モジュール:ET - 版の履歴

2024年8月20日 (火) 16:16にTessyrrh1016による

2024-08-20T16:16:42Z

← 古い版		2024年8月20日 (火) 16:16時点における版
153行目:		153行目:
	local markers = {}		local markers = {}
	if zeta_peak then		if zeta_peak then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Peak EDOs~~\|Zeta peak]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta peak edos\|Zeta peak]]")
	elseif zeta_peak == nil then		elseif zeta_peak == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Peak EDOs~~\|Zeta peak?]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta peak edos\|Zeta peak?]]")
	end		end

	if zeta_peak_integer then		if zeta_peak_integer then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Peak EDOs~~\|Zeta peak integer]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta peak edos\|Zeta peak integer]]")
	elseif zeta_peak_integer == nil then		elseif zeta_peak_integer == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Peak EDOs~~\|Zeta peak integer?]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta peak edos\|Zeta peak integer?]]")
	end		end

	if zeta_integral then		if zeta_integral then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Integral of~~ Zeta ~~EDOs~~\|Zeta integral]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta integral edos\|Zeta integral]]")
	elseif zeta_integral == nil then		elseif zeta_integral == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #~~Integral of~~ Zeta ~~EDOs~~\|Zeta integral?]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta integral edos\|Zeta integral?]]")
	end		end

	if zeta_gap then		if zeta_gap then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta ~~Gap EDOs~~\|Zeta gap]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta gap edos\|Zeta gap]]")
	elseif zeta_gap == nil then		elseif zeta_gap == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta ~~Gap EDOs~~\|Zeta gap?]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta gap edos\|Zeta gap?]]")
	end		end

2024年8月20日 (火) 16:13にTessyrrh1016による

2024-08-20T16:13:27Z

← 古い版		2024年8月20日 (火) 16:13時点における版
153行目:		153行目:
	local markers = {}		local markers = {}
	if zeta_peak then		if zeta_peak then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|~~ゼータピーク~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|Zeta peak]]")
	elseif zeta_peak == nil then		elseif zeta_peak == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|~~ゼータピーク？~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|Zeta peak?]]")
	end		end

	if zeta_peak_integer then		if zeta_peak_integer then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|~~ゼータピーク整数~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|Zeta peak integer]]")
	elseif zeta_peak_integer == nil then		elseif zeta_peak_integer == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|~~ゼータピーク整数？~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|Zeta peak integer?]]")
	end		end

	if zeta_integral then		if zeta_integral then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|~~ゼータ積分~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|Zeta integral]]")
	elseif zeta_integral == nil then		elseif zeta_integral == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|~~ゼータ積分？~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|Zeta integral?]]")
	end		end

	if zeta_gap then		if zeta_gap then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|~~ゼータギャップ~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|Zeta gap]]")
	elseif zeta_gap == nil then		elseif zeta_gap == nil then
	table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|~~ゼータギャップ？~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|Zeta gap?]]")
	end		end

2024年8月20日 (火) 16:10にTessyrrh1016による

2024-08-20T16:10:30Z

← 古い版		2024年8月20日 (火) 16:10時点における版
153行目:		153行目:
	local markers = {}		local markers = {}
	if zeta_peak then		if zeta_peak then
	table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs\|~~Zeta peak~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|ゼータピーク]]")
	elseif zeta_peak == nil then		elseif zeta_peak == nil then
	table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs\|~~Zeta peak?~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|ゼータピーク？]]")
	end		end

	if zeta_peak_integer then		if zeta_peak_integer then
	table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs\|~~Zeta peak integer~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|ゼータピーク整数]]")
	elseif zeta_peak_integer == nil then		elseif zeta_peak_integer == nil then
	table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs\|~~Zeta peak integer?~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Peak EDOs\|ゼータピーク整数？]]")
	end		end

	if zeta_integral then		if zeta_integral then
	table.insert(markers, "[[The Riemann zeta function and tuning #Integral of Zeta EDOs\|~~Zeta integral~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|ゼータ積分]]")
	elseif zeta_integral == nil then		elseif zeta_integral == nil then
	table.insert(markers, "[[The Riemann zeta function and tuning #Integral of Zeta EDOs\|~~Zeta integral?~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Integral of Zeta EDOs\|ゼータ積分？]]")
	end		end

	if zeta_gap then		if zeta_gap then
	table.insert(markers, "[[The Riemann zeta function and tuning #Zeta Gap EDOs\|~~Zeta gap~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|ゼータギャップ]]")
	elseif zeta_gap == nil then		elseif zeta_gap == nil then
	table.insert(markers, "[[The Riemann zeta function and tuning #Zeta Gap EDOs\|~~Zeta gap?~~]]")		table.insert(markers, "[[:en:The Riemann zeta function and tuning #Zeta Gap EDOs\|ゼータギャップ？]]")
	end		end

Tessyrrh1016: p.new関数内の、edoを平均律に強引に変換。あまり良くないので、将来的に他の「ed何某」の名前が確定したらそれに合わせて実装するべき

2024-08-17T15:05:43Z

p.new関数内の、edoを平均律に強引に変換。あまり良くないので、将来的に他の「ed何某」の名前が確定したらそれに合わせて実装するべき

← 古い版		2024年8月17日 (土) 15:05時点における版
35行目:		35行目:
	else		else
	suffix = suffix .. equave_ratio		suffix = suffix .. equave_ratio
			end
			if equave_ratio == "2/1" then
			suffix = "平均律"
	end		end
	end		end

2024年7月4日 (木) 01:46にR-4981による

2024-07-04T01:46:00Z

← 古い版		2024年7月4日 (木) 01:46時点における版
46行目:		46行目:
	return nil		return nil
	else		else
	return p.new(tonumber(size), 2, "o")		return p.new(tonumber(size), 2, "平均律")
	end		end
	local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")		local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")

2024年7月4日 (木) 01:45にR-4981による

2024-07-04T01:45:13Z

← 古い版		2024年7月4日 (木) 01:45時点における版
46行目:		46行目:
	return nil		return nil
	else		else
	return p.new(size, 2, "o")		return p.new(tonumber(size), 2, "o")
	end		end
	local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")		local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")

2024年7月4日 (木) 01:44にR-4981による

2024-07-04T01:44:21Z

← 古い版		2024年7月4日 (木) 01:44時点における版
42行目:		42行目:
	-- parse a ET structure		-- parse a ET structure
	function p.parse(unparsed)		function p.parse(unparsed)
			local size, equave = unparsed:match("^(%d+%.%d)(平均律)$")
			if equave == nil then
			return nil
			else
			return p.new(size, 2, "o")
			end
	local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")		local size, suffix, equave = unparsed:match("^(%d+%.%d)([Ee][Dd](.+))$")
	-- local size, suffix, equave = unparsed:match("^(%d+%.%d)([Cc]?[Ee][Dd]?[Tt]?(.*))$")		-- local size, suffix, equave = unparsed:match("^(%d+%.%d)([Cc]?[Ee][Dd]?[Tt]?(.*))$")

R-4981: ページの作成:「local rat = require("Module:Rational") local seq = require("Module:Sequence") local p = {} local common_suffix = { ["3/2"] = "f", ["2"] = "o", ["2/1"] = "o", ["3"] =…」

2024-07-04T01:15:50Z

ページの作成:「local rat = require("Module:Rational") local seq = require("Module:Sequence") local p = {} local common_suffix = { ["3/2"] = "f", ["2"] = "o", ["2/1"] = "o", ["3"] =…」

新規ページ

local rat = require("Module:Rational")
local seq = require("Module:Sequence")
local p = {}

local common_suffix = {
["3/2"] = "f",
["2"] = "o",
["2/1"] = "o",
["3"] = "t",
["3/1"] = "t",
}

local common_ratio = {
["f"] = rat.new(3, 2),
["o"] = 2,
["t"] = 3,
["ϕ"] = (1 + math.sqrt(5)) / 2,
["n"] = math.exp(1),
["π"] = math.pi
}

-- create a ET structure <size>ed<equave>
function p.new(size, equave, suffix)
size = size or 12
equave = equave or 2
if suffix == nil then
local equave_n, equave_m = rat.as_pair(equave)
local equave_ratio = rat.as_ratio(equave)
equave_ratio = equave_ratio:lower()
suffix = "ed"
if common_suffix[equave_ratio] then
suffix = suffix .. common_suffix[equave_ratio]
elseif equave_m == 1 then
suffix = suffix .. equave_n
else
suffix = suffix .. equave_ratio
end
end
return { size = size, equave = equave, suffix = suffix }
end

-- parse a ET structure
function p.parse(unparsed)
local size, suffix, equave = unparsed:match("^(%d+%.*%d*)([Ee][Dd](.+))$")
-- local size, suffix, equave = unparsed:match("^(%d+%.*%d*)([Cc]?[Ee][Dd]?[Tt]?(.*))$")
if equave == nil then
return nil
end
suffix = suffix:lower()
size = tonumber(size)
equave = common_ratio[equave] or rat.parse(equave)
if size == nil or equave == nil then
return nil
end
return p.new(size, equave, suffix)
end

-- construct a string representation for a ET structure
function p.as_string(et)
return et.size .. et.suffix
end

-- convert steps to a proper ratio (except that it is a float approximation)
function p.backslash_ratio(et, steps)
if et.size == 0 then
return 1
end
return rat.as_float(et.equave) ^ (steps / et.size)
end

function p.backslash_display(et, steps)
if et.size == 0 then
return 1
end
return steps .. p.backslash_modifier(et)
end

function p.backslash_modifier(et)
if not rat.eq(et.equave, 2) then
return "\\" .. et.size .. et.suffix
end
return "\\" .. et.size
end

-- convert steps to cents
function p.cents(et, steps)
if et.size == 0 then
return 0
end
steps = steps or 1
return 1200 * steps / et.size * math.log(rat.as_float(et.equave)) / math.log(2)
end

-- convert ratio to steps
-- ratio is a float!
-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
function p.approximate(et, ratio, towards)
towards = towards or 0
if et.size == 0 then
return 0
end
local exact = math.log(ratio) / math.log(rat.as_float(et.equave)) * et.size
if towards < 0 then
return math.floor(exact)
elseif towards > 0 then
return math.ceil(exact)
else
return math.floor(exact + 0.5)
end
end

-- whether this ET tempers out the provided rational number
function p.tempers_out(et, ratio)
local t = 0
for factor, power in pairs(ratio) do
if type(factor) == "number" then
t = t + power * p.approximate(et, factor)
end
end
return t == 0
end

-- determine whether ET is highly composite
function p.is_highly_composite(et)
et.highly_composite = et.highly_composite or rat.is_highly_composite(et.size)
return et.highly_composite
end

-- determine whether ET's size could be within one of zeta function-related sequences
function p.is_zeta(et)
return seq.contains(seq.zeta_peak, et.size)
or seq.contains(seq.zeta_peak_integer, et.size)
or seq.contains(seq.zeta_integral, et.size)
or seq.contains(seq.zeta_gap, et.size)
end

-- describe why
function p.why_zeta(et)
local zeta_peak = seq.contains(seq.zeta_peak, et.size)
local zeta_peak_integer = seq.contains(seq.zeta_peak_integer, et.size)
local zeta_integral = seq.contains(seq.zeta_integral, et.size)
local zeta_gap = seq.contains(seq.zeta_gap, et.size)

local markers = {}
if zeta_peak then
table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs|Zeta peak]]")
elseif zeta_peak == nil then
table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs|Zeta peak?]]")
end

if zeta_peak_integer then
table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs|Zeta peak integer]]")
elseif zeta_peak_integer == nil then
table.insert(markers, "[[The Riemann zeta function and tuning #Peak EDOs|Zeta peak integer?]]")
end

if zeta_integral then
table.insert(markers, "[[The Riemann zeta function and tuning #Integral of Zeta EDOs|Zeta integral]]")
elseif zeta_integral == nil then
table.insert(markers, "[[The Riemann zeta function and tuning #Integral of Zeta EDOs|Zeta integral?]]")
end

if zeta_gap then
table.insert(markers, "[[The Riemann zeta function and tuning #Zeta Gap EDOs|Zeta gap]]")
elseif zeta_gap == nil then
table.insert(markers, "[[The Riemann zeta function and tuning #Zeta Gap EDOs|Zeta gap?]]")
end

return table.concat(markers, "<br>")
end

return p