モジュール:Chord consistency

このモジュールについての説明文ページを モジュール:Chord consistency/doc に作成できます

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

-- determine maximum error
function p.max_error(et, ratios)
	local maxe = 0.0
	for a_key, a in pairs(ratios) do
		local a_approx = ET.approximate(et, rat.as_float(a))
		local e = math.abs((ET.cents(et, a_approx) - rat.cents(a)) / ET.cents(et, 1))
		if (e > maxe) then
			maxe = e
		end
	end
	return maxe
end

function p.consistent_edos(harmonics, distance, ed, maxlen)
	distance = distance or 1.0
	ed = ed or 'edo' or '平均律'
	local max_n = 72
	maxlen = maxlen or max_n
	if max_n < maxlen then max_n = maxlen end
	local all_interval = {}

	for i, h in ipairs(harmonics) do
		-- compute all ratio
		for j, g in ipairs(harmonics) do
			if j > i then
				local a = rat.new(g, h)
				all_interval[rat.as_ratio(a)] = a
			end
		end
	end

	local vals = {}
	for i = 1, max_n do
		local et = ET.parse('' .. i .. ed)
		local consistent = limits.additively_consistent(et, all_interval, false, false, nil)
		if consistent then
			local maxe = p.max_error(et, all_interval)
			if maxe <= 5.0e-11 then
				table.insert(vals, "[[" .. i .. ed .. "]]" .. "(just)")
				break
			end
			local dist = 0.5/maxe
			local up = (dist >= distance)
			local llevel = 0
			while (dist >= 2) do
				llevel = llevel + 1
				dist = dist / 2
			end
			if up then
				if #vals >= maxlen then
					table.insert(vals, "&hellip;")
					break
				end
				table.insert(vals, "[[" .. i .. ed .. "]]" .. string.rep("*", llevel))
			end
		end
	end

	return table.concat(vals, ", ")
end

function p.noinfobox_chord(frame)
	local distance = tonumber(frame.args["Distance"])
	local debug_data = ""
	local infobox_data = {}
	local cats = ""

	--if utils.value_provided(frame.args["Harmonics"]) then
		local harmonics = {}
		for hs in string.gmatch(frame.args["Harmonics"], "[^:]+") do
			h = tonumber(hs)  -- TODO: support rational entries?
			assert(h > 0, "invalid harmonic")
			table.insert(harmonics, h)
		end

		if distance == nil then
			if #harmonics >= 5 then
				distance = 1.5
			elseif #harmonics >= 3 then
				distance = 2.0
			else
				distance = 3.0
			end
		end

		-- reduce harmonics to simplest terms, in case the user accidentally failed to reduce them
		local gcd = harmonics[1]
		for i, h in ipairs(harmonics) do
			gcd = utils._gcd(gcd, h)
			if gcd == 1 then break end
		end
		if gcd > 1 then
			for i, h in ipairs(harmonics) do
				harmonics[i] = harmonics[i] / gcd
			end
		end

		local root = harmonics[1]

		local root_interval_links = {}
		local step_interval_links = {}
		for i, h in ipairs(harmonics) do
			-- compute ratio of this harmonic relative to the root
			local gcd = utils._gcd(h, root)
			local numer = h / gcd
			local denom = root / gcd
			table.insert(root_interval_links, "[[" .. numer .. "/" .. denom .. "]]")

			-- compute ratio of this harmonic relative to the previous
			if i > 1 then
				local prev = harmonics[i-1]
				local step_gcd = utils._gcd(h, prev)
				local step_numer = h / step_gcd
				local step_denom = prev / step_gcd
				table.insert(step_interval_links, "[[" .. step_numer .. "/" .. step_denom .. "]]")
			end
		end
		
		cat = "(d >= " .. distance .. ") " .. p.consistent_edos(harmonics, distance, 'edo', 4)
	--end

	return cat
end

return p