Xenharmonic Wiki

Module:Q-odd-limit intervals: Difference between revisions

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m Fix
experiment with a larger limit
 
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Line 1: Line 1:
local p = {}
bit32 = require("bit32")
bit32 = require("bit32")
utils = require("Module:Utils")
ET = require("Module:ET")
ET = require("Module:ET")
getArgs = require("Module:Arguments").getArgs
limits = require("Module:Limits")
limits = require("Module:Limits")
 
utils = require("Module:Utils")
local p = {}
yesno = require("Module:Yesno")


local PRIME_LIST = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
local PRIME_LIST = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
Line 86: Line 88:


local function find_error(val, subgroup, monzo_list)
local function find_error(val, subgroup, monzo_list)
local step_size = 1200/val[1]
local step_size = 1200 / val[1]
local true_size
local true_size
local approx_size
local approx_size
Line 100: Line 102:
error_rel_direct = 100 * error_abs_direct / step_size
error_rel_direct = 100 * error_abs_direct / step_size
error_rel_val = 100 * error_abs_val / step_size
error_rel_val = 100 * error_abs_val / step_size
error_list[i] =  
error_list[i] = {
{
ratio = ratio,  
ratio = ratio,  
comp = comp,  
comp = comp,  
Line 110: Line 111:
}
}
end
end
table.sort(error_list, function(a, b) return a.error_abs_val < b.error_abs_val end)
table.sort(error_list, function(a, b)
return a.error_abs_val < b.error_abs_val
end)
return error_list
return error_list
end
end
Line 120: Line 125:
local errlist_val = {}
local errlist_val = {}
local val = {}
local val = {}
local bgclr, result


for i = 1, #subgroup do
for i = 1, #subgroup do
Line 126: Line 132:
error_list = find_error(val, subgroup, monzo_list)
error_list = find_error(val, subgroup, monzo_list)
for i = 1, #error_list do
for i = 1, #error_list do
ratiocomp = string.format("%d/%d, %d/%d", error_list[i].ratio.num, error_list[i].ratio.den, 2 * error_list[i].ratio.den, error_list[i].ratio.num)
ratiocomp = string.format("%d/%d, %d/%d",
error_list[i].ratio.num, error_list[i].ratio.den,
2 * error_list[i].ratio.den, error_list[i].ratio.num)
eav = error_list[i].error_abs_val
eav = error_list[i].error_abs_val
erv = error_list[i].error_rel_val
erv = error_list[i].error_rel_val
Line 135: Line 143:
error_abs_direct = string.format("%.3f", ead)
error_abs_direct = string.format("%.3f", ead)
error_rel_direct = string.format("%.1f", erd)
error_rel_direct = string.format("%.1f", erd)
if bit32.band(error_list[i].ratio.den, error_list[i].ratio.den - 1) == 0 and utils.table_contains(subgroup, error_list[i].ratio.num) then -- check power of 2 for den and prime for num
if bit32.band(error_list[i].ratio.den, error_list[i].ratio.den - 1) == 0
and utils.table_contains(subgroup, error_list[i].ratio.num) then -- check power of 2 for den and prime for num
ratiocomp = "'''" .. ratiocomp .. "'''"
ratiocomp = "'''" .. ratiocomp .. "'''"
error_abs_val = "'''" .. error_abs_val .. "'''"
error_abs_val = "'''" .. error_abs_val .. "'''"
Line 141: Line 151:
error_abs_direct = "'''" .. error_abs_direct .. "'''"
error_abs_direct = "'''" .. error_abs_direct .. "'''"
error_rel_direct = "'''" .. error_rel_direct .. "'''"
error_rel_direct = "'''" .. error_rel_direct .. "'''"
bgclr = ""
end
end
if error_list[i].error_rel_val > 50 then
if error_list[i].error_rel_val > 50 then
Line 148: Line 159:
error_abs_direct = "''" .. error_abs_direct .. "''"
error_abs_direct = "''" .. error_abs_direct .. "''"
error_rel_direct = "''" .. error_rel_direct .. "''"
error_rel_direct = "''" .. error_rel_direct .. "''"
bgclr = " style=\"background-color: #dddddd;\""
else
bgclr = ""
end
end
errlist_direct[i] = {
errlist_direct[i] = {
bgclr = bgclr,
ratiocomp = ratiocomp,
ratiocomp = ratiocomp,
ead = ead,
ead = ead,
Line 159: Line 174:
errlist_val[i] = {
errlist_val[i] = {
bgclr = bgclr,
ratiocomp = ratiocomp,
ratiocomp = ratiocomp,
eav = eav,
eav = eav,
Line 167: Line 183:
end
end
table.sort(errlist_direct, function(a, b) return a.ead < b.ead end)
table.sort(errlist_direct, function(a, b)
return a.ead < b.ead
end)
for i = 1, #error_list do
for i = 1, #error_list do
t_body_direct[i] = string.format("|-\n| %s || %s || %s", errlist_direct[i].ratiocomp, errlist_direct[i].error_abs_direct, errlist_direct[i].error_rel_direct)
t_body_direct[i] = string.format("|-%s\n| %s || %s || %s",
t_body_val[i] = string.format("|-\n| %s || %s || %s", errlist_val[i].ratiocomp, errlist_val[i].error_abs_val, errlist_val[i].error_rel_val)
errlist_direct[i].bgclr,
errlist_direct[i].ratiocomp,
errlist_direct[i].error_abs_direct,
errlist_direct[i].error_rel_direct)
t_body_val[i] = string.format("|-%s\n| %s || %s || %s",
errlist_val[i].bgclr,
errlist_val[i].ratiocomp,
errlist_val[i].error_abs_val,
errlist_val[i].error_rel_val)
end
end
local t_head_0 = "{| class=\"wikitable center-all mw-collapsible mw-collapsed sortable\"\n"
local t_head_0 = "{| class=\"wikitable center-all mw-collapsible mw-collapsed sortable\"\n"
.. "|+ style=\"white-space: nowrap;\" | "
.. "|+ style=\"font-size: 105%; white-space: nowrap;\" | "
local t_head_1 = "|-\n"
local t_head_1 = "|-\n"
.. "! class=\"unsortable\" | Interval and complement !! Error (abs, [[Cent|¢]]) !! Error (rel, [[Relative cent|%]])\n"
.. "! class=\"unsortable\" | Interval and complement"
.. " !! Error (abs, [[Cent|&#162;]])"
.. " !! Error (rel, [[Relative cent|%]])\n"
local t_foot = "\n|}"
local t_foot = "\n|}"
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if approx_t == "direct" then
if approx_t == "direct" then
local out_str_direct = t_head_0 .. t_title .. tag_direct .. "\n" .. t_head_1 .. table.concat(t_body_direct, "\n") .. t_foot
result = t_head_0 .. t_title .. tag_direct .. "\n" .. t_head_1 .. table.concat(t_body_direct, "\n") .. t_foot
return out_str_direct
elseif approx_t == "val" then
elseif approx_t == "val" then
local out_str_val = t_head_0 .. t_title .. tag_val .. "\n" .. t_head_1 .. table.concat(t_body_val, "\n") .. t_foot
result = t_head_0 .. t_title .. tag_val .. "\n" .. t_head_1 .. table.concat(t_body_val, "\n") .. t_foot
return out_str_val
else
result = ""
end
end
return result
end
end
-- local function prec_by_equal (steps)
-- return math.floor (math.log (steps*1.9)/math.log (10))
-- end


function p.q_odd_limit_intervals(frame)
function p.q_odd_limit_intervals(frame)
local args = getArgs(frame)
local steps = tonumber(frame.args["steps"])
local steps = tonumber(frame.args["steps"])
local limit = math.max(tonumber(frame.args["limit"]), 2)
local limit = math.max(tonumber(frame.args["limit"]), 2)
local constcy = limits.consistency_limit(ET.parse(steps .. "edo"), false, 43)
local constcy = limits.consistency_limit(ET.parse(steps .. "edo"), false, 63)
-- local prec = tonumber (frame.args['prec']) or prec_by_equal (steps)
    local wtext = yesno(frame.args["wtext"] or args["wtext"])
local note = frame.args["note"]
local note = frame.args["note"]
local title = frame.args["title"]
local title = frame.args["title"]
local header = string.lower(frame.args["header"]:gsub("%s+", ""))
local header = string.lower(frame.args["header"]:gsub("%s+", ""))
local apx = string.lower(frame.args["apx"]:gsub("%s+", ""))
local tag
local tag
local apx = string.lower(frame.args["apx"]:gsub("%s+", ""))
if not utils.value_provided (title) then
if not utils.value_provided(title) then
title = string.format("%d-odd-limit intervals in " .. steps .. "edo", limit)
title = string.format("%d-odd-limit intervals in %dedo", limit, steps)
end
end
local subgroup = table_filter(PRIME_LIST, limit)
local subgroup = table_filter(PRIME_LIST, limit)
local monzo_list = odd_limit_monzo_list_gen(limit)
local monzo_list = odd_limit_monzo_list_gen(limit)
local out_str
local result
if header ~= "none" then
if header ~= "none" then
out_str = "The following "
if constcy >= limit then
if constcy >= limit then
apx = "val"
apx = "val"
end
end
if apx == "direct" or apx == "val" then
result = string.format("The following %s how [[%d-odd-limit]] intervals are represented in %dedo. ",
out_str = out_str .. "table shows"
string.gsub("table show", "()", {[((apx == "direct" or apx == "val") and 11 or 6)] = "s"}), limit, steps)
else
.. "Prime harmonics are in '''bold'''"
out_str = out_str .. "tables show"
.. (constcy >= limit and string.format(".\n\nAs %dedo is consistent in the %d-odd-limit, "
end
.. "the mappings by direct approximation and through the patent val are identical.", steps, limit)
out_str = out_str .. " how [[" .. limit .. "-odd-limit]] intervals are represented in " .. steps .. "edo. Prime harmonics are in '''bold'''"
or "; inconsistent intervals are in ''italics''.")
.. "\n\n"
if constcy >= limit then
if constcy >= limit then
out_str = out_str .. ".\n\nAs " .. steps .. "edo is consistent in the " .. limit .. "-odd-limit, the mappings by direct approximation and through the patent val are identical."
tag = "none"
tag = "none"
else
out_str = out_str .. "; inconsistent intervals are in ''italics''."
end
end
out_str = out_str .. "\n\n"
if note ~= "" then
if note ~= "" then
out_str = out_str .. note .. "\n\n"
result = result .. note .. "\n\n"
end
end
if steps == 12 then
if steps == 12 then
out_str = out_str .. "Note that since the [[cent]] was defined in terms of 12edo, the absolute and relative errors for 12edo are identical.\n\n"
result = result .. "Note that, since the [[cent]] was defined in terms of 12edo, the absolute and relative errors for 12edo are identical.\n\n"
end
end
else
else
tag = string.lower(frame.args["tag"]:gsub("%s+", ""))
tag = string.lower(frame.args["tag"]:gsub("%s+", ""))
out_str = ""
result = ""
end
end
if utils.value_provided (apx) then
if utils.value_provided(apx) then
out_str = out_str .. approx(steps, subgroup, monzo_list, title, tag, apx)
result = result .. approx(steps, subgroup, monzo_list, title, tag, apx)
else
else
out_str = out_str .. approx(steps, subgroup, monzo_list, title, tag, "direct") .. "\n\n" .. approx(steps, subgroup, monzo_list, title, tag, "val")
result = result .. approx(steps, subgroup, monzo_list, title, tag, "direct") .. "\n\n" .. approx(steps, subgroup, monzo_list, title, tag, "val")
end
end
return out_str
if wtext then
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end
return frame:preprocess(result)
end
end


return p;
return p
Retrieved from "https://en.xen.wiki/w/Module:Q-odd-limit_intervals"