Module:MOS in EDO: Difference between revisions

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@@ Line 150: / Line 150: @@
      return next_step_array
+end
+-- Helper function
+-- Create a step visualization that's based on the table on the diasem page
+function p.step_pattern_to_simple_visualization(step_pattern, edosteps_per_period)
+	local step_pattern = step_pattern or { 2, 2, 2, 1, 2, 2, 1 }
+	local edosteps_per_period = edosteps_per_period or #step_pattern
+	local left_border = "├"
+	local right_border = "┤"
+	local no_border = "─"
+	local single_border = "┼"
+	local double_border = "╫"
+	local step_visualization = ""
+	-- For each step size of k, print a single border, followed by k-1 no-border symbols
+	-- If this is the first step, print the left border instead
+	-- If this step is for a non-root non-equave period, print a double border instead
+	-- If this is the last step, add a right border after the entire sequence
+	for i = 1, #step_pattern do
+		local current_step_vis = ""
+		local current_step_size = step_pattern[i]
+		if i == 1 then
+			current_step_vis = left_border .. string.rep(no_border, current_step_size - 1)
+		elseif (i - 1) % edosteps_per_period == 0 and i ~= 1  and i ~= #step_pattern then
+			current_step_vis = double_border .. string.rep(no_border, current_step_size - 1)
+		else
+			current_step_vis = single_border .. string.rep(no_border, current_step_size - 1)
+		end
+		step_visualization = step_visualization .. current_step_vis
+	end
+	step_visualization = step_visualization .. right_border
+	return step_visualization
 end
@@ Line 246: / Line 285: @@
 			end
 		end
+		-- Add the scale sig
+		local scale_sig = p.mos_step_pattern_to_scale_sig(current_scale)
+		-- Get the tamnams name, if there is one
+		-- Don't show tamnams names for mosses with 5 notes or fewer (to keep the table from being cluttered)
+		local tamnams_name = mos.tamnams_name[scale_sig]
+		local current_step_count = #current_scale
+		-- Use step sizes to determine whether the mos is an edo
+		local reduced_large_step_size = current_step_sizes["L"] / step_ratio_gcd
+		local reduced_small_step_size = current_step_sizes["s"] / step_ratio_gcd
+		if reduced_large_step_size == reduced_small_step_size then
+			result = result .. string.format("| [[%iedo]]\n", edo / step_ratio_gcd)
+		elseif tamnams_name ~= nil and current_step_count > 5 then
+			result = result .. string.format("| [[%s]] (%s)\n", scale_sig, tamnams_name)
+		else
+			result = result .. string.format("| [[%s]]\n", scale_sig)
+		end
+		-- Add the step ratio
+		result = result .. string.format("| %s:%s\n", current_step_sizes["L"] / step_ratio_gcd, current_step_sizes["s"] / step_ratio_gcd)
+		-- Add the temperament name, if there is one
+		if show_temperament then
+			local current_step_count = #current_scale
+			result = result .. string.format("| %s[%i]\n", temperament, current_step_count)
+		end
+		-- Produce the next scale in the sequence
+		current_scale = p.calculate_next_mos_step_pattern(current_scale)
+	end
+	result = result .. string.format('|}\n')
+	return result
+end
+-- Alternate primary function
+-- Instead of a "rectangular horogram", use the same type of visualization shown
+-- on the diasem page
+function p.mos_in_edo_simplified(edo, gen_in_edosteps, number_of_periods, temperament)
+	local edo = edo or 24
+	local gen_in_edosteps = gen_in_edosteps or 14
+	local number_of_periods = number_of_periods or 1
+	local temperament = temperament --or "meantone"
+	-- Check whether the number of periods divides the edo
+	-- If so, the starting scale will be a multiperiod mos
+	local period_in_edosteps = edo
+	local verified_number_of_periods = 1
+	if edo % number_of_periods == 0 then
+		period_in_edosteps = edo / number_of_periods
+		verified_number_of_periods = number_of_periods
+	end
+	-- Calculate whether to include temperament names
+	local show_temperament = temperament ~= "" and temperament ~= nil
+	-- Calculate the generator complement
+	local comp_in_edosteps = period_in_edosteps - gen_in_edosteps
+	-- Are the args for the starting mos valid?
+	-- The number of steps in the generator must be between 1 (inclusive) and the number of steps in the period (exclusive)
+	local starting_mos_valid = gen_in_edosteps >= 1 and gen_in_edosteps <= period_in_edosteps
+	-- Calculate the starting mos
+	local current_scale = {}
+	for i = 1, number_of_periods do
+		table.insert(current_scale, gen_in_edosteps)
+		table.insert(current_scale, comp_in_edosteps)
+	end
+	-- Create table, starting with headers
+	local result = string.format('{| class="wikitable center-all"\n')
+	result = result .. string.format('|+ Generators %i\\%i and %i\\%i\n', gen_in_edosteps, edo, comp_in_edosteps, edo)
+	result = result .. string.format('|-\n')
+	result = result .. string.format('! Steps\n')
+	result = result .. string.format('!MOS (name)\n')
+	result = result .. string.format('!Step ratio\n')
+	if show_temperament then
+		result = result .. string.format('!Temperament\n')
+	end
+	-- Add the step pattern for successive mosses until the pattern becomes that for an edo
+	while current_scale ~= nil and starting_mos_valid do
+		-- Calculate current step ratio
+		-- Use this to determine which cell colors to use
+		local current_step_sizes = p.calculate_step_sizes(current_scale)
+		local step_ratio_gcd = utils._gcd(current_step_sizes["L"], current_step_sizes["s"])
+		local large_step_size = current_step_sizes["L"]
+		local small_step_size = current_step_sizes["s"]
+		-- Is the first step a large step?
+		local first_step_is_large_step = current_scale[1] == large_step_size
+		-- Add the step visualization
+		local step_vis = p.step_pattern_to_simple_visualization(current_scale, period_in_edosteps)
+		result = result .. string.format('|-\n')
+		result = result .. string.format('| %s\n', step_vis)
 		-- Add the scale sig
@@ Line 293: / Line 433: @@
 	local number_of_periods = tonumber(frame.args["Number of Periods"])
-	local result = p.mos_in_edo(edo, gen_in_edosteps, number_of_periods, temperament)
+	local result = ""
+	if frame.args["Step Visualization"] == "Simplifed" then
+		result = p.mos_in_edo_simplified(edo, gen_in_edosteps, number_of_periods, temperament)
+	else
+		result = p.mos_in_edo(edo, gen_in_edosteps, number_of_periods, temperament)
+	end
 	return result