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Module:Harmonics in equal: Difference between revisions

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local p = {}
local p = {}
local utils = require("Module:Utils")
local yesno = require("Module:yesno")


-- direct mapping
-- direct mapping
local function map(p, steps, num, denom)
local function map(p, steps, num, denom)
local s = math.log(p) / math.log(num/denom)
local s = math.log(p) / math.log(num/denom)
return math.floor(s*steps + .5)
return math.floor(s * steps + 0.5)
end
end
-- check consistency for 9, 15 and 21
-- check consistency for 9, 15 and 21
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local p21 = map(21, steps, num, denom)
local p21 = map(21, steps, num, denom)
return (p9 == 2*p3) and (p15 == p3+p5) and (p21 == p3+p7)
return (p9 == 2 * p3) and (p15 == p3 + p5) and (p21 == p3 + p7)
end
end


local function approx(steps, num, denom, intervals, title, prec)
local function approx(steps, num, denom, intervals, title, prec, reduction, collapsed)
local tpri = {'! colspan="2" | Prime number '}
local thead
local tabs = {'! rowspan="2" | Error \n! absolute ([[cent|¢]]) '}
if collapsed then
local trel = {'! [[Relative interval error|relative]] (%) '}
thead = "{| class=\"wikitable center-all mw-collapsible mw-collapsed\"\n"
local tdeg = {'! colspan="2" | Steps<br>([[Octave_reduction|reduced]])'}
else
local fmt_abs = string.format(' %%+.%df', prec)
thead = "{| class=\"wikitable center-all\"\n"
local fmt_rel = ' %+.0f'
end
local tpri = {"! colspan=\"2\" | Harmonic "}
local tabs = {"! rowspan=\"2\" | Error \n! [[Error|Absolute]] ([[cent|¢]]) "}
local trel = {"! [[Relative interval error|Relative]] ([[relative cent|%]]) "}
local tdeg
if reduction then
tdeg = {"! colspan=\"2\" | Steps<br />([[octave reduction|reduced]])"}
else
tdeg = {"! colspan=\"2\" | Step"}
end
local fmt_abs = string.format("%%+.%df", prec)
local fmt_rel = "%+.1f"
local equave = math.log(num/denom) / math.log(2)
local equave = math.log(num/denom) / math.log(2)
for _, p in pairs(intervals) do
for _, p in pairs(intervals) do
s = math.log(p) / math.log(num/denom)
s = math.log(p) / math.log(num/denom)
v = s*steps
v = s * steps
ev = math.floor(v + .5)
ev = math.floor(v + 0.5)
table.insert(tpri, ' ' .. p)
table.insert(tpri, "" .. p)
table.insert(tabs, string.format(fmt_abs, 1200 * equave * (ev - v ) / steps))
table.insert(tabs, "" .. string.gsub(string.format(fmt_abs, 1200 * equave * (ev - v ) / steps), "%-", "-"))
table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))
table.insert(trel, "" .. string.gsub(string.format(fmt_rel, 100 * (ev - v)), "%-", "-"))
table.insert(tdeg, ' ' .. ev .. '<br>('.. ev % steps .. ')')
if reduction then
table.insert(tdeg, "" .. ev .. "<br />(".. ev % steps .. ")")
else
table.insert(tdeg, "" .. ev)
end
end
end
local titleMarkup = ''
local titleMarkup = ""
if title then
if title then
titleMarkup = '|-\n|+ ' .. title .. '\n'
titleMarkup = "|+ style=\"font-size: 105%; white-space: nowrap;\" | " .. title .. "\n"
end
end
return '{| class="wikitable center-all"\n' ..
thead = thead ..
titleMarkup ..
titleMarkup ..
'|-\n' ..
"|-\n" ..
table.concat(tpri, '\n!') .. '\n' ..
table.concat(tpri, "\n! ") .. "\n" ..
'|-\n' ..
"|-\n" ..
table.concat(tabs, '\n|') .. '\n' ..
table.concat(tabs, "\n| ") .. "\n" ..
'|-\n' ..
"|-\n" ..
table.concat(trel, '\n|') .. '\n' ..
table.concat(trel, "\n| ") .. "\n" ..
'|-\n' ..
"|-\n" ..
table.concat(tdeg, '\n|') .. '\n' ..
table.concat(tdeg, "\n| ") .. "\n" ..
'|}'
"|}"
return thead
end
end


local intervals = {}
local intervals = {}


intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251 }
intervals.prime_no2 = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127 }
intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 }
intervals.integer = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128 }
intervals.integer = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27}


-- evaluate input on error use default
-- evaluate input on error use default
local function eval_num_arg(input, def_value)
local function eval_num_arg(input, def_value)
local result = input
local result = input
if type(input) ~= 'number' then
if type(input) ~= "number" then
result = def_value
result = def_value
if type(input) == 'string' then
if type(input) == "string" then
input = input:match("^%s*(.-)%s*$")
input = input:match("^%s*(.-)%s*$")
if string.len(input) > 0 then
if string.len(input) > 0 then
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-- calculate default precision
-- calculate default precision
local function prec_by_equal(steps, num, denom)
local function prec_by_equal(steps, num, denom)
return math.floor(math.log(steps*1.9*math.log(2)/math.log(num/denom))/math.log(10))
return math.floor(10 * math.log(steps * 1.9 * math.log(2) / math.log(num / denom)) / math.log(10)) / 10
end
end


function p.primes_in_equal (frame)
function p.harmonics_in_equal (frame)
-- optional number of steps, default: 12
-- optional number of steps, default: 12
local steps = eval_num_arg(frame.args['steps'], 12)
local steps = eval_num_arg(frame.args["steps"], 12)
-- numerator, default: 2
-- numerator, default: 2
local num = eval_num_arg(frame.args['num'], 2)
local num = eval_num_arg(frame.args["num"], 2)
-- denominator, default: 1
-- denominator, default: 1
local denom = eval_num_arg(frame.args['denom'], 1)
local denom = eval_num_arg(frame.args["denom"], 1)
-- optional number of columns, default: 10
-- optional number of columns, default: 11
local columns = eval_num_arg(frame.args['columns'], 10)
local columns = eval_num_arg(frame.args["columns"], 11)
-- optional start column, default: start with prime 2
-- optional start column, default: start with prime 2
local start = eval_num_arg(frame.args['start'], 1)
local start = eval_num_arg(frame.args["start"], 1)
-- option intervals
-- option intervals
local select_intervals = "integer"
local select_intervals = "integer"


local name = steps .. 'ed' .. num .. '/' .. denom
local name = steps .. "ed" .. num .. "/" .. denom
if denom == 1 then
if denom == 1 then
if num == 2 then
if num == 2 then
name = steps .. 'edo'
name = steps .. "edo"
select_intervals = "odd"
select_intervals = "odd"
if check_consistency(steps, num, denom) then
if check_consistency(steps, num, denom) then
select_intervals = "prime_no2"
-- select_intervals = "prime_no2"
select_intervals = "prime"
end
end
elseif num == 3 then
elseif num == 3 then
name = steps .. 'edt'
name = steps .. "edt"
else
else
name = steps .. 'ed' .. num
name = steps .. "ed" .. num
end
end
end
end
if num == 3 and denom == 2 then
if num == 3 and denom == 2 then
name = steps .. 'edf'
name = steps .. "edf"
end
end
-- override default intervals
-- override default intervals
if frame.args['intervals'] and string.len(frame.args['intervals']) > 0 then
if frame.args["intervals"] and string.len(frame.args["intervals"]) > 0 then
select_intervals = frame.args['intervals']
select_intervals = frame.args["intervals"]
end
end
title_intervals = "prime harmonics"
if select_intervals == "odd" then
if select_intervals == "odd" then
title_intervals = "odd harmonics"
title_intervals = "odd harmonics"
elseif select_intervals == "integer" then
elseif select_intervals == "integer" then
title_intervals = "harmonics"
title_intervals = "harmonics"
else
title_intervals = "prime harmonics"
end
end
local title = frame.args['title']
local title = frame.args["title"]
if title == nil or string.len(title) == 0 then
if title == nil or string.len(title) == 0 then
title = "Approximation of ".. title_intervals .. " in " .. name
title = "Approximation of ".. title_intervals .. " in " .. name
end
end
-- optional precision for abs error, default about 3 digits
-- optional precision for abs error, default about 3 digits
local prec = eval_num_arg(frame.args['prec'], prec_by_equal(steps, num, denom))
local prec = eval_num_arg(frame.args["prec"], prec_by_equal(steps, num, denom))
return approx( steps, num, denom, {unpack(intervals[select_intervals], start, start+columns-1)}, title, prec)
local reduction = true
if steps == 1 then
reduction = false
end
local collapsed = utils.value_provided(frame.args["collapsed"])
local debugg = yesno(frame.args["debug"])
local result = approx(steps, num, denom, {unpack(intervals[select_intervals], start, start + columns - 1)}, title, prec, reduction, collapsed)
if debugg == true 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:Harmonics_in_equal"