Module:MOS tuning spectrum

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This module should not be invoked directly; use its corresponding template instead: Template:MOS tuning spectrum.

This template displays the tuning spectrum of a given mos scale, showing various step ratios between 1:1 to 1:0 (by default).

Introspection summary for Module:MOS tuning spectrum
Functions provided (2) Line Function Params 10 _mos_tuning_spectrum (main) (args) 152 mos_tuning_spectrum (invokable) (frame)	Lua modules required (6) Variable Module Functions used ET Module:ET new cents as_string mediants Module:Mediants find_mediants MOS Module:MOS new bright_gen as_string parse rat Module:Rational eq new as_ratio utils Module:Utils _gcd yesno Module:yesno yesno

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

---

local MOS = require("Module:MOS")
local ET = require("Module:ET")
local rat = require("Module:Rational")
local mediants = require("Module:Mediants")
local utils = require("Module:Utils")
local yesno = require("Module:yesno")
local p = {}

-- Re-re-rewrite of tuning spectrum
function p._mos_tuning_spectrum(args)
	local default_ratios, default_depths
	local default_depth = 5
	default_ratios, default_depths = mediants.find_mediants({{1,1}, {1,0}}, default_depth);
	
	local input_mos   = args["Input MOS"] or MOS.new(5, 2)
	local depth       = args["Depth"] or 5
	local comments    = args["Comments"] or {}
	local step_ratios = args["Ratios"] or default_ratios
	local depths      = args["Depths"] or default_depths
	
	local equave = input_mos.equave
	local L = input_mos.nL		-- Large steps in mos
	local s = input_mos.ns		-- Small steps in mos
	local n = utils._gcd(L, s)		-- Number of periods
	local abstract_bright_gen = MOS.bright_gen(input_mos)
	
	-- What is the equave suffix (edo, edt, edf, ed-p/q)
	local equave_suffix = ""
	if rat.eq(input_mos.equave, rat.new(2)) then
		equave_suffix = "o"
	elseif rat.eq(input_mos.equave, rat.new(3)) then
		equave_suffix = "t"
	elseif rat.eq(input_mos.equave, rat.new(3, 2)) then
		equave_suffix = "f"
	else
		equave_suffix = rat.as_ratio(input_mos.equave)
	end
	
	-- Default comments for TAMNAMS-named step ratios
	local default_comments = {}
	local mos_as_string = MOS.as_string(input_mos)
	default_comments["1/1"] = string.format("'''Equalized %s'''", mos_as_string)
	default_comments["4/3"] = string.format("'''Supersoft %s'''", mos_as_string)
	default_comments["3/2"] = string.format("'''Soft %s'''", mos_as_string)
	default_comments["5/3"] = string.format("'''Semisoft %s'''", mos_as_string)
	default_comments["2/1"] = string.format("'''Basic %s'''", mos_as_string)
	default_comments["5/2"] = string.format("'''Semihard %s'''", mos_as_string)
	default_comments["3/1"] = string.format("'''Hard %s'''", mos_as_string)
	default_comments["4/1"] = string.format("'''Superhard %s'''", mos_as_string)
	default_comments["1/0"] = string.format("'''Collapsed %s'''", mos_as_string)
	
	-- Append boundary of proper scales to basic comment, if applicable
	-- Monosmall mosses and knL ns mosses are always proper, but all other mosses
	-- are proper if the step ratio is within the soft-of-basic range
	if n < s then
		default_comments["2/1"] = default_comments["2/1"] .. "<br />Scales with tunings softer than this are proper"
	end
	
	-- Produce table header for the comments
	local comments_header_text = "Comments"
	if s == 1 then
		comments_header_text = comments_header_text .. "<sup><abbr title=\"Every tuning produces a proper scale.\">(always proper)</abbr></sup>"
	elseif s == n and n > 1 then
		comments_header_text = comments_header_text .. "<sup><abbr title=\"Every true-MOS tuning produces a proper scale.\">(always proper)</abbr></sup>"
	end
	
	-- Table headers
	-- There are 6 columns:
	-- - Steps of ED
	-- - Bright and dark gens in cents
	-- - Step ratio and hardness
	-- - Comments
	local result = "{| class=\"wikitable center-all\"\n"
		.. "|+ style=\"font-size: 105%; white-space: nowrap;\" | " .. string.format("Scale tree and tuning spectrum of %s\n", mos_as_string)
		.. "|-\n"
		.. string.format("! rowspan=\"2\" colspan=\"%d\" | Generator<sup><abbr title=\"In steps of ed%s.\">(ed%s)</abbr></sup>\n", depth + 1, equave_suffix, equave_suffix)
		.. "! colspan=\"2\" | Cents\n"
		.. "! colspan=\"2\" | Step ratio\n"
		.. "! rowspan=\"2\" | " .. comments_header_text .. "\n"
		.. "|-\n"
		.. "! Bright\n"
		.. "! Dark\n"
		.. "! L:s\n"
		.. "! Hardness\n"

	-- Rounding is done using string.format, to 3 decimal places (%.3f)
	
	-- Create each row of the table
	for i = 1, #step_ratios do
		local step_ratio = step_ratios[i]
		local steps_per_equave = step_ratio[1] * L + step_ratio[2] * s
		local steps_per_period = steps_per_equave / n
		local et = ET.new(steps_per_equave, equave)
		
		-- Calculate the bright gen and cent value
		local bright_generator_steps = step_ratio[1] * abstract_bright_gen["L"] + step_ratio[2] * abstract_bright_gen["s"]
		local bright_generator_cents = ET.cents(et, bright_generator_steps)
		
		-- Calculate dark generator step count and cent value
		local dark_generator_steps = steps_per_period - bright_generator_steps
		local dark_generator_cents = ET.cents(et, dark_generator_steps)
		
		-- New row
		result = result .. "|-\n"	
		
		-- Cells for bright generator, as steps in et
		local current_depth = depths[i]
		for i = 1, depth + 1 do
			result = result .. "| "
			if i == current_depth then
				result = result .. string.format("[[%s|%d\\%s]]", ET.as_string(et), bright_generator_steps, et.size)
			end
			result = result .. "\n"
		end
		
		-- Cells for generators in cents
		result = result .. string.format("| %.3f\n", bright_generator_cents)
		result = result .. string.format("| %.3f\n", dark_generator_cents)
		
		-- Cell for step ratio
		result = result .. string.format("| %d:%d\n", step_ratio[1], step_ratio[2])
		
		-- Cell for hardness, with divide-by-zero check
		local hardness = ""
		if step_ratio[2] == 0 then
			hardness = "&rarr;&nbsp;&#8734;"
		else
			hardness = string.format("%.3f", step_ratio[1] / step_ratio[2])
		end
		result = result .. string.format("| %s\n", hardness)
		
		-- Cell for comment
		-- Default comments are on their own line before custom comments
		local key = step_ratios[i][1] .. "/" .. step_ratios[i][2]		-- The step ratio is (literally and figuratively) the key to add comments!
		local comment = ""
		local default_comment = default_comments[key] or ""
		local custom_comment = comments[key] or ""
		if default_comment == "" then
			comment = custom_comment
		else
			comment = default_comment .. "<br />" .. custom_comment
		end
		result = result .. string.format("| style=\"text-align: left;\" | %s\n", comment)
		
	end
	
	result = result .. "|}"
	return result
end

-- Wrapper function; to be called by template
function p.mos_tuning_spectrum(frame)
	local args = getArgs(frame)
	
	-- Parse scalesig
	local input_mos = MOS.parse(args["Scale Signature"])
	args["Input MOS"] = input_mos
	args["Scale Signature"] = nil
	
	-- Parse depth
	local depth = tonumber(args["Depth"])
	frame.args["Depth"] = tonumber(args["Depth"])
	
	-- Generate mediants and depths
	local ratios, depths
	ratios, depths = mediants.find_mediants({{1,1}, {1,0}}, depth)
	frame.args["Ratios"] = ratios
	frame.args["Depths"] = depths
	
	-- Transfer comments from args to comments
	local comments = {}
	for i = 1, #ratios do
		local key = string.format("%d/%d", ratios[i][1], ratios[i][2])
		if args[key] ~= nil then
			comments[key] = args[key]
			args[key] = nil
		end
	end
	
	-- Parse debug option
	local debugg = yesno(args["debug"])
	
	-- Output
	local out_str = p._scale_tree(args)
	return frame:preprocess(debugg == true and "<pre>" .. out_str .. "</pre>" or out_str)
end

return p