Module:MOS notation: Difference between revisions

Newer edit →

@@ Line 53: / Line 53: @@
 	local note_name = note_symbol .. string.rep(chroma_symbol, math.abs(chromas))
 	return note_name
+end
+-- Helper function for creating a genchain, or specifically, a nominal-accidental chain.
+-- This can only work in one direction at a time, so it's necessary to call this twice,
+-- once for each direction (going up by the bright generator, or down). One genchain
+-- is generated for each period, so this returns an array of arrays.
+-- This genchain is agnostic of notation, and only denotes the mossteps needed to reach
+-- a note, followed by the number of chromas. For example, F# is reached going up 3
+-- mossteps and adding one chroma; Fb is the same except subtracting one chroma.
+-- Specific notation is needed to interpret this into note names.
+-- Parameters:
+-- - input_mos - the mos itself represented as a data structure from Module:MOS
+-- - genchain_init_per_period - how many named pitches per period are there without accidentals added?
+--   This is either the value u or d for the UDP of up|dp.
+-- - genchain_length_per_period - how many generators should the genchain extend after the root?
+-- - going_up - bool; whether the genchain is going up or down; true for up, false for down
+function p.mos_nomacc_chain(input_mos, genchain_init_per_period, genchain_length_per_period, going_up)
+	-- Default parameters for testing
+	--[[
+	local input_mos = input_mos or mos.new(5, 2, 2)
+	local genchain_init_per_period = genchain_init_per_period or 5
+	local genchain_length_per_period = genchain_length_per_period or 10
+	local note_symbols = note_symbols or "CDEFGAB"
+	local chroma_symbol = chroma_symbol or "#"
+	local going_up = going_up or true
+	]]--
+	-- Get the number of mossteps per period and equave
+	local mossteps_per_equave = input_mos.nL + input_mos.ns
+	local periods_per_equave = rat.gcd(input_mos.nL, input_mos.ns)
+	local mossteps_per_period = mossteps_per_equave / periods_per_equave
+	--[[
+	-- Split the note symbols string into subsets
+	-- This is only necessary if the mos is multi-period
+	local note_subsets = {}
+	for i = 1, periods_per_equave do
+		local start_index = (i - 1) * mossteps_per_period + 1
+		local stop_index = i * mossteps_per_period
+		local substr = string.sub(note_symbols, start_index, stop_index)
+		table.insert(note_subsets, substr)
+	end
+	]]--
+	-- Create the genchain for each period
+	local genchains = {}
+	for i = 1, periods_per_equave do
+		--local note_names = note_subsets[i]
+		-- Get the size of the generator in mossteps
+		local gen = mos.bright_gen(input_mos)
+		local gen_in_mossteps = gen['L'] + gen['s']
+		-- If the genchain is descending (ie, going_up is false), switch to
+		-- using the dark gen in mossteps, which is the period complement
+		-- of the bright gen; going up by the dark gen is the same as going
+		-- down by the bright gen
+		if not going_up then
+			gen_in_mossteps = mossteps_per_period - gen_in_mossteps
+		end
+		-- Use this value, with modular arithmteic, as an index to get the note name
+		local accumulator = 0
+		-- Create a genchain that initially starts at the root
+		--local root = string.sub(note_names, 1, 1)
+		--local genchain = { root }
+		local root_offest = (i - 1) * mossteps_per_period		-- To make sure that, across all periods, every note has a unique index
+		local root = { ['mossteps'] = root_offest, ['chromas'] = 0 }
+		local genchain = { root }
+		-- Create the rest of the genchain
+		for j = 1, genchain_length_per_period do
+			-- Increment the index by the generator
+			accumulator = accumulator + gen_in_mossteps
+			-- Convert the accumulator into an index
+			local index = accumulator % mossteps_per_period
+			-- Add accidentals
+			-- This is negative if the genchain is descending
+			local accidentals_to_add = 0
+			if j > genchain_init_per_period then
+				accidentals_to_add = math.ceil((j - genchain_init_per_period) / mossteps_per_period)
+			end
+			if not going_up then
+				accidentals_to_add = accidentals_to_add * -1
+			end
+			-- Get the final note name
+			local note_name = {}
+			note_name['mossteps'] = index + root_offest	-- Mossteps needed to reach a note
+			note_name['chromas'] = accidentals_to_add	-- How many chromas
+			-- Add the note name
+			table.insert(genchain, note_name)
+		end
+		-- Add the genchain
+		table.insert(genchains, genchain)
+	end
+	return genchains
 end
@@ Line 98: / Line 201: @@
 -- - -2 = 1x diminished
 -- - -3 = 2x diminished
-function p.mos_degrees(input_mos, genchain_length_per_period, going_up)
+function p.mos_degree_chain(input_mos, genchain_length_per_period, going_up)
 	-- Default parameters for testing
 	--[[