Module:MOS

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Documentation for this module may be created at Module:MOS/doc 

local rat = require('Module:Rational')
local seq = require('Module:Sequence')
local utils = require('Module:Utils')
local et = require('Module:ET')
local p = {}

-- Table of official tamnams names (2/1-equave only)
p.tamnams_name = { -- Only mosses with 2/1-equave names in TAMNAMS
	['1L 1s'] = 'monowood',
	['2L 2s'] = 'biwood',
	['1L 5s'] = 'antimachinoid',
	['2L 4s'] = 'malic',
	['3L 3s'] = 'triwood',
	['4L 2s'] = 'citric',
	['5L 1s'] = 'machinoid',
	['1L 6s'] = 'onyx',
	['2L 5s'] = 'antidiatonic',
	['3L 4s'] = 'mosh',
	['4L 3s'] = 'smitonic',
	['5L 2s'] = 'diatonic',
	['6L 1s'] = 'archaeotonic',
	['1L 7s'] = 'antipine',
	['2L 6s'] = 'subaric',
	['3L 5s'] = 'checkertonic',
	['4L 4s'] = 'tetrawood',
	['5L 3s'] = 'oneirotonic',
	['6L 2s'] = 'ekic',
	['7L 1s'] = 'pine',
	['1L 8s'] = 'antisubneutralic',
	['2L 7s'] = 'balzano',
	['3L 6s'] = 'tcherepnin',
	['4L 5s'] = 'gramitonic',
	['5L 4s'] = 'semiquartal',
	['6L 3s'] = 'hyrulic',
	['7L 2s'] = 'armotonic',
	['8L 1s'] = 'subneutralic',
	['1L 9s'] = 'antisinatonic',
	['2L 8s'] = 'jaric',
	['3L 7s'] = 'sephiroid',
	['4L 6s'] = 'lime',
	['5L 5s'] = 'pentawood',
	['6L 4s'] = 'lemon',
	['7L 3s'] = 'dicoid',
	['8L 2s'] = 'taric',
	['9L 1s'] = 'sinatonic'
}

-- Prefixes
p.tamnams_prefix = { -- Only mosses with 2/1-equave names in TAMNAMS
	['1L 1s'] = 'monwd-',
	['2L 2s'] = 'biwd-',
	['1L 5s'] = 'amech-',
	['2L 4s'] = 'mal-',
	['3L 3s'] = 'triwd-',
	['4L 2s'] = 'citro-',
	['5L 1s'] = 'mech-',
	['1L 6s'] = 'on-',
	['2L 5s'] = 'pel-',
	['3L 4s'] = 'mosh-',
	['4L 3s'] = 'smi-',
	['5L 2s'] = 'dia-',
	['6L 1s'] = 'arch-',
	['1L 7s'] = 'apine-',
	['2L 6s'] = 'subar-',
	['3L 5s'] = 'check-',
	['4L 4s'] = 'tetrawd-',
	['5L 3s'] = 'oneiro-',
	['6L 2s'] = 'ek-',
	['7L 1s'] = 'pine-',
	['1L 8s'] = 'ablu-',
	['2L 7s'] = 'bal-',
	['3L 6s'] = 'cher-',
	['4L 5s'] = 'gram-',
	['5L 4s'] = 'cthon-',
	['6L 3s'] = 'hyru-',
	['7L 2s'] = 'arm-',
	['8L 1s'] = 'blu-',
	['1L 9s'] = 'asina-',
	['2L 8s'] = 'jara-',
	['3L 7s'] = 'seph-',
	['4L 6s'] = 'lime-',
	['5L 5s'] = 'pentawd-',
	['6L 4s'] = 'lem-',
	['7L 3s'] = 'dico-',
	['8L 2s'] = 'tara-',
	['9L 1s'] = 'sina-'
}

-- Abbreviations (most abbrevs are the same as the prefixes but there are exceptions)
p.tamnams_abbrev = { -- Only mosses with 2/1-equave names in TAMNAMS
	['1L 1s'] = 'wood',
	['2L 2s'] = 'bw',
	['1L 5s'] = 'amech',
	['2L 4s'] = 'mal',
	['3L 3s'] = 'trw',
	['4L 2s'] = 'cit',
	['5L 1s'] = 'mech',
	['1L 6s'] = 'on',
	['2L 5s'] = 'pel',
	['3L 4s'] = 'mosh',
	['4L 3s'] = 'smi',
	['5L 2s'] = 'dia',
	['6L 1s'] = 'arch',
	['1L 7s'] = 'apine',
	['2L 6s'] = 'subar',
	['3L 5s'] = 'chk',
	['4L 4s'] = 'ttw',
	['5L 3s'] = 'onei',
	['6L 2s'] = 'ek',
	['7L 1s'] = 'pine',
	['1L 8s'] = 'ablu',
	['2L 7s'] = 'bal',
	['3L 6s'] = 'ch',
	['4L 5s'] = 'gram',
	['5L 4s'] = 'cth',
	['6L 3s'] = 'hyru',
	['7L 2s'] = 'arm',
	['8L 1s'] = 'blu',
	['1L 9s'] = 'asi',
	['2L 8s'] = 'jar',
	['3L 7s'] = 'seph',
	['4L 6s'] = 'lime',
	['5L 5s'] = 'pw',
	['6L 4s'] = 'lem',
	['7L 3s'] = 'dico',
	['8L 2s'] = 'tar',
	['9L 1s'] = 'si'
}


function table_invert(t)
   local s={}
   for k,v in pairs(t) do
     s[v]=k
   end
   return s
end

-- Create a table that parses a mos string from the TAMNAMS name.
p.parse_name = table_invert(p.tamnams_name)

-- create a MOS structure (nL)L (ns)s <equave>
function p.new(nL, ns, equave)
	local nL = nL or 5
	local ns = ns or 2
	local equave = equave or 2
	return { nL = nL, ns = ns, equave = equave }
end

function round(num, numDecimalPlaces)
  local mult = 10^(numDecimalPlaces or 0)
  return math.floor(num * mult + 0.5) / mult
end

-- parse a MOS structure
function p.parse(unparsed)
	local nL, ns, equave = unparsed:match('^(%d+)[Ll]%s*(%d+)[Ss]%s*(.*)$')
	nL = tonumber(nL)
	ns = tonumber(ns)
	equave = equave:match('^%((.*)-equivalent%)$') or equave:match('^⟨(.*)⟩$') or equave:match('^<(.*)>$') or '2/1' -- Assumes this is a rational ratio written a/b
	equave = rat.parse(equave)
	if nL == nil or ns == nil or equave == nil then
		return nil
	end
	return p.new(nL, ns, equave)
end

-- construct a string representation for a MOS structure
function p.as_string(mos)
	local suffix = ''
	if not rat.eq(mos.equave, 2) then
		suffix = '⟨' .. rat.as_ratio(mos.equave):lower() .. '⟩'
	end
	return '' .. mos.nL .. 'L ' .. mos.ns .. 's' .. suffix
end

-- construct a long string representation for a MOS structure
function p.as_long_string(mos)
	local suffix = ''
	if not rat.eq(mos.equave, 2) then
		suffix = string.format(" (%s-equivalent)", rat.as_ratio(mos.equave):lower())
	end
	return '' .. mos.nL .. 'L ' .. mos.ns .. 's' .. suffix
end

-- Find the brightest mode of a mos (the Christoffel word)
-- using its definition as a closest integer approximation to line y = #s/#L*x
function p.brightest_mode(mos)
	local nL = mos.nL
	local ns = mos.ns
	local d = utils._gcd(nL, ns)
	if d > 1 then -- use single period mos, with period as new equave
		nL = round(nL/d)
		ns = round(ns/d)
	end
	local current_L, current_s = 0, 0
	local result = ''
	while current_L < nL or current_s < ns do
		if (current_s + 1) * nL <= ns * (current_L) then
            current_s = current_s + 1
            result = result .. 's'
        else
            current_L = current_L + 1
            result = result .. 'L'
        end
	end
	return string.rep(result, d)
end

function p.bright_gen(mos) -- Compute the abstract, equave-agnostic bright generator as a "vector" of L and s steps.
	local nL = mos.nL
	local ns = mos.ns
	local d = utils._gcd(nL, ns)
	if d > 1 then -- use single period mos, with period as new equave
		nL = round(nL/d)
		ns = round(ns/d)
	end
	local min_dist = 2; -- the distance we get will always be <= sqrt(2)
	local current_L, current_s = 0, 0
	local result = {['L'] = 0, ['s'] = 0} 
	while current_L < nL or current_s < ns do
		if (current_s + 1) * nL <= ns * (current_L) then
            current_s = current_s + 1
        else
            current_L = current_L + 1
		end
    	if current_L < nL or current_s < ns then -- check to exclude (current_L, current_s) = (nL, ns)
    		local distance_here = math.abs(nL*current_s - ns*current_L)/math.sqrt(nL^2 + ns^2)
    		if distance_here < min_dist then
    			min_dist = distance_here
    			result['L'] = current_L
    			result['s'] = current_s
    		end
    	end
	end
	return result
end

-- Given mos a MOS structure, hardness = L/s a rational number,
-- return the et and the bright MOS generator corresponding to the hardness.
function p.et_tuning_by_hardness(mos, hardness)
	local nL, ns, equave = mos.nL, mos.ns, mos.equave
	hardness = rat.parse(hardness) or rat.new(hardness) or hardness
	if nL == nil or ns == nil or equave == nil or hardness == nil then
		return nil
	end
	L_in_et_steps, s_in_et_steps = rat.as_pair(hardness)
	local et = et.new(nL*L_in_et_steps + ns*s_in_et_steps, equave)
	local gen = p.bright_gen(mos)
	local gen_steps = gen['L']*L_in_et_steps + gen['s']*s_in_et_steps
	return et, gen_steps
end

-- Given a mos, find the ancestor mos with a target note count (default 10)
-- or less
function p.find_ancestor(mos, target_note_count)
	local mos = mos or p.new(5, 2)
	local target_note_count = target_note_count or 10
	
	local z = mos.nL
	local w = mos.ns
	
	while (z ~= w) and (z + w > target_note_count) do
		local m1 = math.max(z, w)
		local m2 = math.min(z, w)
		
		-- For use with updating ancestor mos chunks
		local z_prev = z
		
		-- Update step ratios
		z = m2
		w = m1 - m2
	end
	
	return p.new(z, w, mos.equave)
end

return p
Retrieved from "https://en.xen.wiki/index.php?title=Module:MOS&oldid=141245"