-- This is a helper module that contains commonly used functions for:
-- - MOS degrees
-- - MOS gamut
local mos = require('Module:MOS')
local mosg = require('Module:MOS gamut') -- TODO: move gamut function to here
local rat = require('Module:Rational')
local p = {}
-- Helper function for parsing a step ratio entered as a string "p/q"
function p.parse_step_ratio(step_ratio_unparsed)
local parsed = {}
for entry in string.gmatch(step_ratio_unparsed, '([^/]+)') do
local trimmed = entry:gsub("^%s*(.-)%s*$", "%1")
table.insert(parsed, trimmed) -- Add to array
end
local ratio = { tonumber(parsed[1]), tonumber(parsed[2]) }
return ratio
end
-- Helper function to simplify step ratio
function p.simplify_step_ratio(step_ratio_unsimplified)
local kp = step_ratio_unsimplified[1]
local kq = step_ratio_unsimplified[2]
local k = rat.gcd(kp, kq)
local num = kp / k
local den = kq / k
return { num, den }
end
-- Helper function for parsing a UDP entered as a string "up,dp"
-- To avoid potential issues, the "," character is used instead of "|"
function p.parse_udp(step_ratio_unparsed)
local parsed = {}
for entry in string.gmatch(step_ratio_unparsed, '([^,]+)') do
local trimmed = entry:gsub("^%s*(.-)%s*$", "%1")
table.insert(parsed, trimmed) -- Add to array
end
local udp = { tonumber(parsed[1]), tonumber(parsed[2]) }
return udp
end
-- Helper function that converts a note name given as a quantity of mossteps
-- and chromas (see gamut function) into a name, such as "C#"
-- To be used in conjunction with the genchain function
function p.mosstep_and_chroma_to_note_name(mossteps, chromas, note_symbol, chroma_symbol)
local note_name = note_symbol .. string.rep(chroma_symbol, math.abs(chromas))
return note_name
end
-- Helper function that converts a scale degree given as a quantity of mossteps
-- and a numeric quality (0=perf, 1=maj, -1=min, 2=aug, -2=dim, etc) into a
-- scale degree
-- To be used in conjunction with the degrees function
-- TODO: add options to change naming and enumeration scheme; options include:
-- - Abbreviations (Major/Minor vs Maj/Min vs M/m)
-- - TAMNAMS indexing vs regular indexing (0-mossteps vs mos-1st)
-- - Ability to pass in a prefix (default is "mos")
function p.mosstep_and_quality_to_degree(mossteps, quality)
local degree_name = mossteps .. "-mosstep"
if quality == 0 then
degree_name = "Perf. " .. degree_name
elseif quality == 1 then
degree_name = "Maj. " .. degree_name
elseif quality == 2 then
degree_name = "Aug. " .. degree_name
elseif quality > 2 then
degree_name = (quality - 1) .. "× aug. " .. degree_name
elseif quality == -1 then
degree_name = "Min. " .. degree_name
elseif quality == -2 then
degree_name = "Dim. " .. degree_name
elseif quality < -2 then
degree_name = (math.abs(quality) - 1) .. "× dim. " .. degree_name
end
return degree_name
end
-- Function that produces a chain of scale degrees. What scale degrees are
-- reached by stacking a generator?
-- (EG, major 2nd, augmented 2nd, etc)
-- This function only works one direction at a time, so it's necessary to call
-- it twice, one for each direction.
-- Quality encodes maj/min/aug/perf/dim numerically:
-- - 3 = 2x augmented
-- - 2 = 1x augmented
-- - 1 = major
-- - 0 = perfect (used for generators and root)
-- - -1 = minor
-- - -2 = 1x diminished
-- - -3 = 2x diminished
function p.mos_degrees(input_mos, genchain_length_per_period, going_up)
-- Default parameters for testing
--[[
local input_mos = input_mos or mos.new(5, 2, 2)
local genchain_length_per_period = genchain_length_per_period or 10
local going_up = false
]]--
-- Get the number of mossteps per period and equave
local mossteps_per_equave = input_mos.nL + input_mos.ns
local periods_per_equave = rat.gcd(input_mos.nL, input_mos.ns)
local mossteps_per_period = mossteps_per_equave / periods_per_equave
-- Get the number of mossteps for the generators
local bright_gen = mos.bright_gen(input_mos)
local mossteps_per_bright_gen = bright_gen['L'] + bright_gen['s']
local mossteps_per_dark_gen = mossteps_per_period - mossteps_per_bright_gen
local degreechain = {}
for j = 1, periods_per_equave do
local chain_for_period = {}
for i = 1, genchain_length_per_period do
-- Calculate mossteps
local mossteps = 0
if going_up then
mossteps = (i - 1) * mossteps_per_bright_gen % mossteps_per_period + (j - 1) * mossteps_per_period
else
mossteps = (i - 1) * mossteps_per_dark_gen % mossteps_per_period + (j - 1) * mossteps_per_period
end
-- Calculate quality
-- The first two elements in the chain are always perfect
-- All intervals after that are major (or minor if going down)
-- After the major intervals are augmented intervals, which starts
-- with the augmented dark generator, which comes before the
-- augmented unison. (or minor and dim bright gen if going down)
-- For nL ns mosses, generators are major and minor instead, so only
-- the root is perfect
local quality = 0
if input_mos.nL ~= input_mos.ns then
if i == 1 or i == 2 then
quality = 0
else
-- Offsetting i by +1 will make it so the dark generator
-- before the augmented unison is denoted as augmented,
-- but lua's start-from-1 indexing offsets it by 1 already.
quality = math.floor(i / mossteps_per_period) + 1
if not going_up then
quality = quality * -1
end
end
else
if i == 1 then
quality = 0
else
quality = math.floor((i + 1) / mossteps_per_period)
if not going_up then
quality = quality * -1
end
end
end
-- Put together the name
local degree = { ['mossteps'] = mossteps, ['quality'] = quality }
table.insert(chain_for_period, degree)
end
table.insert(degreechain, chain_for_period)
end
return degreechain
end
return p
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