Xenharmonic Wiki

Module:Ups and downs notation: Difference between revisions

← Older edit
C-indexed -> D-indexed; "major" -> "diatonic"
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
 
(17 intermediate revisions by 4 users not shown)
Line 1: Line 1:
local p = {}
local ET = require("Module:ET")
local ET = require("Module:ET")
local u = require("Module:Utils")
local utils = require("Module:Utils")
local p = {}
local yesno = require("Module:Yesno")


-- Returns a table of note names
-- Returns a table of note names
Line 20: Line 22:
--  [12] = {"D"}
--  [12] = {"D"}
-- }
-- }
local function round(x)
-- rounds half-integers towards 0.
return x >= 0 and math.ceil(x - 0.5) or math.floor(x + 0.5)
end


function p.get_note_names_table(et, fifth)
function p.get_note_names_table(et, fifth)
local note_names = {}
local note_names = {}
for i = 0,et.size do
for i = 0, et.size do
note_names[i] = {}
note_names[i] = {}
i = i + 1
end
end
 
fifth = fifth or math.floor(math.log(3/2)/math.log(2) * et.size + 0.5)
fifth = fifth or math.floor(math.log(3 / 2) / math.log(2) * et.size + 0.5)
local fourth = et.size - fifth -- 4/3 = [2 -1>
local fourth = et.size - fifth -- 4/3 = [2 -1>
local chroma = (fifth * 7) % et.size -- 2187/2048 = [-11 7>
local chroma = (fifth * 7) % et.size -- 2187/2048 = [-11 7>
local is_mavila = fifth/et.size < 4/7
local is_mavila = fifth / et.size < 4 / 7
if is_mavila then
if is_mavila then
chroma = et.size - chroma
chroma = et.size - chroma
end
end


local diatonic_note_idx = {
local diatonic_note_idx = {
0,  
0,
(fifth * 2) % et.size,
(fifth * 2) % et.size,
(fifth * -3) % et.size,
(fifth * -3) % et.size,
Line 45: Line 50:
(fifth * 3) % et.size,
(fifth * 3) % et.size,
(fifth * -2) % et.size,
(fifth * -2) % et.size,
et.size
et.size,
}
}


-- Add major scale notes
-- Add D dorian scale notes
table.insert(note_names[diatonic_note_idx[1]], "D")
table.insert(note_names[diatonic_note_idx[1]], "D")
table.insert(note_names[diatonic_note_idx[2]], "E")
table.insert(note_names[diatonic_note_idx[2]], "E")
Line 59: Line 64:


local last_diatonic_note = 0
local last_diatonic_note = 0
 
-- Add sharp/up notes
-- Add sharp/up notes
for i = 0, et.size - 1 do
for i = 0, et.size - 1 do
if u.table_contains(diatonic_note_idx, i) then
if utils.table_contains(diatonic_note_idx, i) then
last_diatonic_note = i
last_diatonic_note = i
else
else
local num_double_sharps = math.floor((i - last_diatonic_note) / (2 * chroma))
local num_double_sharps = 0
local num_sharps = math.floor((i - last_diatonic_note) / chroma) % 2
local num_sharps = round((i - last_diatonic_note) / chroma)
if num_sharps > 1 then
num_double_sharps = math.floor(num_sharps / 2)
num_sharps = num_sharps % 2
end
local num_ups = (i - last_diatonic_note) % chroma
local num_ups = (i - last_diatonic_note) % chroma
local num_downs = 0
if chroma == 0 then
if chroma == 0 then
num_double_sharps = 0
num_double_sharps = 0
num_sharps = 0
num_sharps = 0
num_ups = (i - last_diatonic_note)
num_ups = (i - last_diatonic_note)
end
if num_ups > chroma / 2 then
num_downs = chroma - num_ups
num_ups = 0
end
end
local last_diatonic_names = note_names[last_diatonic_note]
local last_diatonic_names = note_names[last_diatonic_note]
for j = 1, (#last_diatonic_names) do
for j = 1, #last_diatonic_names do
if num_ups >= 3 then
if num_downs >= 3 then
table.insert(note_names[i], "^<sup>" .. num_ups .. "</sup>" .. last_diatonic_names[j] .. string.rep("#", num_sharps) .. string.rep("x", num_double_sharps))
table.insert(
note_names[i],
"v<sup>"
.. num_downs
.. "</sup>"
.. last_diatonic_names[j]
.. string.rep("♯", num_sharps)
.. string.rep("𝄪", num_double_sharps)
)
elseif num_downs > 0 then
table.insert(
note_names[i],
string.rep("v", num_downs)
.. last_diatonic_names[j]
.. string.rep("♯", num_sharps)
.. string.rep("𝄪", num_double_sharps)
)
elseif num_ups >= 3 then
table.insert(
note_names[i],
"^<sup>"
.. num_ups
.. "</sup>"
.. last_diatonic_names[j]
.. string.rep("♯", num_sharps)
.. string.rep("𝄪", num_double_sharps)
)
else
else
table.insert(note_names[i], string.rep("^", num_ups) .. last_diatonic_names[j] .. string.rep("#", num_sharps) .. string.rep("x", num_double_sharps))
table.insert(
note_names[i],
string.rep("^", num_ups)
.. last_diatonic_names[j]
.. string.rep("♯", num_sharps)
.. string.rep("𝄪", num_double_sharps)
)
end
end
end
end
end
end
end
end
 
last_diatonic_note = et.size
last_diatonic_note = et.size


-- Add flat/down notes
-- Add flat/down notes
for i = et.size - 1, 0, -1 do
for i = et.size - 1, 0, -1 do
if u.table_contains(diatonic_note_idx, i) then
if utils.table_contains(diatonic_note_idx, i) then
last_diatonic_note = i
last_diatonic_note = i
else
else
local num_flats = math.floor((last_diatonic_note - i) / chroma)
local num_flats = round((last_diatonic_note - i) / chroma)
local num_downs = (last_diatonic_note - i) % chroma
local num_downs = (last_diatonic_note - i) % chroma
local num_ups = 0
if chroma == 0 then
if chroma == 0 then
num_flats = 0
num_flats = 0
num_downs = (last_diatonic_note - i)
num_downs = (last_diatonic_note - i)
end
end
last_diatonic_names = note_names[last_diatonic_note]  
if num_downs > chroma / 2 then
for j = 1, (#last_diatonic_names) do
num_ups = chroma - num_downs
if num_downs >= 3 then
num_downs = 0
table.insert(note_names[i], "v<sup>" .. num_downs .. "</sup>" .. last_diatonic_names[j] .. string.rep("b", num_flats))
end
local last_diatonic_names = note_names[last_diatonic_note]
for j = 1, #last_diatonic_names do
if num_ups >= 3 then
table.insert(
note_names[i],
"^<sup>" .. num_ups .. "</sup>" .. last_diatonic_names[j] .. string.rep("♭", num_flats)
)
elseif num_ups > 0 then
table.insert(
note_names[i],
string.rep("^", num_ups) .. last_diatonic_names[j] .. string.rep("♭", num_flats)
)
elseif num_downs >= 3 then
table.insert(
note_names[i],
"v<sup>" .. num_downs .. "</sup>" .. last_diatonic_names[j] .. string.rep("♭", num_flats)
)
else
else
table.insert(note_names[i], string.rep("v", num_downs) .. last_diatonic_names[j] .. string.rep("b", num_flats))
table.insert(
note_names[i],
string.rep("v", num_downs) .. last_diatonic_names[j] .. string.rep("♭", num_flats)
)
end
end
end
end
end
end
end
end
 
return note_names
return note_names
end
end
Line 113: Line 180:
function p.ups_and_downs_note_name(frame)
function p.ups_and_downs_note_name(frame)
local et = ET.parse(frame.args["tuning"]) or ET.parse("12edo")
local et = ET.parse(frame.args["tuning"]) or ET.parse("12edo")
local debugg = yesno(frame.args["debug"])
local fifth = tonumber(frame.args["fifth"])
local fifth = tonumber(frame.args["fifth"])
local step = tonumber(frame.args["step"])
local step = tonumber(frame.args["step"])
return table.concat(p.get_note_names_table(et, fifth)[step], ", "):sub(0, -1)
local result = table.concat(p.get_note_names_table(et, fifth)[step], ", "):sub(0, -1)
if debugg == true then
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end
return frame:preprocess(result)
end
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:Ups_and_downs_notation"