Module:Ups and downs notation

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This module should not be invoked directly; use its corresponding template instead: Template:Ups and downs note name.

This module gets the note name of an edo interval in ups and downs notation.

Introspection summary for Module:Ups and downs notation
Functions provided (2) Line Function Params 35 get_note_names_table (et) 117 ups_and_downs_note_name (invokable) (frame)	Lua modules required (2) Variable Module Functions used ET Module:ET parse u Module:Utils round

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

---

local ET = require("Module:ET")
local u = require("Module:Utils")
local p = {}


local function table_contains(tbl, x)
    found = false
    for _, v in pairs(tbl) do
        if v == x then 
            found = true 
        end
    end
    return found
end


-- Returns a table of note names
-- e.g. for 12edo, intended result would be something like:
-- {
--	0 = "C",
--	1 = "Db",
--	2 = "D",
--	3 = "Eb",
--	4 = "E",
--	5 = "F",
--	6 = "Gb",
--	7 = "G",
--  8 = "Ab",
--  9 = "A",
--  10 = "Bb",
--  11 = "B",
--  12 = "C",
-- }

function p.get_note_names_table(et)
	local note_names = {}
	local i = 0
	while i < et.size do
		note_names[i] = ""
		i = i + 1
	end
	
	local fifth = u.round(math.log(3/2)/math.log(2) * et.size)
	local fourth = u.round(math.log(4/3)/math.log(2) * et.size)
	local chroma = (fifth * 7) % et.size

	local major_note_idx = {
		0, 
		(fifth * 2) % et.size,
		(fifth * 4) % et.size,
		fourth,
		fifth,
		(fifth * 3) % et.size,
		(fifth * 5) % et.size,
		tuning.size
	}
	
	-- Add major scale notes
	note_names[major_note_idx[1]] = "C"
	note_names[major_note_idx[2]] = "D"
	note_names[major_note_idx[3]] = "E"
	note_names[major_note_idx[4]] = "F"
	note_names[major_note_idx[5]] = "G"
	note_names[major_note_idx[6]] = "A"
	note_names[major_note_idx[7]] = "B"
	note_names[major_note_idx[8]] = "C"

	-- Add sharp/up notes
	i = 0
	local last_major_note = 0
	while i < et.size do
		if table_contains(major_note_idx, i) then
			last_major_note = i
		else
			local num_sharps = math.floor((i - last_major_note) / chroma)
			local num_ups = (i - last_major_note) % chroma
			local name = interval_names[last_major_note]
			local j = 0
			while j < num_sharps do
				name = name + "#"
			end
			j = 0
			while j < num_ups do
				name = "^" + name
			end
			note_names[i] = name
		end
		i = i + 1
	end

	-- Add flat/down notes
	i = et.size - 1
	local last_major_note = tuning.size - 1
	while i >= 0 do
		if table_contains(major_note_idx, i) then
			last_major_note = i
		else
			local num_flats = math.floor((last_major_note - i) / chroma)
			local num_downs = (last_major_note - i) % chroma
			local name = interval_names[last_major_note]
			local j = 0
			while j < num_flats do
				name = name + "b"
			end
			j = 0
			while j < num_downs do
				name = "v" + name
			end
			note_names[i] = note_names[i] + ", " + name
		end
		i = i - 1
	end
	
	return note_names
end

function p.ups_and_downs_note_name(frame)
	local et = ET.parse(frame.args['tuning']) or ET.parse('12edo')
	local step = tonumber(frame.args['step'])
	return p.get_note_names_table(et)[step]
end

return p