Module:Harmonics in cet

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Harmonics in cet.

This module depends on the following other modules: Module: Utils Module: Yesno

Calculates approximations for harmonics in equal-step tunings and presents them in form of a table.

---

local p = {}

local function approx(step, intervals, title, prec)
	local tpri = {"! colspan=\"2\" | Harmonic "}
	local tabs = {"! rowspan=\"2\" | Error \n! Absolute ([[cent|¢]]) "}
	local trel = {"! [[Relative interval error|Relative]] (%) "}
	local tdeg = {"! colspan=\"2\" | Steps"}
	
	local fmt_abs = string.format(" %%+.%df", prec)
	local fmt_rel = " %+.0f"
	local size = step / 1200
	
	for _, p in pairs(intervals) do
		s = math.log(p) / math.log(2)
		v = s/size
		ev = math.floor(v + 0.5)
		table.insert(tpri, "" .. p)
		table.insert(tabs, "" .. string.gsub(string.format(fmt_abs, 1200 * (ev - v) * size), "%-", "-"))
		table.insert(trel, "" .. string.gsub(string.format(fmt_rel, 100 * (ev - v)), "%-", "-"))
		table.insert(tdeg, "" .. ev)
	end
	
	return "{| class=\"wikitable center-all\"\n"
		.. "|+ style=\"font-size: 105%;\" | " .. title .. "\n"
		.. "|-\n"
		.. table.concat(tpri, "\n!") .. "\n"
		.. "|-\n"
		.. table.concat(tabs, "\n|") .. "\n"
		.. "|-\n"
		.. table.concat(trel, "\n|") .. "\n"
		.. "|-\n"
		.. table.concat(tdeg, "\n|") .. "\n"
		.. "|}"
end

local intervals = {}

intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
-- intervals.prime_no2 = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 }
intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 }
intervals.integer = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64}

-- evaluate input on error use default
local function eval_num_arg(input, def_value)
	local result = input
	if type(input) ~= "number" then
		result = def_value
		if type(input) == "string" then
			input = input:match("^%s*(.-)%s*$")
			if string.len(input) > 0 then
				result = tonumber(input)
			end
		end
	end
	return result
end

-- calculate default precision
local function prec_by_cet(step)
	return math.floor(math.log(1.9 * 1200 / step) / math.log(10))
end

function p.harmonics_in_cet (frame)
	-- step size in cents, default: 65
	local step = eval_num_arg(frame.args["step"], 63.1578947368)
	-- optional number of columns, default: 10
	local columns = eval_num_arg(frame.args["columns"], 10)
	-- optional start column, default: start with prime 2
	local start = eval_num_arg(frame.args["start"], 1)
	-- option intervals
	local select_intervals = "integer"
	if frame.args["intervals"] and string.len(frame.args["intervals"]) > 0 then
		select_intervals = frame.args["intervals"]
	end
	
	local name = "1ed" .. step .. "c"
	
	title_intervals = "prime harmonics"
	if select_intervals == "odd" then
		title_intervals = "odd harmonics"
	elseif select_intervals == "integer" then
		title_intervals = "harmonics"
	end
	
	local title = frame.args["title"]
	if title == nil or string.len(title) == 0 then
		title = "Approximation of ".. title_intervals .. " in " .. name
	end
	-- optional precision for abs error, default about 3 digits
	local prec = eval_num_arg(frame.args["prec"], prec_by_cet(step))
	
	return approx(step, {unpack(intervals[select_intervals], start, start + columns - 1)}, title, prec)
end

return p