Module:Temperament data

Module documentation[view] [edit] [history] [purge]

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 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

function p.get_comma_list(subgroup, mapping)
	local te_generator = get_te_generator(subgroup, mapping)
	local te_tuning_map = {}
	for i = 1, #subgroup do
		mw.logObject(te_generator[2])
		-- te_tuning_map[i] = te_generator[1] * mapping[1][i] + te_generator[2] * mapping[2][i]
	end
	
	-- 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 = 1
	-- 				for i = 1,#subgroup do
	-- 					local comma_num = comma_num * te_tuning_map[i]^comma[i]
	-- 				end
					
	-- 				if comma_num >= 1 and comma_num < 1.0000000001 then
	-- 					commas.append(comma)
	-- 				end
					
	-- 			end
	-- 		end
	-- 	end
	-- end
	
	return commas
end

return p