Module:Interval table

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This module should not be invoked directly; use its corresponding template instead: Template:Interval table.

This module automatically generates a table of intervals for an equal-step tuning, showing which just intervals are approximated relatively accurately.

Introspection summary for Module:Interval table
Functions provided (1) Line Function Params 69 interval_table (invokable) (frame)	Lua modules required (4) Variable Module Functions used ET Module:ET parse approximate cents rat Module:Rational cents new eq ud Module:Ups and downs notation get_note_names_table utils Module:Utils get_monzo _gcd table_contains _round _log

No function descriptions were provided. The Lua code may have further information.

---

local p = {}
local utils = require("Module:Utils")
local rat = require("Module:Rational")
local ud = require("Module:Ups and downs notation")
local ET = require("Module:ET")

-- Note: some of these helper functions may be moved to utils module

-- Get prime limit of n/d
local function get_limit(n, d)
	local result = 2
	local monzo = utils.get_monzo(n, d)
	for k, _ in pairs(monzo) do
		if k > result then
			result = k
		end
	end
	return result
end

--  Gets mapping of a monzo in a val
local function mapping(monzo, val)
	local result = 0
	for k, _ in pairs(val) do
		result = result + val[k] * (monzo[k] or 0)
	end
	return result
end

-- Generates list of ratios up to a max numerator & denominator, max ratio size, and prime limit
local function get_ratios_list(max_nd, max_size, prime_limit)
	local ratios = {}
	local ratio_strings = {}
	for i = 1, max_nd do
		for j = 1, max_nd do
			local t = i / utils._gcd(i, j) .. "/" .. j / utils._gcd(i, j)
			if
				(i / j) >= 1
				and (i / j) <= max_size
				and get_limit(i, j) <= prime_limit
				and not utils.table_contains(ratio_strings, t)
			then
				ratios[#ratios + 1] = { i / utils._gcd(i, j), j / utils._gcd(i, j) }
				ratio_strings[#ratio_strings + 1] = t
			end
		end
	end

	return ratios
end

-- Utility fuunction to get specific note name with ud.get_note_names_table
-- (this is essentially what "Template:Ups and downs note name" does)
local function ud_note(et, fifth, step)
	return table.concat(ud.get_note_names_table(et, fifth)[step], ", "):sub(0, -1)
end

local function mysplit(inputstr, sep)
	if sep == nil then
		sep = "%s"
	end
	local t = {}
	for str in string.gmatch(inputstr, "([^" .. sep .. "]+)") do
		table.insert(t, str)
	end
	return t
end

function p.interval_table(frame)
	local additional = frame.args["additional"] or ""
	local additional_split = mysplit(additional, "\n")
	for i = 1, #additional_split do
		additional_split[i] = mysplit(additional_split[i], ";")
	end
	local tuning = frame.args["tuning"]
	local et = ET.parse(tuning) or ET.parse("12edo")
	local patent_val = {
		[2] = ET.approximate(et, 2),
		[3] = ET.approximate(et, 3),
		[5] = ET.approximate(et, 5),
		[7] = ET.approximate(et, 7),
		[11] = ET.approximate(et, 11),
		[13] = ET.approximate(et, 13),
		[17] = ET.approximate(et, 17),
		[19] = ET.approximate(et, 19),
		[23] = ET.approximate(et, 23),
		[29] = ET.approximate(et, 29),
		[31] = ET.approximate(et, 31),
		[37] = ET.approximate(et, 37),
		[41] = ET.approximate(et, 41),
		[43] = ET.approximate(et, 43),
		[47] = ET.approximate(et, 47),
	}

	local wikitext = '{|class="wikitable"\n'
	local fifth = patent_val[3] - patent_val[2]
	local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
	local dual_fifth = math.abs(fifth_error) > (400 / et.size)
	local dual_flat_fifth = ET.approximate(et, 3 / 2, -1)
	local dual_sharp_fifth = ET.approximate(et, 3 / 2, 1)

	-- List of all 13-limit ratios with numerator and denominator <= 81 and in the range 1/1 - 5/1
	local ratios_list = get_ratios_list(81, 5, 13)

	wikitext = wikitext .. "!Steps\n"
	wikitext = wikitext .. "!Cents\n"
	if rat.eq(et.equave, 2) then
		if dual_fifth then
			wikitext = wikitext
				.. "![[Ups and downs notation]]<br>(dual flat fifth "
				.. dual_flat_fifth
				.. "\\"
				.. et.size
				.. ")\n"
			wikitext = wikitext
				.. "![[Ups and downs notation]]<br>(dual sharp fifth "
				.. dual_sharp_fifth
				.. "\\"
				.. et.size
				.. ")\n"
		else
			wikitext = wikitext .. "![[Ups and downs notation]]\n"
		end
	end

	wikitext = wikitext .. "!Approximate ratios\n"

	if #additional_split > 0 then
		for i = 1, #additional_split[1] do
			wikitext = wikitext .. "!" .. additional_split[1][i] .. "\n"
		end
	end

	for i = 0, et.size do
		wikitext = wikitext .. "|-\n"
		wikitext = wikitext .. "|" .. i .. "\n"
		wikitext = wikitext .. "|" .. utils._round(ET.cents(et, i), 6) .. "\n"
		if rat.eq(et.equave, 2) then
			if dual_fifth then
				wikitext = wikitext .. "|" .. ud_note(et, dual_flat_fifth, i) .. "\n"
				wikitext = wikitext .. "|" .. ud_note(et, dual_sharp_fifth, i) .. "\n"
			else
				wikitext = wikitext .. "|" .. ud_note(et, fifth, i) .. "\n"
			end
		end
		wikitext = wikitext .. "|"
		for j = 1, #ratios_list do
			-- Go through all ratios.
			-- If they are mapped to the current step in the ET's patent val and <2/5 edo step error,
			-- add to approximate ratios column.
			local t = mapping(utils.get_monzo(ratios_list[j][1], ratios_list[j][2]), patent_val)
			if
				t == i
				and math.abs(ET.cents(et, i) - utils._log(ratios_list[j][1] / ratios_list[j][2], 2) * 1200)
					< (1200 / (2.5 * et.size))
			then
				wikitext = wikitext .. "[[" .. ratios_list[j][1] .. "/" .. ratios_list[j][2] .. "]], "
			end
		end
		if wikitext:sub(-1, -1) == "|" then
			wikitext = wikitext .. "\n"
		else
			wikitext = wikitext:sub(0, -3) .. "\n"
		end
		if (i + 2) <= #additional_split then
			for j = 1, #additional_split[i + 2] do
				wikitext = wikitext .. "|" .. additional_split[i + 2][j] .. "\n"
			end
		end
	end

	wikitext = wikitext .. "|}"

	if wikitext:len() > 5000 then
		wikitext = '{| class="wikitable mw-collapsible mw-collapsed"\n' .. wikitext:sub(20)
	end

	return wikitext
end

return p