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Module:Ups and downs notation: Difference between revisions

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C-indexed -> D-indexed; "major" -> "diatonic"
Line 2: Line 2:
local u = require("Module:Utils")
local u = require("Module:Utils")
local p = {}
local p = {}


-- Returns a table of note names
-- Returns a table of note names
-- e.g. for 12edo, intended result would be something like:
-- e.g. for 12edo, intended result would be something like:
-- {
-- {
-- [0] = {"C"},
-- [0] = {"D"},
-- [1] = {"C#", "Db"},
-- [1] = {"D#", "Eb"},
-- [2] = {"D"},
-- [2] = {"E"},
-- [3] = {"D#", "Eb"},
-- [3] = {"F"},
-- [4] = {"E"},
-- [4] = {"F#", "Gb"},
-- [5] = {"F"},
-- [5] = {"G"},
-- [6] = {"F#", "Gb"},
-- [6] = {"G#", "Ab"},
--  [7] = {"G"},
--  [7] = {"A"},
--  [8] = {"G#", Ab"},
--  [8] = {"A#", Bb"},
--  [9] = {"A"},
--  [9] = {"B"},
--  [10] = {"A#", "Bb"},
--  [10] = {"C"},
--  [11] = {"B"},
--  [11] = {"C#", "Db"},
--  [12] = {"C"}
--  [12] = {"D"}
-- }
-- }


Line 31: Line 29:
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
local fourth = et.size - fifth -- 4/3 = [2 -1>
local chroma = (fifth * 7) % et.size
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
Line 39: Line 37:


local major_note_idx = {
local diatonic_note_idx = {
0,  
0,  
(fifth * 2) % et.size,
(fifth * 2) % et.size,
(fifth * 4) % et.size,
(fifth * -3) % et.size,
fourth,
fourth,
fifth,
fifth,
(fifth * 3) % et.size,
(fifth * 3) % et.size,
(fifth * 5) % et.size,
(fifth * -2) % et.size,
et.size
et.size
}
}


-- Add major scale notes
-- Add major scale notes
table.insert(note_names[major_note_idx[1]], "C")
table.insert(note_names[diatonic_note_idx[1]], "D")
table.insert(note_names[major_note_idx[2]], "D")
table.insert(note_names[diatonic_note_idx[2]], "E")
table.insert(note_names[major_note_idx[3]], "E")
table.insert(note_names[diatonic_note_idx[3]], "F")
table.insert(note_names[major_note_idx[4]], "F")
table.insert(note_names[diatonic_note_idx[4]], "G")
table.insert(note_names[major_note_idx[5]], "G")
table.insert(note_names[diatonic_note_idx[5]], "A")
table.insert(note_names[major_note_idx[6]], "A")
table.insert(note_names[diatonic_note_idx[6]], "B")
table.insert(note_names[major_note_idx[7]], "B")
table.insert(note_names[diatonic_note_idx[7]], "C")
table.insert(note_names[major_note_idx[8]], "C")
table.insert(note_names[diatonic_note_idx[8]], "D")


local last_major_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(major_note_idx, i) then
if u.table_contains(diatonic_note_idx, i) then
last_major_note = i
last_diatonic_note = i
else
else
local num_double_sharps = math.floor((i - last_major_note) / (2 * chroma))
local num_double_sharps = math.floor((i - last_diatonic_note) / (2 * chroma))
local num_sharps = math.floor((i - last_major_note) / chroma) % 2
local num_sharps = math.floor((i - last_diatonic_note) / chroma) % 2
local num_ups = (i - last_major_note) % chroma
local num_ups = (i - last_diatonic_note) % chroma
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_major_note)
num_ups = (i - last_diatonic_note)
end
end
local last_major_names = note_names[last_major_note]
local last_diatonic_names = note_names[last_diatonic_note]
for j = 1,(#last_major_names) do
for j = 1, (#last_diatonic_names) do
if num_ups >= 3 then
if num_ups >= 3 then
table.insert(note_names[i], "^<sup>" .. num_ups .. "</sup>" .. last_major_names[j] .. string.rep("#", num_sharps)  .. string.rep("x", num_double_sharps))
table.insert(note_names[i], "^<sup>" .. num_ups .. "</sup>" .. last_diatonic_names[j] .. string.rep("#", num_sharps)  .. string.rep("x", num_double_sharps))
else
else
table.insert(note_names[i], string.rep("^", num_ups) .. last_major_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("x", num_double_sharps))
end
end
end
end
Line 86: Line 84:
end
end
last_major_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(major_note_idx, i) then
if u.table_contains(diatonic_note_idx, i) then
last_major_note = i
last_diatonic_note = i
else
else
local num_flats = math.floor((last_major_note - i) / chroma)
local num_flats = math.floor((last_diatonic_note - i) / chroma)
local num_downs = (last_major_note - i) % chroma
local num_downs = (last_diatonic_note - i) % chroma
if chroma == 0 then
if chroma == 0 then
num_flats = 0
num_flats = 0
num_downs = (last_major_note - i)
num_downs = (last_diatonic_note - i)
end
end
last_major_names = note_names[last_major_note]  
last_diatonic_names = note_names[last_diatonic_note]  
for j = 1,(#last_major_names) do
for j = 1, (#last_diatonic_names) do
if num_downs >= 3 then
if num_downs >= 3 then
table.insert(note_names[i], "v<sup>" .. num_downs .. "</sup>" .. last_major_names[j] .. string.rep("b", num_flats))
table.insert(note_names[i], "v<sup>" .. num_downs .. "</sup>" .. last_diatonic_names[j] .. string.rep("b", num_flats))
else
else
table.insert(note_names[i], string.rep("v", num_downs) .. last_major_names[j] .. string.rep("b", num_flats))
table.insert(note_names[i], string.rep("v", num_downs) .. last_diatonic_names[j] .. string.rep("b", num_flats))
end
end
end
end
end
end
end
end
return note_names
return note_names
Retrieved from "https://en.xen.wiki/w/Module:Ups_and_downs_notation"