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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)
local function gcd(a,b)
   if type(a) == "number" and type(b) == "number" and  
   if type(a) == "number" and type(b) == "number" and  
Line 66: Line 66:


local function matinv(a)
local function matinv(a)
dbl_identity = {}
local dbl_identity = {}
for i = 1, #a do
for i = 1, #a do
dbl_identity[i] = {}
dbl_identity[i] = {}
Line 78: Line 78:
end
end


xn = scalarmatmul(a, 0.000001)
local xn = scalarmatmul(a, 0.000001)
for i = 1, 30 do
for i = 1, 30 do
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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)
Line 101: Line 113:
end
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


-- Actual temperament-related functions start here
return matsub(identity, matmul(pseudoinv(mapping), mapping))
-- 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
end
-- 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 function mapping_from_basis(comma_basis)
return antitranspose(nullspace(antitranspose(comma_basis)))
end
 
local function get_te_tuning_mpa(subgroup, mapping, preimage)
local w = {}
local w = {}
for i = 1, #subgroup do
for i = 1, #subgroup do
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local vw = matmul(mapping, w)
local vw = matmul(mapping, w)
local g = matmul(jw, pseudoinv(vw))
local g = matmul(jw, pseudoinv(vw))
local result = {}
local mapping_cols = #mapping[1]
return g
local tempered_subgroup = {}
for i = 1, #subgroup do
tempered_subgroup[i] = 0
for j = 1, #mapping do
tempered_subgroup[i] = tempered_subgroup[i] + g[1][j] * mapping[j][i]
end
end
return tempered_subgroup
end
end






return p
return p
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