Module:Infobox ET

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Infobox ET.

This module depends on the following other modules: Module: ET Module: Infobox Module: Limits Module: Rational Module: Utils

This module automatically fills in information about a specified equal temperament tuning.

---

local p = {}
local utils = require("Module:Utils")
local rat = require("Module:Rational")
local limits = require("Module:Limits")
local ET = require("Module:ET")
local infobox = require("Module:Infobox")

-- check whether the input is a non-empty string
local function value_provided(s)
	return type(s) == "string" and #s > 0
end

-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximation(et, interval, towards, precomputed_approx)
	local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)

	local tuning = et.size
	if not rat.eq(et.equave, 2) then
		tuning = tuning .. et.suffix
	end

	local ratio = rat.new(approx, et.size)

	local convergement_notice = ""
	local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
	if converges then
		convergement_notice = "<br/>(" .. converges .. ")"
	end

	if rat.as_table(ratio)[1] ~= approx then
		convergement_notice = ""
		local link = rat.as_table(ratio)[2] .. et.suffix
		ratio = " (→[[" .. link .. "|" .. rat.as_ratio(ratio, "\\")
		if not rat.eq(et.equave, 2) then
			ratio = ratio .. et.suffix
		end
		ratio = ratio .. "]])"
	else
		ratio = ""
	end

	local cents = utils._round(ET.cents(et, approx), 6)

	return approx .. "\\" .. tuning .. " (" .. cents .. "¢)" .. ratio .. convergement_notice
end

function p.infobox_ET(frame)
	-- debug mode will disable the categories
	local debug_mode = frame.args["debug"]
	local categories = ""

	local tuning = frame.args["tuning"]
	local et = ET.parse(tuning) or ET.parse("12edo")

	-- category of the main article
	categories = categories .. "[[Category:" .. tuning .. "| ]]"
	-- category of the equal division
	if rat.eq(et.equave, 2) then
		categories = categories
			.. "[[Category:Equal divisions of the octave|"
			.. string.rep("#", string.len(et.size))
			.. "]]"
	else
		categories = categories .. "[[Category:" .. 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 .. "[[Category:Prime EDO|" .. 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 = not zeta_override:match("^[Nn][Oo]$")
	else
		zeta_switch = rat.eq(et.equave, 2) and ET.is_zeta(et)
	end

	-- navigation arrows
	local increment = 1
	if rat.eq(et.equave, 9 / 4) or rat.eq(et.equave, 4) or rat.eq(et.equave, 9) then
		increment = 2
	end
	local prev_one = ""
	if et.size >= increment then
		prev_one = "[[" .. (et.size - increment) .. et.suffix .. "|← " .. (et.size - increment) .. et.suffix .. "]]"
	end
	local next_one = "[[" .. (et.size + increment) .. et.suffix .. "|" .. (et.size + increment) .. et.suffix .. " →]]"

	-- step size
	local step_size = ET.cents(et, 1)
	local note_12edo = ""
	if rat.eq(et.equave, 2) and et.size == 12 then
		note_12edo = "<sup>by definition</sup>"
	end

	-- octave, twelfth, and fifth sizes
	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 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,
	})

	table.insert(infobox_data, {
		"Step size",
		utils._round(step_size, 6) .. "¢" .. note_12edo,
	})

	if not rat.eq(et.equave, 2) then
		table.insert(infobox_data, {
			"Octave",
			approximation(et, 2),
		})
		if not rat.eq(et.equave, 3) then
			table.insert(infobox_data, {
				"Twelfth",
				approximation(et, 3),
			})
		end
	else
		table.insert(infobox_data, {
			"Fifth",
			approximation(et, 3 / 2),
		})
		table.insert(infobox_data, {
			"Semitones (A1:m2)",
			A1 .. ":" .. m2 .. " (" .. A1_cents .. "¢ : " .. m2_cents .. "¢)",
		})
		if 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
				.. "[[Category:Dual-fifth temperaments|"
				.. string.rep("#", string.len(et.size))
				.. "]]"
		end
	end

	local consistency = tonumber(frame.args["Consistency"])
	if consistency == nil then
		consistency = limits.consistency_limit(et, false, 43)
	end
	if consistency == nil then
		consistency = "at least 43"
	end
	if consistency ~= nil then
		table.insert(infobox_data, {
			"Consistency limit",
			consistency,
		})
	end
	local distinct_consistency = tonumber(frame.args["Distinct consistency"])
	if distinct_consistency == nil then
		distinct_consistency = limits.consistency_limit(et, consistency or true, 43)
	end
	if distinct_consistency == nil then
		distinct_consistency = "at least 43"
	end
	if distinct_consistency ~= nil then
		table.insert(infobox_data, {
			"Distinct consistency limit",
			distinct_consistency,
		})
	end

	-- special properties
	if ET.is_highly_composite(et) or zeta_switch then
		local text = ""
		if ET.is_highly_composite(et) then
			text = text .. "[[Highly composite equal division|highly composite]]"
			if rat.eq(et.equave, 2) then
				categories = categories
					.. "[[Category:Highly composite EDO|"
					.. string.rep("#", string.len(et.size))
					.. "]]"
			end
		end
		if zeta_switch then
			if #text > 0 then
				text = text .. "<br>"
			end
			if not value_provided(zeta_override) then
				text = text .. ET.why_zeta(et)
			else
				text = text .. zeta_override
			end
			categories = categories .. "[[Category:Zeta|" .. string.rep("#", string.len(et.size)) .. "]]"
		end
		table.insert(infobox_data, {
			"Special properties",
			'<div style="max-width: 270px;">' .. text .. "</div>",
		})
	end

	local result = infobox.build("[[" .. et.suffix .. "|" .. tuning .. "]]", infobox_data, prev_one, next_one)
	if not value_provided(debug_mode) then
		result = result .. categories
	end
	return result
end

return p