Module:ChordVoicings
Documentation for this module may be created at Module:ChordVoicings/doc
-- Module:ChordVoicings (hardened against CPU limit / signal 24)
-- Usage: {{ChordVoicingTable|rchord=4:5:6:7}}
local p = {}
-- ---------- utilities ----------
local function split_enum(s)
local t = {}
for num in string.gmatch(s or "", "%d+") do
t[#t+1] = tonumber(num)
end
return t
end
local function gcd(a,b)
while b ~= 0 do a, b = a % b, b end
return math.abs(a)
end
local function gcd_list(t)
local g = t[1]
for i=2,#t do g = gcd(g, t[i]) end
return g
end
local function odd_part(n)
while n % 2 == 0 do n = math.floor(n/2) end
return n
end
local function to_str(t)
local parts = {}
for i=1,#t do parts[i]=tostring(t[i]) end
return table.concat(parts, ":")
end
local function sort_key(t)
local parts = {}
for i=1,#t do parts[i]=string.format("%03d", t[i]) end
return table.concat(parts, "-")
end
local function span_ratio(t)
local mn, mx = t[1], t[1]
for i=2,#t do
if t[i]<mn then mn=t[i] end
if t[i]>mx then mx=t[i] end
end
return mx/mn
end
-- memoized reduction
local reduce_cache = {}
local function key_of(t) return sort_key(t) end
local function clone(t)
local u = {}
for i=1,#t do u[i]=t[i] end
return u
end
local function reduce_irreducible(t)
local k = key_of(t)
local cached = reduce_cache[k]
if cached then return cached end
local g = gcd_list(t)
local u
if g>1 then
u = {}
for i=1,#t do u[i]=math.floor(t[i]/g) end
else
u = clone(t)
end
reduce_cache[k] = u
return u
end
-- two-octave rotation step
local function rot2_once(t)
local n = #t
local u = {}
for i=2,n do u[#u+1] = t[i] end
u[#u+1] = t[1]*4
return reduce_irreducible(u)
end
local function toodds(enum)
local odds = {}
for i=1,#enum do odds[i] = odd_part(enum[i]) end
return odds
end
local function unique_in_order(t)
local seen, out = {}, {}
for _,x in ipairs(t) do if not seen[x] then seen[x]=true; out[#out+1]=x end end
return out
end
-- subsets
local function all_nonempty_subsets(arr)
local res = {}
local function rec(i, cur)
if i > #arr then
if #cur > 0 then
local add = {}
for k=1,#cur do add[k]=cur[k] end
res[#res+1] = add
end
return
end
rec(i+1, cur) -- exclude
cur[#cur+1] = arr[i]; rec(i+1, cur); cur[#cur] = nil -- include
end
rec(1, {})
return res
end
local function subset_labels(nonroot_odds)
local nums = {}
for i,x in ipairs(nonroot_odds) do nums[i]=x end
table.sort(nums)
local labels = {}
labels[#labels+1] = { text="Root", set={} }
local subsets = all_nonempty_subsets(nums)
table.sort(subsets, function(a,b)
if #a ~= #b then return #a < #b end
for i=1,math.min(#a,#b) do
if a[i] ~= b[i] then return a[i] < b[i] end
end
return #a < #b
end)
for _,set in ipairs(subsets) do
local parts={}
for i,od in ipairs(set) do parts[i] = "'" .. tostring(od) end
labels[#labels+1] = { text=table.concat(parts, ""), set=set }
end
return labels
end
local function apply_octaves(enum, odds, chosen_set)
local out = {}
for i=1,#enum do
local v = enum[i]
if chosen_set[odds[i]] then v = v * 2 end
out[i] = v
end
return out
end
local function italicize(s) return "''" .. s .. "''" end
local function bold_italic(s) return "'''''" .. s .. "'''''" end
-- ---------- hardened rotation cycle with cap ----------
local function build_rotation_map(start_vec)
local map = {}
local seen = {}
local v = reduce_irreducible(start_vec)
local steps, MAX = 0, 512 -- hard cap to avoid CPU overruns
while true do
local fodd = odd_part(v[1])
if not map[fodd] then map[fodd] = v end
local sig = key_of(v)
if seen[sig] then break end
seen[sig] = true
local nextv = rot2_once(v)
steps = steps + 1
if steps > MAX then break end
v = nextv
end
return map
end
-- ---------- main render ----------
function p.render(frame)
local args = frame.args or frame:getParent().args
local rchord_str = (args.rchord or args[1] or ""):gsub("%s+", "")
if rchord_str == "" then
return "<strong class=\"error\">Missing parameter: rchord</strong>"
end
local width = args.width or "120px"
local title = args.title or "Voicings and rotations around two octaves"
local cls = args.class or "wikitable sortable"
-- parse & sanity
local enum = split_enum(rchord_str)
if #enum < 3 then
return "<strong class=\"error\">rchord must have at least 3 integers</strong>"
end
-- optional global guard for pathological inputs
if #enum > 7 then
return "<strong class=\"error\">rchord too large for on-wiki render (max 7 terms)</strong>"
end
local odds = toodds(enum)
local root_odd = odd_part(enum[1])
local odd_rows = unique_in_order(odds)
-- columns: Root + subsets of non-root odds
local nonroot_odds_unique = {}
for _,o in ipairs(odd_rows) do
if o ~= root_odd then nonroot_odds_unique[#nonroot_odds_unique+1] = o end
end
local col_specs = subset_labels(nonroot_odds_unique) -- {text,set}
-- trivial case: if there are no non-root odds, only the Root column exists
if #col_specs == 1 then
local only = reduce_irreducible(enum)
local out = {}
out[#out+1] = "== " .. title .. " =="
out[#out+1] = string.format('{| class="%s" style="text-align:center;"', cls)
out[#out+1] = "|+"
out[#out+1] = string.format('! style="width:%s;" {{diagonal split header|Rotation|Voicing}}', width)
out[#out+1] = string.format('! style="width:%s;" | Root', width)
for _,rowodd in ipairs(odd_rows) do
out[#out+1] = "|-"
out[#out+1] = string.format('! style="width:%s;" | On %s', width, tostring(rowodd))
local rotated_map = build_rotation_map(enum)
local r = rotated_map[rowodd] or reduce_irreducible(enum)
local disp = to_str(r)
local shown = (rowodd == root_odd) and bold_italic(disp) or disp
out[#out+1] = string.format('| data-sort-value="%s" | %s', sort_key(r), shown)
end
out[#out+1] = "|}"
out[#out+1] = "Enumerations in italics map to an existing octave-reduced rotation."
return table.concat(out, "\n")
end
-- header
local out = {}
out[#out+1] = "== " .. title .. " =="
out[#out+1] = string.format('{| class="%s" style="text-align:center;"', cls)
out[#out+1] = "|+"
out[#out+1] = string.format('! style="width:%s;" {{diagonal split header|Rotation|Voicing}}', width)
for _,spec in ipairs(col_specs) do
out[#out+1] = string.format('! style="width:%s;" | %s', width, spec.text)
end
-- Precompute one rotation map per column (voicing)
local rotation_maps = {}
for c, spec in ipairs(col_specs) do
local chosen = {}
for _,od in ipairs(spec.set) do chosen[od] = true end
local base_voicing = apply_octaves(enum, odds, chosen)
rotation_maps[c] = build_rotation_map(base_voicing)
end
-- Emit rows
for _,rowodd in ipairs(odd_rows) do
out[#out+1] = "|-"
out[#out+1] = string.format('! style="width:%s;" | On %s', width, tostring(rowodd))
for c, spec in ipairs(col_specs) do
local rotated = rotation_maps[c][rowodd]
if not rotated then
-- fallback (rare): use reduced base voicing
local chosen = {}
for _,od in ipairs(spec.set) do chosen[od] = true end
rotated = reduce_irreducible(apply_octaves(enum, odds, chosen))
end
local disp = to_str(rotated)
local sortv = sort_key(rotated)
local shown
local is_two_octaves = (span_ratio(rotated) >= 4.0)
if rowodd == root_odd and #spec.set == 0 then
shown = bold_italic(disp)
elseif not is_two_octaves then
shown = italicize(disp)
else
shown = disp
end
out[#out+1] = string.format('| data-sort-value="%s" | %s', sortv, shown)
end
end
out[#out+1] = "|}"
out[#out+1] = "Enumerations in italics map to an existing octave-reduced rotation."
return table.concat(out, "\n")
end
return p