local mos = require("Module:MOS")
local rat = require("Module:Rational")
local et = require("Module:ET")
local tamnams = require("Module:TAMNAMS")
local interval_extension = require("Module:Interval_extension")
local yesno = require("Module:Yesno")
local p = {}
-- TODO:
-- - Move harmonic entropy to separate module/template pair????
-- Main function; to be called by wrapper
function p._mos_intervals(input_mos, mos_prefix, mos_abbrev, is_collapsed)
-- Default param for input mos is 5L 2s
local input_mos = input_mos or mos.new(5, 2, 2)
local mos_prefix = mos_prefix or "mos"
local mos_abbrev = mos_abbrev or "m"
local is_collapsed = is_collapsed == true
-- Get the scale sig
local scale_sig = mos.as_string(input_mos)
-- Get the brightest and darkest modes as step matrices
local bright_step_matrix = mos.mode_to_step_matrix(mos.brightest_mode(input_mos))
local dark_step_matrix = mos.mode_to_step_matrix(mos.darkest_mode(input_mos))
-- Get the number of steps per period and equave
local equave_step_count = mos.equave_step_count(input_mos)
local period_step_count = mos.period_step_count(input_mos)
-- Get the step counts for the bright and dark generators
local bright_gen_step_count = mos.bright_gen_step_count(input_mos)
local dark_gen_step_count = mos.dark_gen_step_count(input_mos)
-- Setup for harmonic entropy
local step_ratios = {
{ 4, 3 },
{ 3, 2 },
{ 5, 3 },
{ 2, 1 },
{ 5, 2 },
{ 3, 1 },
{ 4, 1 },
}
-- Create the table
local result = "{| class=\"wikitable mw-collapsible" .. (is_collapsed and " mw-collapsed\"\n" or "\"\n")
-- Create table caption
result = result
.. "|+ style=\"font-size: 105%;\" | Intervals of " .. scale_sig .. "\n"
-- Create table headers
result = result
.. "! colspan=\"3\" | Intervals"
.. "!! rowspan=\"2\" | Steps subtended"
.. "!! rowspan=\"2\" | Range in cents"
.. "!! rowspan=\"2\" | Average of [[HE]]<br/>(from [http://www.mikebattagliamusic.com/HE-JS/HE.html HE Calc])\n"
.. "!! rowspan=\"2\" | Min of [[HE]]\n"
.. "|-\n" -- Start of second row of header cells
.. "! Generic"
.. "!! Specific"
.. "!! Abbrev.\n"
-- Write each row
for i = 1, #bright_step_matrix do
-- Compare the bright and dark intervals. If they're the same, then the
-- current interval class is a period interval.
local current_bright_interval = bright_step_matrix[i]
local current_dark_interval = dark_step_matrix[i]
local is_period = mos.interval_eq(current_bright_interval, current_dark_interval)
-- If it's a period interval, then there is only one row to write.
-- Otherwise, there are two rows to write, one for each size.
if is_period then
local cents = mos.interval_to_cents(current_bright_interval, input_mos, {1, 1})
result = result .. "|-\n"
.. string.format("| '''%s-%sstep''' ", i - 1, mos_prefix)
.. string.format("|| %s " , tamnams.interval_quality(current_bright_interval, input_mos, "sentence-case", mos_prefix))
.. string.format("|| %s " , tamnams.interval_quality(current_bright_interval, input_mos, "abbrev" , mos_abbrev))
.. string.format("|| %s " , mos.interval_as_string(current_bright_interval))
.. string.format("|| %.1f¢ ", cents)
.. string.format("|| ~%.4f nats ", interval_extension.harmonic_entropy_with_lookup_table(cents))
.. string.format("|| ~%.4f nats", interval_extension.harmonic_entropy_with_lookup_table(cents))
else
-- Calculate the best and average harmonic entropies
local he_dark_average = 0
local he_bright_average = 0
local he_dark_best = 1000
local he_bright_best = 1000
for i = 1, #step_ratios do
local step_ratio = step_ratios[i]
local he_dark = interval_extension.harmonic_entropy_with_lookup_table(mos.interval_to_cents(current_dark_interval, input_mos, step_ratio))
local he_bright = interval_extension.harmonic_entropy_with_lookup_table(mos.interval_to_cents(current_bright_interval, input_mos, step_ratio))
he_dark_average = he_dark_average + he_dark / #step_ratios
he_bright_average = he_bright_average + he_bright / #step_ratios
if he_dark_best > he_dark then
he_dark_best = he_dark
end
if he_bright_best > he_bright then
he_bright_best = he_bright
end
end
-- Calculate the cent values min and max for the current intervals
local sm_min_cents = mos.interval_to_cents(current_dark_interval, input_mos, {1,1})
local sm_max_cents = mos.interval_to_cents(current_dark_interval, input_mos, {1,0})
local lg_min_cents = mos.interval_to_cents(current_bright_interval, input_mos, {1,1})
local lg_max_cents = mos.interval_to_cents(current_bright_interval, input_mos, {1,0})
-- Then sort, as the min and max may be swapped
-- This happens if the dark interval has more small steps than large steps
local dark_interval_range = string.format("%.1f¢ to %.1f¢", math.min(sm_min_cents, sm_max_cents), math.max(sm_min_cents, sm_max_cents))
local bright_interval_range = string.format("%.1f¢ to %.1f¢", math.min(lg_min_cents, lg_max_cents), math.max(lg_min_cents, lg_max_cents))
result = result .. "|-\n"
.. string.format("| rowspan=\"2\" | %s-%sstep ", i - 1, mos_prefix)
.. string.format("|| %s " , tamnams.interval_quality(current_dark_interval, input_mos, "sentence-case", mos_prefix))
.. string.format("|| %s " , tamnams.interval_quality(current_dark_interval, input_mos, "abbrev" , mos_abbrev))
.. string.format("|| %s " , mos.interval_as_string(current_dark_interval))
.. string.format("|| %s " , dark_interval_range)
.. string.format("|| ~%.4f nats " , he_dark_average)
.. string.format("|| ~%.4f nats\n" , he_dark_best)
.. "|-\n"
.. string.format("| %s " , tamnams.interval_quality(current_bright_interval, input_mos, "sentence-case", mos_prefix))
.. string.format("|| %s " , tamnams.interval_quality(current_bright_interval, input_mos, "abbrev" , mos_abbrev))
.. string.format("|| %s " , mos.interval_as_string(current_bright_interval))
.. string.format("|| %s " , bright_interval_range)
.. string.format("|| ~%.4f nats " , he_bright_average)
.. string.format("|| ~%.4f nats" , he_bright_best)
end
result = result .. "\n"
end
result = result .. "|}"
return result
end
function p.mos_intervals_description(input_mos, mos_prefix)
local input_mos = input_mos or mos.new(5,2)
local mos_prefix = mos_prefix or "dia"
local scalesig = mos.as_string(input_mos)
-- How many periods?
-- What are the period intervals?
local period_count = mos.period_count(input_mos)
local period_interval = mos.period(input_mos)
local period_intervals = {}
for i = 1, period_count + 1 do
local interval = mos.interval_mul(period_interval, i-1)
table.insert(period_intervals, interval)
end
-- As a sentence piece
local period_intervals_as_text = ""
if #period_intervals == 2 then
period_intervals_as_text = string.format("%s and %s", tamnams.interval_quality(period_intervals[1], input_mos, "none", mos_prefix), tamnams.interval_quality(period_intervals[2], input_mos, "none", mos_prefix))
else
for i = 1, period_count do
period_intervals_as_text = period_intervals_as_text
.. string.format("%s, ", tamnams.interval_quality(period_intervals[i], input_mos, "none", mos_prefix))
end
period_intervals_as_text = period_intervals_as_text
.. string.format("and %s", tamnams.interval_quality(period_intervals[period_count + 1], input_mos, "none", mos_prefix))
end
local result = string.format("The intervals of %s are named after the number of mossteps (L and s) they subtend.", scalesig)
local period_interval_desc = ""
if period_count == 1 then
period_interval_desc = "the root and " .. (rat.eq(input_mos.equave, 2) and "octave" or "equave")
else
period_interval_desc = "the period intervals"
end
result = result
.. string.format(" Each interval, apart from %s (%s), has two varieties, or sizes, each.", period_interval_desc, period_intervals_as_text)
result = result
.. " Interval varieties are named major and minor for the large and small sizes, respectively"
.. (input_mos.nL == input_mos.ns and "." or ", and augmented, perfect, and diminished for the scale's generators.")
return result
end
-- Wrapper function; to be called by template
function p.mos_intervals(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)
-- 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_intervals_description(input_mos, mos_prefix) .. "\n" .. p._mos_intervals(input_mos, mos_prefix, mos_abbrev, is_collapsed)
end
return p
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