@@ Line 1: / Line 1: @@
 local p = {}
-local i = require('Module:Interval')
-local u = require('Module:Utils')
-local rat = require('Module:Rational')
-local l = require('Module:Limits')
--- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
+local ET = require("Module:ET")
-local function approximate(size, equave, interval, towards)
+local getArgs = require("Module:Arguments").getArgs
-	towards = towards or 0
+local infobox = require("Module:Infobox")
-	local exact = math.log(interval) / math.log(rat.as_float(equave)) * size
+local limits = require("Module:Limits")
-	local approx = nil
+local rat = require("Module:Rational")
-	if towards < 0 then
+local utils = require("Module:Utils")
-		approx = math.floor(exact)
+local yesno = require("Module:Yesno")
-	elseif towards > 0 then
-		approx = math.ceil(exact)
+-- check whether the input is a non-empty string
-	else
+local function value_provided(s)
-		approx = math.floor(exact + 0.5)
+	return type(s) == "string" and #s > 0
-	end
-	return approx
 end
 -- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
-local function approximation(suffix, size, equave, interval, towards, precomputed_approx)
+local function approximation(et, interval, towards, precomputed_approx)
-	local approx = approximate(size, equave, interval, towards or 0)
+	local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)
-	if precomputed_approx then
-		approx = precomputed_approx
+	-- string for backslash notation
+	-- "edo" is omitted
+	local tuning = et.size
+	if not rat.eq(et.equave, 2) then
+		tuning = tuning .. et.suffix
 	end
-	local tuning = size
-	if not rat.eq(equave, 2) then
+	local ratio = rat.new(approx, et.size)
-		tuning = tuning .. suffix
+	-- convergence notice, suppressed for 1ed's
+	local convergement_notice = ""
+	local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
+	if et.size > 1 and converges then
+		convergement_notice = "<br>(" .. converges .. ")"
 	end
-	local ratio = rat.new(approx, size)
 	if rat.as_table(ratio)[1] ~= approx then
-		local link = rat.as_table(ratio)[2] .. suffix
+		convergement_notice = ""
-		ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
+		local link = rat.as_table(ratio)[2] .. et.suffix
-		if not rat.eq(equave, 2) then
+		ratio = string.format(" (&rarr;&nbsp;[[%s|%s%s]])",
-			ratio = ratio .. suffix
+			link, rat.as_ratio(ratio, "\\"), (rat.eq(et.equave, 2) == false and et.suffix or ""))
-		end
-		ratio = ratio .. ']])'
 	else
-		ratio = ''
+		ratio = ""
 	end
-	local cents = i._to_cents(i._backslash_ratio(approx .. '\\' .. tuning), 6)
-	return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio
+	local cents = utils._round(ET.cents(et, approx), 6)
+	return string.format("%s\\%s (%s{{c}})%s%s",
+		approx, tuning, utils._round(ET.cents(et, approx), 6), ratio, convergement_notice)
 end
 function p.infobox_ET(frame)
-	local tuning = frame.args['tuning']
+	local args = getArgs(frame)
-	local size, equave = i.parse_ET(tuning)
-	local prime = ""
+	-- debug mode will disable the categories
-	if u.is_prime(size) then
+	local debug_mode = yesno(frame.args["debug"] or args["debug"], false)
-		prime = " (prime)"
+	local wtext = yesno(frame.args["wtext"] or args["wtext"])
+	local tuning = frame.args["tuning"]
+	local et = ET.parse(tuning) or ET.parse(tuning .. "edo") or ET.parse("12edo")
+	-- category of the main article
+	local categories = string.format(" {{#ifexist: Category:%s|[[Category:%s| ]]|}}", tuning, tuning)
+	-- category of the equal division
+	if rat.eq(et.equave, 2) then
+		categories = categories
+			.. string.format(" [[Category:Equal divisions of the octave|%s]]",
+				string.rep("#", string.len(et.size)))
+	elseif rat.eq(et.equave, 3) then
+		categories = categories .. string.format(" [[Category:Edts|%s]]",
+			string.rep("#", string.len(et.size)))
+	elseif rat.eq(et.equave, rat.new (3, 2)) then
+		categories = categories .. string.format(" [[Category:Edfs|%s]]",
+			string.rep("#", string.len(et.size)))
+	else
+		categories = categories .. string.format(" [[Category:%s's|%s]]",
+			et.suffix, string.rep("#", string.len(et.size)))
+	end
+	-- prime factorization
+	local prime_factorization_override = frame.args["Prime factorization"]
+	local prime_factorization
+	if not value_provided(prime_factorization_override) then
+		prime_factorization = utils._prime_factorization(et.size)
+		if utils.is_prime(et.size) then
+			prime_factorization = prime_factorization .. " (prime)"
+			if rat.eq(et.equave, 2) then
+				categories = categories
+					.. string.format(" [[Category:Prime EDOs|%s]]",
+						string.rep("#", string.len(et.size)))
+			end
+		end
+		if ET.is_highly_composite(et) and et.size > 1 then
+			prime_factorization = prime_factorization .. " (highly composite)"
+			if rat.eq(et.equave, 2) then
+				categories = categories
+					.. string.format(" [[Category:Highly composite EDOs|%s]]",
+						string.rep("#", string.len(et.size)))
+			end
+		end
+	else
+		prime_factorization = prime_factorization_override
+	end
+	-- zeta test
+	local zeta_override = frame.args["Zeta"]
+	local zeta_switch
+	if value_provided(zeta_override) then
+		zeta_switch = zeta_override:match("^[Yy][Ee][Ss]$") and ET.is_zeta(et)
+	else
+		zeta_switch = false
+	end
+	-- navigation arrows
+	local increment = 1
+	if rat.eq(et.equave, rat.new(9, 4)) or rat.eq(et.equave, 4) or rat.eq(et.equave, 9) then
+		increment = 2
 	end
-	local suffix = tuning:match('%d+(ed.+)')
+	local prev_one = ""
+	if et.size >= increment then
-	local prev_one = ''
+		prev_one = string.format("[[%s|&larr;&nbsp;%s]]",
-	if size > 1 then
+			(et.size - increment) .. et.suffix, (et.size - increment) .. et.suffix)
-		prev_one = '[[' .. (size - 1) .. suffix .. '|← ' .. (size - 1) .. suffix .. ']]'
 	end
-	local next_one = '[[' .. (size + 1) .. suffix .. '|' .. (size + 1) .. suffix .. ' →]]'
+	local next_one = string.format("[[%s|%s&nbsp;&rarr;]]",
+		(et.size + increment) .. et.suffix, (et.size + increment) .. et.suffix)
-	local step_size = i._backslash_ratio('1\\' .. tuning)
-	local fifth = approximate(size, equave, 3/2)
-	local fifth_error = i._to_cents(i._backslash_ratio(fifth .. '\\' .. tuning)) - i._to_cents(3/2)
-	local dual_fifth = math.abs(fifth_error) > i._to_cents(step_size) / 3
-	local note_12edo = ''
+	-- step size in cents
-	if rat.eq(equave, 2) and size == 12 then
+	local step_size = ET.cents(et, 1)
-		note_12edo = '<sup>by definition</sup>'
+	if step_size > 100 then
+		categories = categories .. string.format(" [[Category:Macrotonal|%s]]",
+			string.rep("#", string.len(et.size)))
 	end
+	local note_12edo = ""
-	local octave = approximate(size, equave, 2)
+	if rat.eq(et.equave, 2) and et.size == 12 then
-	local A1 = 7 * fifth - 4 * octave
+		note_12edo = " (by&nbsp;definition)"
-	local m2 = 3 * octave - 5 * fifth
+	end
-	local A1_cents = i._to_cents(i._backslash_ratio(A1 .. '\\' .. tuning), 4)
-	local m2_cents = i._to_cents(i._backslash_ratio(m2 .. '\\' .. tuning), 4)
+	-- octave, twelfth, and fifth in steps
+	local octave = ET.approximate(et, 2)
+	local twelfth = ET.approximate(et, 3)
+	local fifth = -octave + twelfth -- 3/2 = [-1 1>
+	local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
+	local is_dual_fifth = math.abs(fifth_error) > step_size / 3
+	local A1 = -11 * octave + 7 * twelfth -- 2187/2048 = [-11 7>
+	local m2 = 8 * octave - 5 * twelfth -- 256/243 = [8 -5>
+	local A1_cents = utils._round(ET.cents(et, A1), 4)
+	local m2_cents = utils._round(ET.cents(et, m2), 4)
+	-- display
 	local infobox_data = {}
 	table.insert(infobox_data, {
-		'Prime factorization',
+		"Prime factorization",
-		u._prime_factorization(size) .. prime
+		prime_factorization,
 	})
 	table.insert(infobox_data, {
-		'Step size',
+		"Step size",
-		i._to_cents(step_size, 6) .. '¢' .. note_12edo
+		string.format("%s{{c}}%s&nbsp;",
+			utils._round(step_size, 6), note_12edo)
 	})
-	if not rat.eq(equave, rat.new(3, 2)) then
+	if not rat.eq(et.equave, 2) then
 		table.insert(infobox_data, {
-			'Fifth',
+			"Octave",
-			approximation(suffix, size, equave, 3/2)
+			approximation(et, 2),
 		})
-	end
+		if not rat.eq(et.equave, 3) then
-	if not rat.eq(equave, 2) then
+			table.insert(infobox_data, {
+				"Twelfth",
+				approximation(et, 3),
+			})
+		end
+	else
 		table.insert(infobox_data, {
-			'Octave',
+			"Fifth",
-			approximation(suffix, size, equave, 2)
+			approximation(et, 3 / 2),
 		})
-	end
-	table.insert(infobox_data, {
-		'Semitones (A1:m2)',
-		A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
-	})
-	if dual_fifth then
 		table.insert(infobox_data, {
-			'Sharp fifth',
+			"Semitones (A1:m2)",
-			approximation(suffix, size, equave, 3/2, 1)
+			string.format("%s:%s (%s{{c}}&nbsp;:&nbsp;%s{{c}})",
-		})
+				A1, m2, A1_cents, m2_cents)
-		table.insert(infobox_data, {
-			'Flat fifth',
-			approximation(suffix, size, equave, 3/2, -1)
-		})
-		local sharp = approximate(size, equave, 3/2, 1)
-		local flat = approximate(size, equave, 3/2, -1)
-		table.insert(infobox_data, {
-			'Major 2nd',
-			approximation(suffix, size, equave, 9/8, 0, sharp + flat - octave)
 		})
+		if is_dual_fifth and et.size > 0 then
+			table.insert(infobox_data, {
+				"Dual sharp fifth",
+				approximation(et, 3 / 2, 1),
+			})
+			table.insert(infobox_data, {
+				"Dual flat fifth",
+				approximation(et, 3 / 2, -1),
+			})
+			local sharp = ET.approximate(et, 3 / 2, 1)
+			local flat = ET.approximate(et, 3 / 2, -1)
+			table.insert(infobox_data, {
+				"Dual major 2nd",
+				approximation(et, 9 / 8, 0, sharp + flat - octave),
+			})
+			categories = categories
+				.. string.format(" [[Category:Dual-fifth temperaments|%s]]",
+					string.rep("#", string.len(et.size)))
+		end
 	end
-	local consistency = tonumber(frame.args['Consistency'])
+	-- consistency and distinct consistency
+	-- max_limit is used to prevent timeout
+	local consistency = tonumber(frame.args["Consistency"])
+	local max_limit = rat.eq(et.equave, 2) and 43 or 32
 	if consistency == nil then
-		consistency = l.consistency_limit(size, equave, false, 17)
+		consistency = limits.consistency_limit(et, false, max_limit)
 	end
 	if consistency == nil then
-		consistency = 'at least 17'
+		consistency = "at least " .. max_limit
 	end
 	if consistency ~= nil then
 		table.insert(infobox_data, {
-			'Consistency limit',
+			"Consistency limit",
-			consistency
+			consistency,
 		})
 	end
-	local distinct_consistency = tonumber(frame.args['Distinct consistency'])
+	local distinct_consistency = tonumber(frame.args["Distinct consistency"])
 	if distinct_consistency == nil then
-		distinct_consistency = l.consistency_limit(size, equave, true, 29)
+		distinct_consistency = limits.consistency_limit(et, consistency or true, max_limit)
 	end
 	if distinct_consistency == nil then
-		distinct_consistency = 'at least 29'
+		distinct_consistency = "at least " .. max_limit
 	end
 	if distinct_consistency ~= nil then
 		table.insert(infobox_data, {
-			'Distinct consistency limit',
+			"Distinct consistency limit",
-			distinct_consistency
+			distinct_consistency,
 		})
 	end
-	local header = '<table style="width: 100%; margin: 0"><tr>'
+	-- special properties
-		.. '<td style="width: 15%; text-align: left; white-space: nowrap; font-size: smaller">'
+	if ET.is_zeta(et) then
-		.. prev_one
+		local text = ""
-		.. '</td>'
+		if rat.eq(et.equave, 2) then
-		.. '<td style="width: 70%; padding-left: 1em; padding-right: 1em; text-align: center">'
+			categories = categories
-		.. frame.args['tuning']
+				.. string.format(" [[Category:Zeta record EDOs|%s]]",
-		.. '</td>'
+					string.rep("#", string.len(et.size)))
-		.. '<td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">'
+			if zeta_switch then
-		.. next_one
+				text = text .. ET.why_zeta(et)
-		.. '</td>'
+			end
-		.. '</tr></table>'
+		end
-	local s = '<div style="\n' ..
+		if #text > 0 then
-		'border: 1px solid #999;\n' ..
+			table.insert(infobox_data, {
-		'margin: 0;\n' ..
+				"Special properties",
-		'margin-left: 1em;\n' ..
+				"<div style=\"max-width: 300px;\">" .. text .. "</div>",
-		'margin-bottom: 0.5em;\n' ..
+			})
-		'padding: 0.5em;\n' ..
+		end
-		'background-color: #f0f0f0;\n' ..
-		'min-width: 15em;\n' ..
-		'float: right;\n' ..
-		'">\n' ..
-		'{| width="100%" style="border-collapse: collapse;"\n' ..
-		'|+ style="font-weight: bold" | ' .. header .. '\n'
-	for i, entry in ipairs(infobox_data) do
-		local caption = entry[1]
-		local text = entry[2]
-		s = s .. '|-\n' ..
-			'| style="text-align:right; padding-right: 0.25em" | ' .. caption .. '\n' ..
-			'| style="background-color: white; padding-left: 0.25em; font-weight: bold" | ' .. text .. '\n'
 	end
-	s = s .. '|}</div>'
-	return s
+	local result = infobox.build(string.format("[[%s|%s]]", et.suffix, tuning), infobox_data, prev_one, next_one)
+	if not debug_mode then
+		result = result .. categories
+	end
+	if wtext then
+		result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
+	end
+	return frame:preprocess(result)
 end
 return p

Module:Infobox ET: Difference between revisions