Module:Infobox Chord
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Documentation transcluded from /doc
Note: Do not invoke this module directly; use the corresponding template instead: Template:Infobox Chord.
Documentation transcluded from /doc
Note: Do not invoke this module directly; use the corresponding template instead: Template:Infobox Chord.
 |
Todo: Documentation |
local p = {}
local rat = require("Module:Rational")
local utils = require("Module:Utils")
local infobox = require("Module:Infobox")
function p.infobox_chord(frame)
local debug_mode = utils.value_provided(frame.args["debug"])
local page_name = frame:preprocess("{{PAGENAME}}")
local debug_data = ""
local infobox_data = {}
local cats = ""
local color_names = {}
if utils.value_provided(frame.args["ColorName"]) then
color_name = frame.args["ColorName"]
-- search for ", " not "," because many chord names contain commas, e.g. Cz,y6
for name in (color_name .. ", "):gmatch("(.-), ") do
table.insert(color_names, name)
end
else
cats = cats .. "[[Category:Todo:add color name]]"
end
if utils.value_provided(frame.args["Harmonics"]) then
local harmonics = {}
for hs in string.gmatch(frame.args["Harmonics"], "[^:]+") do
h = tonumber(hs) -- TODO: support rational entries?
assert(h > 0, "invalid harmonic")
table.insert(harmonics, h)
end
-- reduce harmonics to simplest terms, in case the user accidentally failed to reduce them
local gcd = harmonics[1]
for i, h in ipairs(harmonics) do
gcd = utils._gcd(gcd, h)
if gcd == 1 then break end
end
if gcd > 1 then
for i, h in ipairs(harmonics) do
harmonics[i] = harmonics[i] / gcd
end
end
local root = harmonics[1]
if utils.value_provided(frame.args["Root"]) then
root = tonumber(frame.args["Root"])
assert(root > 0, "invalid root")
end
assert(root > 0, "no harmonics given")
local prime_limit = 1
local lcm = 1
local otonal_odd_limit = 1
local root_interval_links = {}
local step_interval_links = {}
local root_cents_steps = {}
local step_cents = {}
local genus = {}
for i, h in ipairs(harmonics) do
-- compute LCM of all harmonics to use as the denominator in utonal form, if needed
lcm = lcm * h / (utils._gcd(lcm, h))
-- increase otonal odd limit for this harmonic, if needed
local odd = h
while odd > 0 and odd % 2 == 0 do
odd = odd / 2
end
if odd > otonal_odd_limit then
otonal_odd_limit = odd
end
-- increase prime limit for this harmonic, if needed,
-- and increase genus factors if needed
for prime, n in pairs(utils.prime_factorization_raw(h)) do
if prime > prime_limit then
prime_limit = prime
end
if prime > 2 then
local prev = genus[prime] or 0
if n > prev then
genus[prime] = n
end
end
end
-- compute ratio of this harmonic relative to the root
local gcd = utils._gcd(h, root)
local numer = h / gcd
local denom = root / gcd
table.insert(root_interval_links, "[[" .. numer .. "/" .. denom .. "]]")
local cents_ln2 = 1731.234
-- compute ratio of this harmonic relative to the previous
if i > 1 then
local prev = harmonics[i-1]
local step_gcd = utils._gcd(h, prev)
local step_numer = h / step_gcd
local step_denom = prev / step_gcd
table.insert(step_interval_links, "[[" .. step_numer .. "/" .. step_denom .. "]]")
table.insert(step_cents, utils._round_dec(cents_ln2 * math.log(step_numer / step_denom)) .. "¢")
end
table.insert(root_cents_steps, utils._round_dec(cents_ln2 * math.log(numer / denom)) .. "¢")
end
local utonal_odd_limit = 1
local subharmonics = {}
for i, h in ipairs(harmonics) do
-- find the subharmonics from the harmonics
local gcd = utils._gcd(lcm, h)
local s = lcm / gcd
table.insert(subharmonics, s)
-- find the utonal odd limit
local s_odd = s
while s_odd > 0 and s_odd % 2 == 0 do
s_odd = s_odd / 2
end
if s_odd > utonal_odd_limit then
utonal_odd_limit = s_odd
end
end
-- intervallic odd limit
local odd_limit = 1
for j, b in ipairs(harmonics) do
for i, a in ipairs(harmonics) do
local gcd = utils._gcd(a, b)
local numer = b / gcd
local denom = a / gcd
while numer % 2 == 0 do
numer = numer / 2
end
if numer > odd_limit then
odd_limit = numer
end
while denom > 0 and denom % 2 == 0 do
denom = denom / 2
end
if denom > odd_limit then
odd_limit = denom
end
end
end
-- genus
local genus_terms = {}
local genus_product = 1
local primes = {}
for prime, _ in pairs(genus) do
table.insert(primes, prime)
end
table.sort(primes)
for i, prime in ipairs(primes) do
local exponent = genus[prime]
if exponent == 1 then
table.insert(genus_terms, prime)
else
table.insert(genus_terms, prime .. "<sup>" .. exponent .. "</sup>")
end
genus_product = genus_product * (prime ^ exponent)
end
-- compute tag to add for category sort order: as many "#" as the number of digits in the first harmonic
local sort_tag = ""
local first_num = page_name:match("^(%d+):")
if first_num then
first_num = tonumber(first_num)
sort_tag = "|#"
local sort_bound = 10
while sort_bound <= harmonics[1] do
sort_tag = sort_tag .. "#"
sort_bound = sort_bound * 10
end
end
table.insert(infobox_data, {"Harmonics", table.concat(harmonics, ":")})
if (not utils.value_provided(frame.args["Root"])) and (utonal_odd_limit <= otonal_odd_limit or utonal_odd_limit < 1000) then
table.insert(infobox_data, {"Subharmonics", "1/(" .. table.concat(subharmonics, ":") .. ")"})
end
table.insert(infobox_data, {"Intervals from root", table.concat(root_interval_links, " – ")})
table.insert(infobox_data, {"Cents from root", table.concat(root_cents_steps, " ")})
table.insert(infobox_data, {"Step intervals", table.concat(step_interval_links, ", ")})
table.insert(infobox_data, {"Step cents", table.concat(step_cents, ", ")})
-- TODO: category goes here.
if table.getn(color_names) > 0 then
local label = "Color name"
if table.getn(color_names) > 1 then
label = "Color names"
end
table.insert(infobox_data, {"[[Color notation|" .. label .. "]]", table.concat(color_names, "<br/>")})
end
if prime_limit < 96 then
table.insert(infobox_data, {"[[Prime limit]]", "[[" .. prime_limit .. "-limit|" .. prime_limit .. "]]"})
cats = cats .. "[[Category:" .. prime_limit .. "-limit chords" .. sort_tag .. "]]"
else
table.insert(infobox_data, {"[[Prime limit]]", prime_limit})
cats = cats .. "[[Category:Just intonation chords" .. sort_tag .. "]]"
end
local genus_data = table.concat(genus_terms, " ⋅ ")
-- append the actual product if it's (arbitrarily) 9 digits or fewer
if genus_product < 1000000000 then
genus_data = genus_data .. " (" .. genus_product .. ")"
end
table.insert(infobox_data, {"[[Euler-Fokker genus|Genus]]", genus_data})
if odd_limit < 32 then
table.insert(infobox_data, {"[[Intervallic odd limit]]", "[[" .. odd_limit .. "-odd-limit|" .. odd_limit .. "]]"})
cats = cats .. "[[Category:" .. odd_limit .. "-odd-limit chords" .. sort_tag .. "]]"
else
table.insert(infobox_data, {"[[Intervallic odd limit]]", odd_limit})
end
table.insert(infobox_data, {"[[Otonal odd limit]]", otonal_odd_limit})
table.insert(infobox_data, {"[[Utonal odd limit]]", utonal_odd_limit})
end
if debug_data ~= "" then
table.insert(infobox_data, {
"Debug",
debug_data,
})
end
local s = infobox.build("<u>Chord information</u>", infobox_data)
if not debug_mode then
s = s .. cats
end
return s
end
return p