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 (1) Line Function Params 36 get_note_names (tuning)	Lua modules required (2) Variable Module Functions used et Module:ET approximate rat Module:Rational new

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

---

-- WIP

local et = require('Module:ET')
local rat = require('Module:Rational')
local p = {}

-- Returns a nested 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 = {"F#", "Gb"},
--	7 = {"G"},
--  8 = {"Ab"},
--  9 = {"A"},
--  10 = {"Bb"},
--  11 = {"B"},
--  12 = {"C"}
-- }

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


function p.get_note_names(tuning)
	local note_names = {}
	local i = 0
	while i < tuning.size do
		note_names[i] = {}
	end
	
	local fifth = et.approximate(tuning, rat.new(3, 2))
	local fourth = et.approximate(tuning, rat.new(4, 3))
	local chroma = (fifth * 7) % et.size
	
	local major_note_idx = {
		0, 
		(fifth * 2) % tuning.size,
		(fifth * 4) % tuning.size,
		fourth,
		fifth,
		(fifth * 3) % tuning.size,
		(fifth * 5) % tuning.size,
		tuning.size
	}
	-- Add major scale notes
	table.insert(note_names[major_note_idx[1]], "C")
	table.insert(note_names[major_note_idx[2]], "D")
	table.insert(note_names[major_note_idx[3]], "E")
	table.insert(note_names[major_note_idx[4]], "F")
	table.insert(note_names[major_note_idx[5]], "G")
	table.insert(note_names[major_note_idx[6]], "A")
    table.insert(note_names[major_note_idx[7]], "B")
    table.insert(note_names[major_note_idx[8]], "C")
	
	i = 0
	local last_major_note = 0
	while i < tuning.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
			table.insert(note_names[i], name)
		end
		i = i + 1
	end
	
	
	return note_names
	

end

return p