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 58 interval_table (invokable) (frame)	Lua modules required (5) Variable Module Functions used ET Module:ET parse approximate cents hekts rat Module:Rational max_prime new cents eq ud Module:Ups and downs notation get_note_names_table utils Module:Utils _gcd table_contains _round_dec _log yesno Module:Yesno yesno

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

---

local p = {}

local ET = require("Module:ET")
local rat = require("Module:Rational")
local ud = require("Module:Ups and downs notation")
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")

-- 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 rat.max_prime(rat.new (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 function 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 debugg = yesno(frame.args["debug"])
	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),
	} -- NOTE: indices are prime numbers

	local t_head = "{| class=\"wikitable center-1 right-2"
	if et.size > 20 then
		t_head = t_head .. " mw-collapsible mw-collapsed"
	end
	t_head = t_head .. "\"\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 47-limit ratios with numerator and denominator <= certain cents value and in the range 1/1 - 12/1
	local ratios_list = get_ratios_list((20 + (et.size / 4)), 12, 47)

	result = t_head .. 
		"|-\n" ..
		"! Steps\n" ..
		"! Cents\n"
	
	if rat.eq(et.equave, 3) then
		result = result .. "! [[Hekt]]s\n"
	end
	result = result ..
	"! Approximate ratios\n"
	
	if rat.eq(et.equave, 2) then
		if dual_fifth then
			result = result
				.. string.format("! [[Ups and downs notation]]<br />(Dual flat fifth %s\\%s)\n", dual_flat_fifth, et.size)
				.. string.format("! [[Ups and downs notation]]<br />(Dual sharp fifth %s\\%s)\n", dual_sharp_fifth, et.size)
		else
			result = result .. "! [[Ups and downs notation]]\n"
		end
	end
	
	if #additional_split > 0 then
		for i = 1, #additional_split[1] do
			result = result .. string.format("! %s\n", additional_split[1][i])
		end
	end

    local decimalPlaces = 3 - math.floor(math.log(1200 / et.size, 10))
    if decimalPlaces > 3 then decimalPlaces = 3 end
    if decimalPlaces < 1 then decimalPlaces = 1 end
	for i = 0, et.size do
		result = result .. "|-\n"
			.. string.format("| %s\n", i)
			.. string.format("| %s\n", utils._round_dec(ET.cents(et, i), decimalPlaces))
		
		if rat.eq(et.equave, 3) then
			result = result .. string.format("| %s\n", utils._round_dec(ET.hekts(et, i), decimalPlaces))
		end
		
		result = result .. "| "
		
		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 < specified edostep error,
			-- add to approximate ratios column.
			local t = mapping(rat.new(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 / (math.log(et.size) * (et.size + 5)))
			then
				result = result .. string.format("[[%s/%s]], ", ratios_list[j][1], ratios_list[j][2])
			end
		end
		
		-- ???
		if result:sub(-2, -1) == "| " then
			result = result .. "\n"
		else
			result = result:sub(0, -3) .. "\n"
		end
		
		if rat.eq(et.equave, 2) then
			if dual_fifth then
				result = result .. string.format("| %s\n", ud_note(et, dual_flat_fifth, i))
				result = result .. string.format("| %s\n", ud_note(et, dual_sharp_fifth, i))
			else
				result = result .. string.format("| %s\n", ud_note(et, fifth, i))
			end
		end
		
		if (i + 2) <= #additional_split then
			for j = 1, #additional_split[i + 2] do
				result = result .. string.format("| %s\n", additional_split[i + 2][j])
			end
		end
	end

	result = result .. "|}"
	
	if debugg == true then
		result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
	end
	
	return frame:preprocess(result)
end

return p