbl_identity, matmul(a, xn)))
	end
	return xn
end

local function transpose(a)
	local result = {}
	for i = 1, #a[1] do
		result[i] = {}
		for j = 1, #a do
			result[i][j] = a[j][i]
		end
	end
	return result
end

local function antitranspose(a)
	local result = {}
	for i = 1, #a[1] do
		result[i] = {}
		for j = 1, #a do
			result[i][j] = a[#a - j + 1][#a[1] - i + 1]
		end
	end
	return result
end


local function pseudoinv(a)
	return matmul(transpose(a), matinv(matmul(a, transpose(a))))
end

local function nullspace(mapping)
	local identity = {}
	for i = 1, #mapping[1] do
		identity[i] = {}
		for j = 1, #mapping[1] do
			if i == j then
				identity[i][j] = 1
			else
				identity[i][j] = 0
			end
		end
	end

	-- local w = {{0},{1},{0}}
	-- for i = 1, #mapping[1] do
	-- 	w[i] = {10}
	-- end

	return matsub(identity, matmul(pseudoinv(mapping), mapping))
end

local function unreduced_mapping_from_basis(comma_basis)
	return antitranspose(nullspace(antitranspose(comma_basis)))
end

local function get_te_tuning_map(subgroup, comma_basis)
	local v = unreduced_mapping_from_basis(comma_basis)
	local w = {}
	for i = 1, #subgroup do
		w[i] = {}
		for j = 1, #subgroup do
			if i == j then
				w[i][j] = math.log(2)/math.log(subgroup[i])
			else
				w[i][j] = 0
			end
		end
	end
	
	local jw = {{}}
	for i = 1, #subgroup do
		jw[1][i] = 1
	end
	local vw = matmul(v, w)
	local g = matmul(jw, pseudoinv(vw))
	return g
end

local function get_te_generator(subgroup, comma_basis, preimage)
	return matmul(get_te_tuning_map(subgroup, comma_basis), preimage)
end

-- Parsing/display functions

local function int_to_subgroup_monzo(subgroup, x) 
	local result = {}
	local x2 = x
	for i = 1, #subgroup do
		result[i] = 0
		while true do
			x2 = x2 / subgroup[i]
			if x2 ~= math.floor(x2) then
				break
			end
			result[i] = result[i] + 1
		end
		x2 = x
	end
	
	return result
end


local function rat_to_subgroup_monzo(subgroup, x)
	local n, d = rat.as_pair(x)
	return matsub({int_to_subgroup_monzo(subgroup, n)}, {int_to_subgroup_monzo(subgroup, d)})[1]	
end

local function rat_list_to_matrix(subgroup, list)
	local result = {}
	for j = 1, #subgroup do
		result[j] = {}
	end
	
	for i = 1, #list do
		local smonzo = rat_to_subgroup_monzo(subgroup, list[i])
		for j = 1, #subgroup do
			result[j][i] = smonzo[j]
		end
	end
	
	return result
end

local function mysplit (inputstr, sep)
        if sep == nil then
                sep = "%s"
        end
        local t={}
        for str in string.gmatch(inputstr, "([^"..sep.."]+)") do
                table.insert(t, str)
        end
        return t
end


function p.temperament_data(frame)
	local subgroup = mysplit(frame.args['subgroup'], ".")
	for i = 1, #subgroup do
		subgroup[i] = tonumber(subgroup[i])
	end
	local comma_basis = mysplit(frame.args['comma_list'], ",")
	for i = 1, #comma_list do
		comma_basis[i] = rat.parse(comma_list[i])
	end
	comma_basis = rat_list_to_matrix(subgroup, comma_basis)
	local generators = mysplit(frame.args['generators'], ",")
	for i = 1, #comma_list do
		generators[i] = rat.parse(generators[i])
	end
	generators = rat_list_to_matrix(subgroup, generators)
	local te_generator = ui
end


return p