local mos = require("Module:MOS")
local tamnams = require("Module:TAMNAMS")
local et = require("Module:ET")
local rat = require("Module:Rational")
local yesno = require("Module:Yesno")
local tip = require("Module:Template input parse")
local p = {}
-- Rewritten/simplified module replacement for Module:MOS degrees
-- A new template is chosen because it's a better name than the old one and is
-- far easier to maintain than the old one.
-- TODO:
-- - JI ratio search and input
-- - Diatonic interval category lookup?!!
-- Helper function
-- Capitalizes the first character of a string
function p.capitalize_first(text)
return string.upper(string.sub(text, 1, 1)) .. string.sub(text, 2, -1)
end
-- Helper function
-- Sorts step ratios L:s by their hardnesses
function p.sort_step_ratios(step_ratios)
if #step_ratios < 2 then
return step_ratios
end
-- Sort using selection sort, which is ok for smol datasets.
for i = 1, #step_ratios - 1 do
local index_of_smallest = i
local current_val = step_ratios[i][1] / step_ratios[i][2]
-- Find the ratio with the smallest hardness
for j = i + 1, #step_ratios do
if (step_ratios[j][1] / step_ratios[j][2] < current_val) then
index_of_smallest = j
end
end
if index_of_smallest ~= i then
local temp = step_ratios[index_of_smallest]
step_ratios[index_of_smallest] = step_ratios[i]
step_ratios[i] = temp
end
end
return step_ratios
end
-- Find JI ratios up to an integer limit via mediants
function p.ji_ratio_search(integer_limit)
local SEARCH_MAX = 120
local integer_limit = integer_limit or SEARCH_MAX
integer_limit = math.max(0, math.min(SEARCH_MAX, integer_limit))
local ratios = {{1,1}, {2,1}}
local new_ratios_added = true
while new_ratios_added do
new_ratios_added = false
local new_ratios = {}
for i = 1, #ratios-1 do
local ratio_1 = ratios[i]
local ratio_2 = ratios[i+1]
local mediant = {ratio_1[1]+ratio_2[1], ratio_1[2]+ratio_2[2]}
local int_max = math.max(mediant[1], mediant[2])
table.insert(new_ratios, ratios[i])
if int_max <= integer_limit then
new_ratios_added = true
table.insert(new_ratios, mediant)
end
end
table.insert(new_ratios, ratios[#ratios])
ratios = new_ratios
end
return ratios
end
-- Helper function
-- Finds the step ratio range and sorts step ratios
function p.preprocess_step_ratios(step_ratios)
local step_ratios = p.sort_step_ratios(step_ratios)
local step_ratio_range = ""
-- If the step ratios are 3/2, 2/1, and 3/1 in that order, then they are
-- the simple step ratios: basic, hard, and soft.
-- These should not be sorted, since the basic-hard-soft sorting is a little
-- more intuitive than sorting by hardness.
if #step_ratios == 3 then
if step_ratios[1][1] == 3 and step_ratios[1][2] == 2
and step_ratios[2][1] == 2 and step_ratios[2][2] == 1
and step_ratios[3][1] == 3 and step_ratios[3][2] == 1 then
return "Simple Tunings", {{2,1}, {3,1}, {3,2}}
end
end
-- If there are multiple step ratios, find the step ratio range it
-- corresponds to. If there is one step ratio, find the name of that
-- hardness. If there are zero step ratios, then return "Tunings"
if #step_ratios > 1 then
local lower_ratio = step_ratios[1]
local upper_ratio = step_ratios[#step_ratios]
step_ratio_range = tamnams.find_step_ratio_range_for_ratio_pair(lower_ratio, upper_ratio)
if step_ratio_range ~= nil then
step_ratio_range = p.capitalize_first(step_ratio_range) .. " Tunings"
else
step_ratio_range = "Tunings"
end
elseif #step_ratios == 1 then
step_ratio_range = tamnams.lookup_step_ratio(step_ratios[1])
if step_ratio_range ~= nil then
step_ratio_range = p.capitalize_first(step_ratio_range) .. " Tuning"
else
step_ratio_range = string.format("%s/%s", step_ratios[1][1], step_ratios[1][2]) .. " Tuning"
end
else
step_ratio_range = "Tunings"
end
return step_ratio_range, step_ratios
end
-- Preprocess step ratios
function p.preprocess_ji_ratios(input_mos, modal_union, step_ratios, ji_ratios)
local avg_step_ratio = {0, 0}
for i = 1, #step_ratios do
avg_step_ratio[1] = avg_step_ratio[1] + step_ratios[i][1]
avg_step_ratio[2] = avg_step_ratio[2] + step_ratios[i][2]
end
avg_step_ratio[1] = avg_step_ratio[1] / #step_ratios
avg_step_ratio[2] = avg_step_ratio[2] / #step_ratios
avg_step_ratio[1] = avg_step_ratio[1] / avg_step_ratio[2]
avg_step_ratio[2] = avg_step_ratio[2] / avg_step_ratio[2]
local cent_values = {}
for i = 1, #modal_union do
table.insert(cent_values, mos.interval_to_cents(modal_union[i], input_mos, avg_step_ratio))
end
local tolerance = (rat.cents(input_mos.equave) / (input_mos.nL * avg_step_ratio[1] + input_mos.ns * avg_step_ratio[2])) * 0.25
local sorted_ratios = {}
local curr_index = 1 -- Index of current_ratio
for i = 1, #cent_values do
local lower_bound = cent_values[i] - tolerance
local upper_bound = cent_values[i] + tolerance
local cents_within_range = true
local curr_ratios = {}
for j = curr_index, #ji_ratios do
local curr_ratio = ji_ratios[j]
local curr_cents = math.log(curr_ratio[1]/curr_ratio[2])/math.log(2) * 1200
if lower_bound < curr_cents and curr_cents < upper_bound then
table.insert(curr_ratios, curr_ratio)
--elseif curr_cents > upper_bound then
-- curr_index = j
-- break
end
end
table.insert(sorted_ratios, curr_ratios)
end
return sorted_ratios
end
-- Main function
function p._mos_tunings(input_mos, mos_prefix, mos_abbrev, step_ratios, ji_ratios)
local input_mos = input_mos or mos.new(5,2)
local mos_prefix = mos_prefix or "mos"
local mos_abbrev = mos_abbrev or "m"
local step_ratios = step_ratios or { {2,1}, {3,1}, {3,2} }
local ji_ratios = ji_ratios or p.ji_ratio_search(40)
local modal_union = mos.modal_union(input_mos)
local scale_sig = mos.as_string(input_mos)
-- Sort/preprocess step ratios
local step_ratio_range = ""
step_ratio_range, step_ratios = p.preprocess_step_ratios(step_ratios)
-- Preprocess JI ratios
local sorted_ji_ratios = p.preprocess_ji_ratios(input_mos, modal_union, step_ratios, ji_ratios)
-- Create table
local result = "{| class=\"wikitable sortable right-all left-1 left-2\"\n"
-- Table caption
result = result .. string.format("|+ style=\"font-size: 105%%; white-space: nowrap;\" | %s of %s\n", step_ratio_range, scale_sig)
-- First row of headers
-- First two headers span two rows
result = result .. "! rowspan=\"2\" class=\"unsortable\" | Scale degree\n"
result = result .. "! rowspan=\"2\" class=\"unsortable\" | Abbrev.\n"
-- Headers for tunings; these span two cols
for i = 1, #step_ratios do
local step_ratio_as_text = tamnams.lookup_step_ratio(step_ratios[i])
if step_ratio_as_text == nil then
step_ratio_as_text = string.format("%s:%s", step_ratios[i][1], step_ratios[i][2])
else
step_ratio_as_text = p.capitalize_first(step_ratio_as_text) .. string.format(" (%s:%s)", step_ratios[i][1], step_ratios[i][2])
end
local et_as_string = et.as_string(mos.mos_to_et(input_mos, step_ratios[i]))
local header_text = string.format("%s<br>[[%s]]", step_ratio_as_text, et_as_string)
result = result .. string.format("! colspan=\"2\" | %s\n", header_text)
end
-- Headers for JI ratios; this spans two rows
result = result .. "! rowspan=\"2\" class=\"unsortable\" | Approx.<br>Ratios\n"
result = result .. "|-\n"
-- Second row of headers
for i = 1, #step_ratios do
result = result .. "! Steps\n"
result = result .. "! Cents\n"
end
-- Add a row for each scale degree
for i = 1, #modal_union do
local interval = modal_union[i]
-- Add cells for the degree names
local degree_name = tamnams.degree_quality(interval, input_mos, "sentence-case", mos_prefix)
local degree_abbrev = tamnams.degree_quality(interval, input_mos, "abbrev" , mos_abbrev)
result = result
.. "|-\n"
.. string.format("| %s || %s", degree_name, degree_abbrev)
-- Add cells for each interval's tunings
for j = 1, #step_ratios do
local step_ratio = step_ratios[j]
local step_count = mos.interval_to_et_steps(interval, step_ratio)
local cents = mos.interval_to_cents(interval, input_mos, step_ratio)
result = result
.. " "
.. string.format("|| %s\\%s || %.1f", step_count, input_mos.nL * step_ratio[1] + input_mos.ns * step_ratio[2], cents)
end
-- Add cells for JI ratios
-- TESTING: print only the unison and equave
local ratios = ""
for j = 1, #sorted_ji_ratios[i] do
if j ~= #sorted_ji_ratios[i] then
ratios = ratios .. string.format("%s/%s, ", sorted_ji_ratios[i][j][1], sorted_ji_ratios[i][j][2])
else
ratios = ratios .. string.format("%s/%s", sorted_ji_ratios[i][j][1], sorted_ji_ratios[i][j][2])
end
end
result = result .. string.format("|| %s", ratios)
result = result .. "\n"
end
-- End of table
result = result .. "|}"
return result
end
-- Wrapper function; to be called by template
function p.mos_tunings(frame)
-- Get params
local scalesig = frame.args["Scale Signature"]
local mos_prefix = frame.args["MOS Prefix"]
local mos_abbrev = frame.args["MOS Abbrev"]
local collapsed = yesno(frame.args["Collapsed"], false) -- Currently does nothing
local step_ratios = tip.parse_numeric_pairs(frame.args["Step Ratios"]) or (frame.args["Step Ratios"] == "Central Spectrum" and {{4,3}, {3,2}, {5,3}, {2,1}, {5,2}, {3,1}, {4,1}} or {{2,1}, {3,1}, {3,2}})
local ji_ratios = tip.parse_numeric_pairs(frame.args["JI Ratios"] ) or {{1,1}, {3,2}, {2,1}}
-- Parse scalesig
local input_mos = mos.parse(scalesig)
-- Verify name/prefix/abbrev
mos_prefix = tamnams.verify_prefix(input_mos, mos_prefix)
mos_abbrev = tamnams.verify_abbrev(input_mos, mos_abbrev)
return p._mos_tunings(input_mos, mos_prefix, mos_abbrev, step_ratios)
end
function p.tester()
local range, ratios = p.preprocess_step_ratios({ {7,1}, {3,1}, {2,1} })
local ji_ratios = p.ji_ratio_search(50)
return p.preprocess_ji_ratios(mos.new(5,2), mos.modal_union(mos.new(5,2)), {{3,2}}, ji_ratios)
end
return p
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