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Module:Temperament data: Difference between revisions

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local rat = require('Module:Rational')
local rat = require('Module:Rational')
local p = {}
local p = {}
-- Utility / matrix functions
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


local function matadd(a, b)
local function matadd(a, b)
Line 62: Line 77:
end
end
end
end
 
xn = scalarmatmul(a, 0.0001)
xn = scalarmatmul(a, 0.000001)
for i = 1, 30 do
for i = 1, 30 do
Line 86: Line 101:
end
end


local function get_te_generator(subgroup, mapping)
 
-- Actual temperament-related functions start here
-- Generator list (e.g. 2/1, 3/2 for meantone) is needed so you can input irregular mappings like {{5,8,12},{7,11,16}} for meantone
-- and still have the outputted generators be ~2/1 and ~3/2
-- (this will be important later so people using the template can just input an ET list instead of having to figure out the mapping)
-- Generators are passed as monzos in the specified subgroup here
 
function p.get_te_generator(subgroup, mapping, gens)
local w = {}
local w = {}
for i = 1, #subgroup do
for i = 1, #subgroup do
Line 105: Line 127:
local vw = matmul(mapping, w)
local vw = matmul(mapping, w)
local g = matmul(jw, pseudoinv(vw))
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 mapping_cols = #mapping[1]
local tempered_subgroup = {}
local commas = {}
for i = 1, #subgroup do
if #subgroup == 3 then
tempered_subgroup[i] = 0
for i=-10, 10 do
for j = 1, #mapping do
for j=-10, 10 do
tempered_subgroup[i] = tempered_subgroup[i] + g[1][j] * mapping[j][i]
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
end
end
return commas
return tempered_subgroup
end
end


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