Module:Harmonics intro

Documentation for this module may be created at Module:Harmonics intro/doc

-- Module:Harmonics intro
-- Generates the opening sentences of the "Harmonics n–2n" and "Subharmonics n–2n" pages.
-- Called through Template:Harmonics intro and Template:Subharmonics intro.
local p = {}
local getArgs = require("Module:Arguments").getArgs

local EN_DASH = "–"

-- "n:(n+1):…:2n", written out in full for small n
local function chord(lo, hi)
	if hi - lo <= 7 then
		local t = {}
		for i = lo, hi do
			t[#t + 1] = i
		end
		return table.concat(t, ":")
	end
	return string.format("%d:%d:…:%d", lo, lo + 1, hi)
end

local function page_exists(title)
	local t = mw.title.new(title)
	return t ~= nil and t.exists
end

local function build(args, sub)
	local n = tonumber(args[1] or args.n)
	if not n or n < 1 or n ~= math.floor(n) then
		return '<strong class="error">Template:Harmonics intro requires a positive integer, e.g. <code>{{Harmonics intro|12}}</code>.</strong>'
	end
	local range = n .. EN_DASH .. 2 * n
	local twin_title = (sub and "Harmonics " or "Subharmonics ") .. range

	-- "harmonics 12–24" is a noun phrase, not the name of a scale: plural, lower case
	local phrase = (sub and "subharmonics " or "harmonics ") .. range

	local out = {}
	if sub then
		out[#out + 1] = string.format(
			"The '''%s''' are the [[subharmonic]]s %d through %d of the [[subharmonic series]]. Above the root they form the ratios %d/%d, %d/%d, …, %d/%d and span one octave. ",
			phrase,
			n,
			2 * n,
			2 * n,
			2 * n,
			2 * n,
			2 * n - 1,
			2 * n,
			n
		)
		out[#out + 1] = string.format("Used as a scale, this set is also called mode %d of the subharmonic series. ", n)
	else
		out[#out + 1] = string.format(
			"The '''[[Harmonic series#Segments|harmonic segment]] %d::%d''' (also '''%s''') consists of harmonics %d through %d (%s) and spans one octave above the root. ",
			n,
			2 * n,
			phrase,
			n,
			2 * n,
			chord(n, 2 * n)
		)
		out[#out + 1] = string.format("Used as a scale, it is also called mode %d of the harmonic series. ", n)
	end

	-- other names, given as aka="name; name"
	local akas = {}
	for name in mw.text.gsplit(args.aka or "", "%s*;%s*") do
		if name ~= "" then
			akas[#akas + 1] = "'''" .. name .. "'''"
		end
	end
	if #akas > 0 then
		out[#out + 1] = "It is also known as " .. table.concat(akas, " and ") .. ". "
	end

	-- inverse
	if n ~= 2 and page_exists(twin_title) then -- 2–4 is its own inverse
		out[#out + 1] = string.format(
			"The inverse consists of [[%s|%s]]. ",
			twin_title,
			(sub and "harmonics " or "subharmonics ") .. range
		)
	end
	return (table.concat(out):gsub("%s+$", ""))
end

function p.harmonics(frame)
	return build(getArgs(frame), false)
end

function p.subharmonics(frame)
	return build(getArgs(frame), true)
end

p._build = build

return p