@@ Line 1: / Line 1: @@
 local p = {}
-local rat = require('Module:Rational')
+local he = require("Module:Harmonic entropy")
-local u = require('Module:Utils')
+local infobox = require("Module:Infobox")
-local i = require('Module:Interval')
+local rat = require("Module:Rational")
-local infobox = require('Module:Infobox')
+local utils = require("Module:Utils")
+local yesno = require("Module:Yesno")
+-- check whether the input is a non-empty string
+local function value_provided(s)
+	return type(s) == "string" and #s > 0
+end
 function p.infobox_interval(frame)
-	local debug_mode = frame.args['debug'] ~= nil
+	local debug_mode = yesno(frame.args["debug"])
-	-- TODO: better input parsing + large intervals + irrational intervals
+	local page_name = frame:preprocess("{{PAGENAME}}")
-	local ratio_arg = frame.args['Ratio'] or '2/1'
-	local ratio = rat.parse(ratio_arg) or rat.new(2)
+	local rational = false
+	local small = false -- numerator and denominator can be represented as Lua numbers, or irrational
-	local ratio_str = rat.as_ratio(ratio)
+	local regular = false -- finite and greater than zero
-	local ratio_ket = rat.as_ket(ratio, frame)
-	local ratio_approx = rat.as_float(ratio)
+	local ratio = nil
-	local ratio_cents = rat.cents(ratio)
+	local cents = nil
+	local ket = nil
-	local regular = not ratio.nan and not ratio.zero and not ratio.inf
+	local ratio_string = nil
 	local infobox_data = {}
-	local cats = '[[Category:Rational intervals]]'
+	local cats = ""
-	table.insert(infobox_data, {
+	-- intervals with relatively small powers
-		'Ratio',
+	if value_provided(frame.args["Ratio"]) then
-		ratio_str
+		ratio = rat.parse(frame.args["Ratio"])
-	})
+		if ratio ~= nil then
-	table.insert(infobox_data, {
+			rational = true
-		'Factorization',
+			small = true
-		rat.factorisation(ratio)
+			regular = not ratio.nan and not ratio.inf and not ratio.zero and ratio.sign > 0
-	})
+			cents = rat.cents(ratio)
+			ket = rat.as_ket(ratio, frame)
+			ratio_string = rat.as_ratio(ratio)
+		end
+	end
+	-- intervals with large powers
+	if ratio == nil and value_provided(frame.args["Ket"]) then
+		ratio = rat.from_ket(frame.args["Ket"])
+		if ratio ~= nil then
+			rational = true
+			small = false
+			regular = true
+			cents = rat.cents(ratio)
+			ket = rat.as_ket(ratio, frame)
+			-- display Ratio unless it is page name, in which case it is probably a fallback -- what does this mean?
+			if frame.args["Ratio"] ~= page_name then
+				ratio_string = frame.args["Ratio"] or ""
+			end
+		end
+	elseif ratio ~= nil and value_provided(frame.args["Ket"]) then
+		cats = cats .. "[[Category:Todo:remove explicit ket notation]]"
+	end
+	-- irrational intervals
+	if ratio == nil and value_provided(frame.args["Cents"]) then
+		cents = tonumber(frame.args["Cents"])
+		if cents ~= nil then
+			rational = false
+			small = true
+			regular = true
+			if value_provided(frame.args["Ket"]) then
+				ket = frame.args["Ket"]
+			end
+			-- Ratio is LaTeX unless it is page name, in which case it is probably a fallback -- what does this mean?
+			if frame.args["Ratio"] ~= page_name then
+				ratio_string = frame.args["Ratio"] or ""
+			else
+				cats = cats .. "[[Category:Todo:add interval ratio]]"
+			end
+		end
+	elseif ratio ~= nil and value_provided(frame.args["Cents"]) then
+		cats = cats .. "[[Category:Todo:remove explicit cents]]"
+	end
+	if not (regular or rational) then
+		cats = cats .. "[[Category:Todo:initialise interval]]"
+	end
+	-- categorize by rationality and prime limit
 	if regular then
+		if rational then
+			local prime_limit = 2
+			if not rat.eq(ratio, 1) then
+				prime_limit = rat.max_prime(ratio)
+			end
+			cats = cats .. "[[Category:Rational intervals]]" .. "[[Category:" .. prime_limit .. "-limit intervals]]"
+		else
+			cats = cats .. "[[Category:Irrational intervals]]"
+		end
+	end
+	local special_properties = {}
+	if rational then
+		if small and rat.is_superparticular(ratio) then
+			if rat.is_square_superparticular(ratio) then
+				table.insert(special_properties, "[[Square superparticular|square superparticular]]")
+			else
+				table.insert(special_properties, "[[Superparticular interval|superparticular]]")
+			end
+			cats = cats .. "[[Category:Superparticular ratios]]"
+		end
+		if rat.is_reduced(ratio, 2, not small) then
+			table.insert(special_properties, "[[Octave reduction|reduced]]")
+		end
+		if rat.is_harmonic(ratio) then
+			num, den = rat.as_pair (ratio)
+			table.insert(special_properties, "[[harmonic]]")
+			cats = cats .. "[[Category:Harmonics|" .. string.rep("#", string.len(num)) .. "]]"
+			if rat.is_prime(ratio) then
+				table.insert(special_properties, "[[prime harmonic]]")
+				cats = cats .. "[[Category:Prime harmonics|" .. string.rep("#", string.len(num)) .. "]]"
+			end
+			if rat.is_highly_composite(ratio) then
+				table.insert(special_properties, "[[highly composite harmonic]]")
+				cats = cats .. "[[Category:Highly composite harmonics|" .. string.rep("#", string.len(num)) .. "]]"
+			end
+		elseif rat.is_harmonic(ratio, true, not small) then
+			table.insert(special_properties, "[[Harmonic|reduced harmonic]]")
+			cats = cats .. "[[Category:Octave-reduced harmonics]]"
+		elseif rat.is_subharmonic(ratio, true, not small) then
+			table.insert(special_properties, "[[Subharmonic|reduced subharmonic]]")
+			cats = cats .. "[[Category:Octave-reduced subharmonics]]"
+		end
+	elseif regular then
+		if cents >= 0 and cents < 1200 then
+			table.insert(special_properties, "[[Octave reduction|reduced]]")
+		end
+	end
+	if value_provided(ratio_string) then
+		if rational then
+			table.insert(infobox_data, {
+				"Ratio",
+				ratio_string,
+			})
+		else
+			table.insert(infobox_data, {
+				"Expression",
+				"<math>" .. ratio_string .. "</math>",
+			})
+		end
+	end
+	if regular and rational then
+		if ket:match("<sup>") then
+			-- there was a subsequence of 4+ zeros
+			table.insert(infobox_data, {
+				"[[Subgroup monzos and vals|Subgroup monzo]]",
+				rat.as_subgroup_ket(ratio, frame),
+			})
+		else
+			table.insert(infobox_data, {
+				"Factorization",
+				rat.factorisation(ratio),
+			})
+			table.insert(infobox_data, {
+				"[[Monzo]]",
+				ket,
+			})
+		end
+	elseif rational then
+		table.insert(infobox_data, {
+			"Factorization",
+			rat.factorisation(ratio),
+		})
+	elseif value_provided(ket) then
+		-- irrational ket is provided:
 		table.insert(infobox_data, {
-			'[[Just intonation subgroup|Subgroup]]',
+			"[[Monzo]]",
-			rat.subgroup(ratio)
+			frame:expandTemplate({
+				title = "Monzo",
+				args = { ket },
+			}),
 		})
 	end
 	if regular then
 		table.insert(infobox_data, {
-			'[[Monzo]]',
+			"Size in [[cent]]s",
-			ratio_ket
+			utils._round(cents, 7) .. "¢",
-		})
-		table.insert(infobox_data, {
-			'Size in [[cent]]s',
-			i._to_cents(ratio_approx, 8) .. '¢'
 		})
 	end
-	local name = frame.args['Name']
+	local name = frame.args["Name"]
-	if name and #name > 0 then
+	if value_provided(name) then
-		local caption = 'Name'
+		local caption = "Name"
-		if name:match(',') then caption = 'Names' end
+		if name:match(",") then
+			caption = "Names"
+			-- removing manual line breaks
+			local matches
+			name, matches = name:gsub("<br%s*/?>", "")
+			if matches > 0 then
+				cats = cats .. "[[Category:Todo:remove manual line breaks]]"
+			end
+			-- removing whitespaces after commas
+			name = name:gsub(",%s+", ",")
+			-- placing line breaks after commas
+			name = name:gsub(",", ",<br>")
+		end
 		table.insert(infobox_data, {
 			caption,
-			name
+			name,
 		})
 	else
-		cats = cats .. '[[Category:Todo:add interval name]]'
+		cats = cats .. "[[Category:Todo:add interval name]]"
 		table.insert(infobox_data, {
-			'Name(s)',
+			"Name(s)",
-			'<abbr title="missing value for parameter \'Name\'">\'\'missing\'\'</abbr></span><sup>[[Template:Infobox Interval| ?&nbsp;]]</sup>'
+			"<abbr title=\"missing value for parameter 'Name'\">''missing''</abbr><sup>[[Template:Infobox Interval| ?&nbsp;]]</sup>",
 		})
 	end
-	-- TODO: compute?
+	local colour_name = frame.args["Color name"]
-	local colour_name = frame.args['Color name']
+	if value_provided(colour_name) then
-	if colour_name and #colour_name > 0 then
 		table.insert(infobox_data, {
-			'[[Color notation|Color name]]',
+			"[[Kite's color notation|Color name]]",
-			colour_name
+			colour_name,
 		})
+	elseif regular and rational then
+		cats = cats .. "[[Category:Todo:add color name]]"
 	end
-	local FJS_name = frame.args['FJS name']
+	local FJS_name = frame.args["FJS name"]
-	if not FJS_name or #FJS_name == 0 then
+	if not value_provided(FJS_name) and rational and regular then
 		FJS_name = rat.as_FJS(ratio)
+	elseif value_provided(FJS_name) then
+		local matches
+		FJS_name = FJS_name:gsub("%s", "")
+		FJS_name, matches = FJS_name:gsub("<br%s*/?>", "")
+		if matches > 0 then
+			cats = cats .. "[[Category:Todo:remove manual line breaks]]"
+		end
+		FJS_name, matches = FJS_name:gsub("<sup>(.*)</sup>", "^{%1}")
+		if matches > 0 then
+			cats = cats .. "[[Category:Todo:replace sup and sub with LaTeX]]"
+		end
+		FJS_name, matches = FJS_name:gsub("<sub>(.*)</sub>", "_{%1}")
+		if matches > 0 then
+			cats = cats .. "[[Category:Todo:replace sup and sub with LaTeX]]"
+		end
+	end
+	if value_provided(FJS_name) then
+		FJS_name = FJS_name:gsub("^(%w+)", "\\text{%1}")
+		FJS_name = FJS_name:gsub("(%-%d+)", "{%1}")
+		if #FJS_name <= 200 then
+			table.insert(infobox_data, {
+				"[[Functional Just System|FJS name]]",
+				"<math>" .. FJS_name .. "</math>",
+			})
+		end
+	end
+	if #special_properties > 0 then
+		table.insert(infobox_data, {
+			"Special properties",
+			table.concat(special_properties, ",<br>"),
+		})
 	end
-	if FJS_name and #FJS_name > 0 then
+	-- interval complexity
+	if rational and regular then
+		table.insert(infobox_data, {
+			"[[Tenney norm]] (log<sub>2</sub> ''nd'')",
+			utils._round(rat.tenney_height(ratio), 6),
+		})
 		table.insert(infobox_data, {
-			'[[Functional Just System|FJS name]]',
+			"[[Weil norm]] (log<sub>2</sub> max(''n'', ''d''))",
-			frame:preprocess('<math>' .. FJS_name .. '</math>')
+			utils._round(rat.weil_height(ratio), 6),
 		})
+		table.insert(infobox_data, {
+			"[[Wilson norm]] (sopfr(''nd''))",
+			utils._round(rat.wilson_height(ratio), 6),
+		})
+	end
+	local harmonic_entropy = frame.args["Harmonic entropy"]
+	if regular and value_provided(harmonic_entropy) then
+		harmonic_entropy_switch = harmonic_entropy:match("^[Yy][Ee][Ss]$")
+		if harmonic_entropy_switch then
+			table.insert(infobox_data, {
+				"[[Harmonic entropy]]<br>(Shannon, <math>\\sqrt{nd}</math>)",
+				"~" .. utils._round(he.harmonic_entropy(cents), 6) .. " bits",
+			})
+		end
+	end
+	local is_comma = value_provided(frame.args["Comma"])
+	local comma = nil
+	if is_comma and regular and cents > 0 then
+		-- rational powers are not considered commas
+		if not (rational and rat.is_power(ratio)) then
+			if cents <= 3.5 then
+				comma = "[[Unnoticeable comma|unnoticeable]]"
+				cats = cats .. "[[Category:Unnoticeable commas]]"
+			elseif cents <= 30 then
+				comma = "[[Small comma|small]]"
+				cats = cats .. "[[Category:Small commas]]"
+			elseif cents <= 100 then
+				comma = "[[Medium comma|medium]]"
+				cats = cats .. "[[Category:Medium commas]]"
+			else
+				comma = "[[Large comma|large]]"
+				cats = cats .. "[[Category:Large commas]]"
+			end
+		end
 	end
+	if comma then
-	if regular then
 		table.insert(infobox_data, {
-			'Norms',
+			"[[Comma|Comma size]]",
-			'[[Tenney height|log<sub>2</sub> n⋅d]]: ' .. u._round(rat.tenney_height(ratio), 6) .. '<br/>'
+			comma,
-				.. '[[Weil height|max(n, d)]]: ' .. u._round(rat.weil_height(ratio), 6) .. '<br/>'
-				.. '[[Benedetti height|n⋅d]]: ' .. u._round(rat.benedetti_height(ratio), 6)
 		})
 	end
+	if comma and rational then
-	if regular then
+		local S_expressions = rat.find_S_expression(ratio)
+		if #S_expressions > 0 then
+			local caption = "[[S-expression]]"
+			if #S_expressions > 1 then
+				caption = caption .. "s"
+			end
+			table.insert(infobox_data, {
+				caption,
+				table.concat(S_expressions, ",<br>"),
+			})
+		end
+	end
+	local sound = frame.args["Sound"]
+	if value_provided(sound) then
+		cats = cats .. "[[Category:Pages with internal sound examples]]"
 		table.insert(infobox_data, {
-			'[[Harmonic entropy]]',
+			"[[File:" .. sound .. "|270px]]<br><span style=\"font-size: 75%;\">[[:File:" .. sound .. "|<nowiki>[sound info]</nowiki>]]</span>",
-			'~' .. u._round(i.harmonic_entropy(ratio_cents), 6)
 		})
+	elseif debug_mode and debug_mode ~= "hide" and regular then
+		local hz = 2 ^ (math.log(440) / math.log(2) + cents / 1200)
+		-- is it within hearing range?
+		if hz >= 20 and hz <= 20000 then
+			local html_id = "interval_" .. tostring(math.floor(cents))
+			table.insert(infobox_data, {
+				"<div style=\"display: flex; justify-content: space-around;\"><div style=\"width: 270px; text-align: center;\">"
+					.. frame:expandTemplate({
+						title = "User:Plumtree/Interval Sound",
+						args = {
+							Frequency = tostring(hz),
+							Center = "true",
+							Label = "Audio demonstration",
+							Attributes = "id=\"" .. html_id .. "\"",
+						},
+					})
+					.. "<div class=\"sequence-audio-timbre-selector\" data-target=\""
+					.. html_id
+					.. "\" data-key=\"interval-audio\" data-default=\"semisine\"></div>"
+					.. "</div></div>",
+			})
+		end
 	end
-	local sound = frame.args['Sound']
+	if value_provided(frame.args["Calc"]) or (regular and rational) then
-	if sound and #sound > 0 then
+		local query = frame.args["Calc"] or ""
-		cats = cats .. '[[Category:Pages with internal sound examples]]'
+		if not value_provided(query) then
+			if small then
+				query = ratio_string
+			else
+				query = "|" .. rat.as_ket(ratio, nil, false, true) .. ">"
+			end
+		end
+		query = mw.uri.encode(query)
 		table.insert(infobox_data, {
-			'[[File:' .. sound .. '|270px]]<br/><small>[[:File:' .. sound .. '|[sound info]]]</small>'
+			"<span style=\"font-size: 75%;\">[https://www.yacavone.net/xen-calc/?q=" .. query .. " Open this interval in ''xen-calc'']</span>",
 		})
 	end
+	local result = infobox.build("<u>Interval&nbsp;information</u>", infobox_data)
-	table.insert(infobox_data, {
-		'<small>[https://www.yacavone.net/xen-calc/?q=' .. ratio_str .. ' open this interval in \'\'xen-calc\'\']</small>'
-	})
-	local s = infobox.build(
-		'<u>Interval information</u>',
-		infobox_data
-	)
 	if not debug_mode then
-		s = s .. cats
+		result = result .. cats
 	end
-	return s
+	return frame:preprocess(result)
 end
 return p

Module:Infobox interval: Difference between revisions