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Module:Chord consistency: Difference between revisions

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Created page with "local rat = require('Module:Rational') local utils = require("Module:Utils") local ET = require('Module:ET') local consistency = require('Module:Limits') local p = {} functio..."
 
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Line 1: Line 1:
local ET = require('Module:ET')
local rat = require('Module:Rational')
local rat = require('Module:Rational')
local utils = require("Module:Utils")
local utils = require("Module:Utils")
local ET = require('Module:ET')
local consistency = require('Module:Limits')
local p = {}
local p = {}
-- check additive consistency for a set of ratios (equave-free version):
--  approx(a*b) = approx(a) + approx(b) forall a, b: a, b, ab in ratios
-- `distinct`: whether distinct ratios are required to be mapped to distinct approximations
-- `previous`: already computed ratios for the previous iteraton
function p.additively_consistent_int(et, ratios, distinct, previous)
distinct = distinct or false
previous = previous or {}
if distinct then
local approx_set = {}
for a_key, a in pairs(previous) do
local a_approx = ET.approximate(et, rat.as_float(a)) % et.size
if approx_set[a_approx] then
if not rat.eq(rat.div(a, approx_set[a_approx]), 1) then
mw.log(a_key .. ' -> ' .. a_approx .. ': conflict!')
return false
end
end
approx_set[a_approx] = a
mw.log(a_key .. ' -> ' .. a_approx)
end
for a_key, a in pairs(ratios) do
local a_approx = ET.approximate(et, rat.as_float(a)) % et.size
if approx_set[a_approx] then
if not rat.eq(rat.div(a, approx_set[a_approx]), 1) then
mw.log(a_key .. ' -> ' .. a_approx .. ': conflict!')
return false
end
end
approx_set[a_approx] = a
mw.log(a_key .. ' -> ' .. a_approx)
end
end
if type(distinct) == 'number' then
return true
end
local previous_ordered = {}
for a_key, a in pairs(previous) do
table.insert(previous_ordered, a)
end
local ratios_ordered = {}
for a_key, a in pairs(ratios) do
table.insert(ratios_ordered, a)
end
for i, a in ipairs(ratios_ordered) do
local a_approx = ET.approximate(et, rat.as_float(a))
for j, b in ipairs(previous_ordered) do
local b_approx = ET.approximate(et, rat.as_float(b))
local c = rat.mul(a, b)
local c_approx = ET.approximate(et, rat.as_float(c))
local c_key = rat.as_ratio(c)
if previous[c_key] or ratios[c_key] then
if c_approx ~= a_approx + b_approx then
mw.log('a = ' .. rat.as_ratio(a) .. '; b = ' .. rat.as_ratio(b) .. '; ab = ' .. c_key)
mw.log(a_approx .. ' + ' .. b_approx .. ' != ' .. c_approx)
return false
end
end
end
for j, b in ipairs(ratios_ordered) do
if i <= j then
local b_approx = ET.approximate(et, rat.as_float(b))
local c = rat.mul(a, b)
local c_approx = ET.approximate(et, rat.as_float(c))
local c_key = rat.as_ratio(c)
if previous[c_key] or ratios[c_key] then
if c_approx ~= a_approx + b_approx then
mw.log('a = ' .. rat.as_ratio(a) .. '; b = ' .. rat.as_ratio(b) .. '; ab = ' .. c_key)
mw.log(a_approx .. ' + ' .. b_approx .. ' != ' .. c_approx)
return false
end
end
end
end
end
return true
end
-- determine maximum error
function p.max_error(et, ratios)
local maxe = 0.0
for a_key, a in pairs(ratios) do
local a_approx = ET.approximate(et, rat.as_float(a))
local e = math.abs((ET.cents(et, a_approx) - rat.cents(a)) / ET.cents(et, 1))
if (e > maxe) then
maxe = e
end
end
return maxe
end
function p.consistent_edos(harmonics, distance, ed, maxlen)
distance = distance or 1.0
ed = ed or 'edo'
local max_n = 72
maxlen = maxlen or max_n
if max_n < maxlen then max_n = maxlen end
local all_interval = {}
for i, h in ipairs(harmonics) do
-- compute all ratio
for j, g in ipairs(harmonics) do
if j > i then
local a = rat.new(g, h)
all_interval[rat.as_ratio(a)] = a
end
end
end
local vals = {}
for i = 1, max_n do
local et = ET.parse('' .. i .. ed)
local consistent = p.additively_consistent_int(et, all_interval, false, nil)
if consistent then
local maxe = p.max_error(et, all_interval)
if maxe <= 5.0e-11 then
table.insert(vals, "[[" .. i .. ed .. "]]" .. "(just)")
break
end
local dist = 0.5/maxe
local up = (dist >= distance)
local llevel = 0
while (dist >= 2) do
llevel = llevel + 1
dist = dist / 2
end
if up then
if #vals >= maxlen then
table.insert(vals, "&hellip;")
break
end
table.insert(vals, "[[" .. i .. ed .. "]]" .. string.rep("*", llevel))
end
end
end
return table.concat(vals, ", ")
end


function p.noinfobox_chord(frame)
function p.noinfobox_chord(frame)
local page_name = frame:preprocess("{{PAGENAME}}")
local distance = tonumber(frame.args["Distance"])
local debug_data = ""
local debug_data = ""
local infobox_data = {}
local infobox_data = {}
local cats = ""
local cats = ""


if utils.value_provided(frame.args["Harmonics"]) then
--if utils.value_provided(frame.args["Harmonics"]) then
local harmonics = {}
local harmonics = {}
for hs in string.gmatch(frame.args["Harmonics"], "[^:]+") do
for hs in string.gmatch(frame.args["Harmonics"], "[^:]+") do
Line 18: Line 158:
assert(h > 0, "invalid harmonic")
assert(h > 0, "invalid harmonic")
table.insert(harmonics, h)
table.insert(harmonics, h)
end
if distance == nil then
if #harmonics >= 5 then
distance = 1.5
elseif #harmonics >= 3 then
distance = 2.0
else
distance = 3.0
end
end
end


Line 36: Line 186:
local root_interval_links = {}
local root_interval_links = {}
local step_interval_links = {}
local step_interval_links = {}
local all_interval = {}
for i, h in ipairs(harmonics) do
for i, h in ipairs(harmonics) do
-- compute ratio of this harmonic relative to the root
-- compute ratio of this harmonic relative to the root
Line 51: Line 200:
local step_denom = prev / step_gcd
local step_denom = prev / step_gcd
table.insert(step_interval_links, "[[" .. step_numer .. "/" .. step_denom .. "]]")
table.insert(step_interval_links, "[[" .. step_numer .. "/" .. step_denom .. "]]")
end
-- compute all ratio
for j, g in ipairs(harmonics) do
if j > i then
local step_gcd = utils._gcd(g, h)
local step_numer = g / step_gcd
local step_denom = h / step_gcd
local a = rat.new(g, h)
all_interval[rat.as_ratio(a)] = a
end
end
end
local vals = {}
for i = 1, 50 do
local et = ET.parse('' .. i .. 'edo')
local consistent = consistency.additively_consistent(et, all_interval, false, previous)
if consistent then
table.insert(vals, "[[" .. i .. "edo]]")
end
end
end
end
end
cat = table.concat(vals, ", ")
cat = "(d >= " .. distance .. ") " .. p.consistent_edos(harmonics, distance, 'edo', 4)
--end


return cat
return cat
Retrieved from "https://en.xen.wiki/w/Module:Chord_consistency"