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Module:Temperament data: Difference between revisions

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local rat = require('Module:Rational')
local p = {}
local p = {}
local rat = require("Module:Rational")
local u = require("Module:Utils")
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 function matadd(a, b)
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local function matinv(a)
local function matinv(a)
dbl_identity = {}
local xn = scalarmatmul(a, 1e-7)
for i = 1, #a do
 
dbl_identity[i] = {}
for i = 1, 75 do
for j = 1, #a do
xn = matsub(scalarmatmul(xn, 2), matmul(xn, matmul(a, xn)))
if i == j then
dbl_identity[i][j] = 2
else
dbl_identity[i][j] = 0
end
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
return xn
end
end
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return result
return result
end
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)
local function pseudoinv(a)
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end
end


local function get_te_generator(subgroup, mapping)
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_reduced_mapping(comma_basis, preimage)
a =  pseudoinv(matmul(unreduced_mapping_from_basis(comma_basis), preimage))
for i = 1, #a do
for j = 1, #a[1] do
a[i][j] = math.floor(a[i][j] + 0.5) -- round each entry (they are not exact integers)
end
end
return a
end
 
local function get_te_generator(subgroup, comma_basis, preimage)
local v = get_reduced_mapping(comma_basis, preimage)
local w = {}
local w = {}
for i = 1, #subgroup do
for i = 1, #subgroup do
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for j = 1, #subgroup do
for j = 1, #subgroup do
if i == j then
if i == j then
w[i][j] = math.log(2)/math.log(subgroup[i])
w[i][j] = math.log(2) / math.log(subgroup[i])
else
else
w[i][j] = 0
w[i][j] = 0
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jw[1][i] = 1
jw[1][i] = 1
end
end
local vw = matmul(mapping, w)
local vw = matmul(v, w)
local g = matmul(jw, pseudoinv(vw))
local g = matmul(jw, pseudoinv(vw))
return g
return g
end
end


local function gcd(a,b)
 
  if type(a) == "number" and type(b) == "number" and
local function get_pote_generator(subgroup, comma_basis, preimage)
        a == math.floor(a) and b == math.floor(b) then
local period = 1
    if b == 0 then
for i = 1, #subgroup do
      return a
period = period * (subgroup[i]^preimage[i][1])
    else
end
      return gcd(b, a % b) -- tail recursion
local te = get_te_generator(subgroup, comma_basis, preimage)
    end
local stretch_factor = te[1][1] * math.log(2) / math.log(period)
  else
return scalarmatmul(te, 1 / stretch_factor)
    error("Invalid argument to gcd (" .. tostring(a) .. "," ..
          tostring(b) .. ")", 2)
  end
end
end






function p.get_comma_list(subgroup, mapping)
-- Parsing/display functions
local te_generator = get_te_generator(subgroup, mapping)
 
-- mw.logObject(te_generator)
local function int_to_subgroup_monzo(subgroup, x)  
local te_tuning_map = {}
local result = {}
local x2 = x
for i = 1, #subgroup do
for i = 1, #subgroup do
te_tuning_map[i] = te_generator[1][1] * mapping[1][i] + te_generator[1][2] * mapping[2][i]
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
end
-- mw.logObject(te_tuning_map)
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
local commas = {}
return result
if #subgroup == 3 then
end
for i=-10, 10 do
 
for j=-10, 10 do
local function mysplit (inputstr, sep)
for k=-10, 10 do
        if sep == nil then
local comma = {i, j, k}
    sep = "%s"
local comma_num = 0
        end
for i = 1,#subgroup do
        local t = {}
comma_num = comma_num + (math.log(subgroup[i])/math.log(2))*comma[i]
        for str in string.gmatch(inputstr, "([^" .. sep .. "]+)") do
end
                table.insert(t, str)
local mapped_comma_num = 0
        end
for i = 1,#subgroup do
        return t
mapped_comma_num = mapped_comma_num + te_tuning_map[i]*comma[i]
end
end
 
local function trim(x)
if comma_num >= 0 and mapped_comma_num >= 0 and mapped_comma_num < 0.000000001 then
local str = x
local comma_gcd = gcd(gcd(comma[1], comma[2]), comma[3])
str = str:gsub("%s+", "")
if comma_gcd == 1 or comma_gcd == -1 then
    str = string.gsub(str, "%s+", "")
commas[#commas + 1] = comma
    return str
end
end
end
 
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_matrix = mysplit(frame.args["comma_list"], ",")
for i = 1, #comma_matrix do
comma_matrix[i] = rat.parse(comma_matrix[i])
end
comma_matrix = rat_list_to_matrix(subgroup, comma_matrix)
local unparsed_gens = mysplit(frame.args["generators"], ",")
local generators = mysplit(frame.args["generators"], ",")
for i = 1, #generators do
generators[i] = rat.parse(generators[i])
end
generators = rat_list_to_matrix(subgroup, generators)
local mapping = get_reduced_mapping(comma_matrix, generators)
local cte_generator = frame.args["cte_generator"]
local pote_generator = get_pote_generator(subgroup, comma_matrix, generators)
local result = "[[Subgroup]]: " .. frame.args["subgroup"]
result = result .. "\n\n[[Comma list]]: " .. frame.args["comma_list"]
result = result .. "\n\n[[Mapping]]: [⟨"
for i = 1, #mapping do
for j = 1, #mapping[1] do
result = result .. mapping[i][j] .. " "
end
result = result:sub(0,-2) .. "], ⟨"
end
result = result:sub(0,-6) .. "]"
result = result .. "\n\n: mapping generators: "
for i = 1, #unparsed_gens do
result = result .. "~" .. trim(unparsed_gens[i]) .. ", "
end
result = result:sub(0, -3)
if cte_generator ~= "" then
cte_generator = mysplit(cte_generator, ",")
for i = 1, #cte_generator do
cte_generator[i] = tonumber(cte_generator[i])
end
result = result .. "\n\n[[Optimal tuning]]s:\n* [[CTE]]:"
for i = 1, #(cte_generator) do
result = result .. "~" .. trim(unparsed_gens[i]) .. " = "
if subgroup[1] == 2 and i == 1 then
result = result .. "1\\1"
elseif subgroup[1] == 3 and i == 1 then
result = result .. "1\\1edt"
else
result = result .. u._round(cte_generator[i], 7)
end
end
result = result .. ", "
end
result = result:sub(0,-3)
if subgroup[1] ~= 2 then
result = result .. "\n* [[Lp tuning|POL2]]:"
else
result = result .. "\n* [[POTE]]:"
end
else
if subgroup[1] ~= 2 then
result = result .. "\n\n[[Optimal tuning]] ([[Lp tuning|POL2]]): "
else
result = result .. "\n\n[[Optimal tuning]] ([[POTE]]): "
end
end
end
end
return commas
for i = 1, #(pote_generator[1]) do
result = result .. "~" .. trim(unparsed_gens[i]) .. " = "
if subgroup[1] == 2 and i == 1 then
result = result .. "1\\1"
elseif subgroup[1] == 3 and i == 1 then
result = result .. "1\\1edt"
else
result = result .. u._round(pote_generator[1][i] * 1200, 7)
end
result = result .. ", "
end
result = result:sub(0,-3)
return result
end
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:Temperament_data"