Module:Chord consistency: Difference between revisions
Dummy index (talk | contribs) No edit summary |
Dummy index (talk | contribs) equave-free veresion of additively_consistent() |
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local utils = require("Module:Utils") | local utils = require("Module:Utils") | ||
local ET = require('Module:ET') | local ET = require('Module:ET') | ||
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 | |||
function p.noinfobox_chord(frame) | function p.noinfobox_chord(frame) | ||
| Line 68: | Line 148: | ||
for i = 1, 50 do | for i = 1, 50 do | ||
local et = ET.parse('' .. i .. 'edo') | local et = ET.parse('' .. i .. 'edo') | ||
local consistent = | local consistent = p.additively_consistent_int(et, all_interval, false, previous) | ||
if consistent then | if consistent then | ||
table.insert(vals, "[[" .. i .. "edo]]") | table.insert(vals, "[[" .. i .. "edo]]") | ||