モジュール:Harmonics in equal - 版の履歴

2024年8月10日 (土) 07:41にTessyrrh1016による

2024-08-10T07:41:50Z

← 古い版		2024年8月10日 (土) 07:41時点における版
109行目:		109行目:
	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
119行目:		119行目:
	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

135行目:		135行目:

	if select_intervals == "odd" then		if select_intervals == "odd" then
	title_intervals = "~~odd harmonics~~"		title_intervals = "奇数倍音"
	elseif select_intervals == "integer" then		elseif select_intervals == "integer" then
	title_intervals = "~~harmonics~~"		title_intervals = "倍音"
	else		else
	title_intervals = "~~prime harmonics~~"		title_intervals = "素数倍音"
	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 = name .. "における" .. title_intervals .. "の近似"
	end		end
	-- optional precision for abs error, default about 3 digits		-- optional precision for abs error, default about 3 digits

2024年8月10日 (土) 07:38にTessyrrh1016による

2024-08-10T07:38:02Z

← 古い版		2024年8月10日 (土) 07:38時点における版
26行目:		26行目:
	thead = "{\| class=\"wikitable center-all\"\n"		thead = "{\| class=\"wikitable center-all\"\n"
	end		end
	local tpri = {"! colspan=\"2\" \| ~~Harmonic~~ "}		local tpri = {"! colspan=\"2\" \| 倍音 "}
	local tabs = {"! rowspan=\"2\" \| ~~Error~~ \n! ~~Absolute~~ ([[~~cent~~\|¢]]) "}		local tabs = {"! rowspan=\"2\" \| 誤差 \n! 絶対 ([[セント\|¢]]) "}
	local trel = {"! [[~~Relative interval error~~\|~~Relative~~]] ([[~~relative cent~~\|%]]) "}		local trel = {"! [[相対音程誤差\|相対]] ([[相対セント\|%]]) "}
	local tdeg		local tdeg
	if reduction then		if reduction then
	tdeg = {"! colspan=\"2\" \| ~~Steps~~<br>([[octave reduction\|reduced]])"}		tdeg = {"! colspan=\"2\" \| ステップ<br>([[octave reduction\|reduced]])"}
	else		else
	tdeg = {"! colspan=\"2\" \| ~~Step~~"}		tdeg = {"! colspan=\"2\" \| ステップ"}
	end		end
	local fmt_abs = string.format(" %%+.%df", prec)		local fmt_abs = string.format(" %%+.%df", prec)

Tessyrrh1016: :en:module:harmonics in equal からコピー

2024-08-10T06:18:46Z

en:module:harmonics in equal からコピー

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

-- direct mapping
local function map(p, steps, num, denom)
local s = math.log(p) / math.log(num/denom)
return math.floor(s * steps + 0.5)
end
-- check consistency for 9, 15 and 21
local function check_consistency(steps, num, denom)
local p3 = map(3, steps, num, denom)
local p5 = map(5, steps, num, denom)
local p7 = map(7, steps, num, denom)
local p9 = map(9, steps, num, denom)
local p15 = map(15, steps, num, denom)
local p21 = map(21, steps, num, denom)

return (p9 == 2 * p3) and (p15 == p3 + p5) and (p21 == p3 + p7)
end

local function approx(steps, num, denom, intervals, title, prec, reduction, collapsed)
local thead
if collapsed then
thead = "{| class=\"wikitable center-all mw-collapsible mw-collapsed\"\n"
else
thead = "{| class=\"wikitable center-all\"\n"
end
local tpri = {"! colspan=\"2\" | Harmonic "}
local tabs = {"! rowspan=\"2\" | Error \n! 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)
for _, p in pairs(intervals) do
s = math.log(p) / math.log(num/denom)
v = s*steps
ev = math.floor(v + 0.5)
table.insert(tpri, "" .. p)
table.insert(tabs, "" .. string.gsub(string.format(fmt_abs, 1200 * equave * (ev - v ) / steps), "%-", "-"))
table.insert(trel, "" .. string.gsub(string.format(fmt_rel, 100 * (ev - v)), "%-", "-"))
if reduction then
table.insert(tdeg, "" .. ev .. "<br />(".. ev % steps .. ")")
else
table.insert(tdeg, "" .. ev)
end
end
local titleMarkup = ""
if title then
titleMarkup = "|-\n|+ style=\"font-size: 105%; white-space: nowrap;\" | " .. title .. "\n"
end

return thead ..
titleMarkup ..
"|-\n" ..
table.concat(tpri, "\n!") .. "\n" ..
"|-\n" ..
table.concat(tabs, "\n|") .. "\n" ..
"|-\n" ..
table.concat(trel, "\n|") .. "\n" ..
"|-\n" ..
table.concat(tdeg, "\n|") .. "\n" ..
"|}"
end

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, 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 }
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, 123, 125, 127 }
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 }

-- evaluate input on error use default
local function eval_num_arg(input, def_value)
local result = input
if type(input) ~= "number" then
result = def_value
if type(input) == "string" then
input = input:match("^%s*(.-)%s*$")
if string.len(input) > 0 then
result = tonumber(input)
end
end
end
return result
end

-- calculate default precision
local function prec_by_equal(steps, num, denom)
return math.floor(10 * math.log(steps * 1.9 * math.log(2) / math.log(num / denom)) / math.log(10)) / 10
end

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

local name = steps .. "ed" .. num .. "/" .. denom
if denom == 1 then
if num == 2 then
name = steps .. "edo"
select_intervals = "odd"
if check_consistency(steps, num, denom) then
-- select_intervals = "prime_no2"
select_intervals = "prime"
end
elseif num == 3 then
name = steps .. "edt"
else
name = steps .. "ed" .. num
end
end

if num == 3 and denom == 2 then
name = steps .. "edf"
end

-- override default intervals
if frame.args["intervals"] and string.len(frame.args["intervals"]) > 0 then
select_intervals = frame.args["intervals"]
end

if select_intervals == "odd" then
title_intervals = "odd harmonics"
elseif select_intervals == "integer" then
title_intervals = "harmonics"
else
title_intervals = "prime harmonics"
end

local title = frame.args["title"]
if title == nil or string.len(title) == 0 then
title = "Approximation of ".. title_intervals .. " in " .. name
end
-- optional precision for abs error, default about 3 digits
local prec = eval_num_arg(frame.args["prec"], prec_by_equal(steps, num, denom))
local reduction = true
if steps == 1 then
reduction = false
end
local collapsed = utils.value_provided(frame.args["collapsed"])

return approx(steps, num, denom, {unpack(intervals[select_intervals], start, start+columns-1)}, title, prec, reduction, collapsed)
end

return p