Xenharmonic Wiki

Module:Chord consistency: Difference between revisions

← Older edit
Dummy index (talk | contribs)
autopatrolled, emailconfirmed
606 edits
equave-free veresion of additively_consistent()
Dummy index (talk | contribs)
autopatrolled, emailconfirmed
606 edits
delete additively_consistent_int() and use new version of Module:Limits.additively_consistent()
 
(8 intermediate revisions by 2 users not shown)
Line 1: Line 1:
local limits = require('Module:Limits')
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 p = {}
local p = {}


-- check additive consistency for a set of ratios (equave-free version):
-- determine maximum error
--  approx(a*b) = approx(a) + approx(b) forall a, b: a, b, ab in ratios
function p.max_error(et, ratios)
-- `distinct`: whether distinct ratios are required to be mapped to distinct approximations
local maxe = 0.0
-- `previous`: already computed ratios for the previous iteraton
for a_key, a in pairs(ratios) do
function p.additively_consistent_int(et, ratios, distinct, previous)
local a_approx = ET.approximate(et, rat.as_float(a))
distinct = distinct or false
local e = math.abs((ET.cents(et, a_approx) - rat.cents(a)) / ET.cents(et, 1))
previous = previous or {}
if (e > maxe) then
if distinct then
maxe = e
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
end
for a_key, a in pairs(ratios) do
end
local a_approx = ET.approximate(et, rat.as_float(a)) % et.size
return maxe
if approx_set[a_approx] then
end
if not rat.eq(rat.div(a, approx_set[a_approx]), 1) then
 
mw.log(a_key .. ' -> ' .. a_approx .. ': conflict!')
function p.consistent_edos(harmonics, distance, ed, maxlen)
return false
distance = distance or 1.0
end
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
approx_set[a_approx] = a
mw.log(a_key .. ' -> ' .. a_approx)
end
end
end
end
if type(distinct) == 'number' then
 
return true
local vals = {}
end
for i = 1, max_n do
local previous_ordered = {}
local et = ET.parse('' .. i .. ed)
for a_key, a in pairs(previous) do
local consistent = limits.additively_consistent(et, all_interval, false, false, nil)
table.insert(previous_ordered, a)
if consistent then
end
local maxe = p.max_error(et, all_interval)
local ratios_ordered = {}
if maxe <= 5.0e-11 then
for a_key, a in pairs(ratios) do
table.insert(vals, "[[" .. i .. ed .. "]]" .. "(just)")
table.insert(ratios_ordered, a)
break
end
end
for i, a in ipairs(ratios_ordered) do
local dist = 0.5/maxe
local a_approx = ET.approximate(et, rat.as_float(a))
local up = (dist >= distance)
for j, b in ipairs(previous_ordered) do
local llevel = 0
local b_approx = ET.approximate(et, rat.as_float(b))
while (dist >= 2) do
llevel = llevel + 1
local c = rat.mul(a, b)
dist = dist / 2
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
if up then
for j, b in ipairs(ratios_ordered) do
if #vals >= maxlen then
if i <= j then
table.insert(vals, "&hellip;")
local b_approx = ET.approximate(et, rat.as_float(b))
break
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
table.insert(vals, "[[" .. i .. ed .. "]]" .. string.rep("*", llevel))
end
end
end
end
end
end
return true
 
return table.concat(vals, ", ")
end
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 = {}
Line 98: Line 78:
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 116: Line 106:
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 131: Line 120:
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 = p.additively_consistent_int(et, all_interval, false, previous)
if consistent then
table.insert(vals, "[[" .. i .. "edo]]")
end
end
end
end
cat = "(d >= " .. distance .. ") " .. p.consistent_edos(harmonics, distance, 'edo', 4)
--end
--end
cat = table.concat(vals, ", ")


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