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 = "→ ∞"
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.scale_tree(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
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