Module:Interval table: Difference between revisions
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local p = {} | local p = {} | ||
local | |||
local ET = require("Module:ET") | |||
local rat = require("Module:Rational") | local rat = require("Module:Rational") | ||
local ud = require("Module:Ups and downs notation") | local ud = require("Module:Ups and downs notation") | ||
local | local utils = require("Module:Utils") | ||
local yesno = require("Module:Yesno") | |||
-- Gets mapping of a monzo in a val | -- Gets mapping of a monzo in a val | ||
| Line 36: | Line 38: | ||
end | end | ||
-- Utility | -- Utility function to get specific note name with ud.get_note_names_table | ||
-- (this is essentially what "Template:Ups and downs note name" does) | -- (this is essentially what "Template:Ups and downs note name" does) | ||
local function ud_note(et, fifth, step) | local function ud_note(et, fifth, step) | ||
| Line 62: | Line 64: | ||
local tuning = frame.args["tuning"] | local tuning = frame.args["tuning"] | ||
local et = ET.parse(tuning) or ET.parse("12edo") | local et = ET.parse(tuning) or ET.parse("12edo") | ||
local debugg = yesno(frame.args["debug"]) | |||
local patent_val = { | local patent_val = { | ||
[2] = ET.approximate(et, 2), | [2] = ET.approximate(et, 2), | ||
| Line 80: | Line 83: | ||
} -- NOTE: indices are prime numbers | } -- NOTE: indices are prime numbers | ||
local t_head = "{| class=\"wikitable center-1 right-2 | local t_head = "{| class=\"wikitable center-1 right-2" | ||
if et.size > | if et.size > 20 then | ||
t_head = " | t_head = t_head .. " mw-collapsible mw-collapsed" | ||
end | end | ||
t_head = t_head .. "\"\n" | |||
local fifth = patent_val[3] - patent_val[2] | local fifth = patent_val[3] - patent_val[2] | ||
local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2)) | local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2)) | ||
local dual_fifth = math.abs(fifth_error) > (400 / et.size) | local dual_fifth = (math.abs(fifth_error) > (400 / et.size)) | ||
local dual_flat_fifth = ET.approximate(et, 3 / 2, -1) | local dual_flat_fifth = ET.approximate(et, 3 / 2, -1) | ||
local dual_sharp_fifth = ET.approximate(et, 3 / 2, 1) | local dual_sharp_fifth = ET.approximate(et, 3 / 2, 1) | ||
-- List of all | -- List of all 47-limit ratios with numerator and denominator <= certain cents value and in the range 1/1 - 12/1 | ||
local ratios_list = get_ratios_list( | local ratios_list = get_ratios_list((20 + (et.size / 4)), 12, 47) | ||
result = t_head .. | |||
"|-\n" .. | |||
"! | "! Steps\n" .. | ||
"! Approximate | "! Cents\n" | ||
if rat.eq(et.equave, 3) then | |||
result = result .. "! [[Hekt]]s\n" | |||
end | |||
result = result .. | |||
"! Approximate ratios\n" | |||
if rat.eq(et.equave, 2) then | if rat.eq(et.equave, 2) then | ||
if dual_fifth then | if dual_fifth then | ||
result = result | |||
.. "! [[Ups and downs notation | .. string.format("! [[Ups and downs notation]]<br />(Dual flat fifth %s\\%s)\n", dual_flat_fifth, et.size) | ||
.. string.format("! [[Ups and downs notation]]<br />(Dual sharp fifth %s\\%s)\n", dual_sharp_fifth, et.size) | |||
.. | |||
else | else | ||
result = result .. "! [[Ups and downs notation]]\n" | |||
end | end | ||
end | end | ||
| Line 118: | Line 120: | ||
if #additional_split > 0 then | if #additional_split > 0 then | ||
for i = 1, #additional_split[1] do | for i = 1, #additional_split[1] do | ||
result = result .. string.format("! %s\n", additional_split[1][i]) | |||
end | end | ||
end | end | ||
local decimalPlaces = 3 - math.floor(math.log(1200 / et.size, 10)) | |||
if decimalPlaces > 3 then decimalPlaces = 3 end | |||
if decimalPlaces < 1 then decimalPlaces = 1 end | |||
for i = 0, et.size do | for i = 0, et.size do | ||
result = result .. "|-\n" | |||
.. string.format("| %s\n", i) | |||
.. string.format("| %s\n", utils._round_dec(ET.cents(et, i), decimalPlaces)) | |||
if rat.eq(et.equave, 3) then | |||
result = result .. string.format("| %s\n", utils._round_dec(ET.hekts(et, i), decimalPlaces)) | |||
end | |||
result = result .. "| " | |||
for j = 1, #ratios_list do | for j = 1, #ratios_list do | ||
-- Go through all ratios. | -- Go through all ratios. | ||
| Line 135: | Line 146: | ||
t == i | t == i | ||
and math.abs(ET.cents(et, i) - utils._log(ratios_list[j][1] / ratios_list[j][2], 2) * 1200) | and math.abs(ET.cents(et, i) - utils._log(ratios_list[j][1] / ratios_list[j][2], 2) * 1200) | ||
< (1200 / (math.log(et.size) * et.size)) | < (1200 / (math.log(et.size) * (et.size + 5))) | ||
then | then | ||
result = result .. string.format("[[%s/%s]], ", ratios_list[j][1], ratios_list[j][2]) | |||
end | end | ||
end | end | ||
-- ??? | -- ??? | ||
if | if result:sub(-2, -1) == "| " then | ||
result = result .. "\n" | |||
else | else | ||
result = result:sub(0, -3) .. "\n" | |||
end | end | ||
if rat.eq(et.equave, 2) then | if rat.eq(et.equave, 2) then | ||
if dual_fifth then | if dual_fifth then | ||
result = result .. string.format("| %s\n", ud_note(et, dual_flat_fifth, i)) | |||
result = result .. string.format("| %s\n", ud_note(et, dual_sharp_fifth, i)) | |||
else | else | ||
result = result .. string.format("| %s\n", ud_note(et, fifth, i)) | |||
end | end | ||
end | end | ||
| Line 159: | Line 170: | ||
if (i + 2) <= #additional_split then | if (i + 2) <= #additional_split then | ||
for j = 1, #additional_split[i + 2] do | for j = 1, #additional_split[i + 2] do | ||
result = result .. string.format("| %s\n", additional_split[i + 2][j]) | |||
end | end | ||
end | end | ||
end | end | ||
result = result .. "|}" | |||
return | if debugg == true then | ||
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>" | |||
end | |||
return frame:preprocess(result) | |||
end | end | ||
return p | return p | ||