Module:Temperament data

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This module should not be invoked directly; use its corresponding template instead: Template:Temperament data.

Module:Temperament data is a draft module. It is incomplete and may not be in active development. If possible, editors are encouraged to help with its development. In the meantime, editors should avoid using this module across the Xenharmonic Wiki, except for testing.

Introspection summary for Module:Temperament data
Functions provided (1) Line Function Params 126 get_comma_list (subgroup, mapping)	Lua modules required (1) Variable Module Functions used rat Module:Rational dependency not used

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

---

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

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)
	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
	
	xn = scalarmatmul(a, 0.0001)
	
	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 pseudoinv(a)
	return matmul(transpose(a), matinv(matmul(a, transpose(a))))
end

local function get_te_generator(subgroup, mapping)
	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(mapping, w)
	local g = matmul(jw, pseudoinv(vw))
	return g
end

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



function p.get_comma_list(subgroup, mapping)
	local te_generator = get_te_generator(subgroup, mapping)
	-- mw.logObject(te_generator)
	local te_tuning_map = {}
	for i = 1, #subgroup do
		te_tuning_map[i] = te_generator[1][1] * mapping[1][i] + te_generator[1][2] * mapping[2][i]
	end
	
	-- mw.logObject(te_tuning_map)
	
	local commas = {}
	if #subgroup == 3 then
		for i=-10, 10 do
			for j=-10, 10 do
				for k=-10, 10 do
					local comma = {i, j, k}
					local comma_num = 0
					for i = 1,#subgroup do
						comma_num = comma_num + (math.log(subgroup[i])/math.log(2))*comma[i]
					end
					local mapped_comma_num = 0
					for i = 1,#subgroup do
						mapped_comma_num = mapped_comma_num + te_tuning_map[i]*comma[i]
					end
				
					if comma_num >= 0 and mapped_comma_num >= 0 and mapped_comma_num < 0.000000001 then
						local comma_gcd = gcd(gcd(comma[1], comma[2]), comma[3])
						if comma_gcd == 1 or comma_gcd == -1 then
							commas[#commas + 1] = comma
						end
					end
				end
			end
		end
	end
	
	return commas
end

return p