local p = {}
local u = require('Module:Utils')
local iv = require('Module:Interval')
local rat = require('Module:Rational')
local ud = require('Module:Ups and downs notation')
local ET = require('Module:ET')
-- Auto-generated list of ratios in 17-limit and with <2 digits
local ratios_list = {{1,1},{2,1},{3,1},{4,1},{3,2},{5,1},{5,2},{5,4},{6,1},{7,2},{7,4},{9,2},{9,4},{9,8},{11,4},{13,4},{15,4},{17,8},{21,8},{25,8},{17,4},{27,8},{33,8},{35,8},{39,8},{11,2},{21,4},{45,8},{65,16},{75,16},{11,8},{13,8},{15,8},{17,16},{21,16},{25,16},{27,16},{33,32},{35,32},{39,32},{56,51},{68,49},{56,45},{68,39},{33,16},{35,16},{39,16},{45,16},{65,32},{75,32},{77,32},{81,32},{65,33},{85,32},{96,35},{98,33},{85,77},{49,16},{26,25},{51,16},{51,25},{55,16},{63,16},{77,50},{99,32},{26,21},{81,65},{68,21},{77,16},{63,55},{52,35},{22,17},{39,17},{56,17},{90,17},{64,33},{81,16},{85,16},{91,16},{26,15},{56,15},{84,55},{40,27},{45,32},{49,32},{16,13},{45,26},{42,13},{51,32},{55,13},{55,32},{27,25},{52,25},{68,13},{77,25},{77,52},{78,35},{51,44},{21,11},{32,11},{75,22},{54,11},{65,11},{91,88},{96,65},{52,21},{77,39},{11,9},{20,9},{49,18},{85,18},{27,17},{44,17},{91,68},{78,17},{28,25},{81,50},{78,25},{91,66},{65,49},{78,77},{22,15},{52,15},{85,81},{91,32},{17,14},{12,7},{45,14},{26,7},{33,7},{40,7},{55,28},{75,56},{80,27},{63,52},{32,13},{45,13},{51,26},{77,26},{77,45},{91,51},{54,25},{54,49},{51,35},{77,68},{32,17},{49,17},{66,17},{81,34},{88,45},{20,11},{51,22},{42,11},{91,44},{64,11},{65,54},{6,5},{11,5},{16,5},{17,10},{21,5},{26,5},{27,10},{39,20},{49,20},{63,40},{91,40},{99,20},{85,66},{55,51},{13,9},{22,9},{35,18},{40,9},{49,9},{77,72},{68,35},{22,13},{35,13},{48,13},{75,52},{20,17},{91,34},{54,17},{88,17},{25,21},{88,21},{56,25},{81,25},{91,33},{81,49},{65,51},{56,39},{32,27},{91,54},{77,65},{51,49},{44,15},{98,85},{27,22},{49,22},{30,11},{65,44},{52,11},{63,11},{70,51},{32,25},{85,39},{10,7},{17,7},{24,7},{27,14},{33,28},{55,14},{75,28},{98,45},{25,17},{42,17},{52,27},{77,54},{56,33},{96,85},{25,13},{63,26},{51,13},{64,13},{77,13},{64,45},{80,51},{33,25},{91,50},{7,6},{5,3},{8,3},{11,3},{13,6},{14,3},{17,3},{17,12},{25,6},{25,24},{35,12},{49,24},{55,24},{65,12},{65,48},{77,48},{85,24},{91,24},{99,70},{78,49},{30,17},{77,34},{64,17},{81,17},{98,17},{55,39},{34,25},{84,25},{25,22},{18,11},{40,11},{51,11},{91,22},{65,27},{81,70},{52,45},{55,48},{63,32},{40,21},{56,55},{65,64},{75,64},{77,64},{81,64},{15,13},{28,13},{85,64},{54,13},{99,52},{80,77},{7,5},{12,5},{17,5},{22,5},{27,5},{33,20},{39,10},{49,10},{51,40},{63,20},{81,40},{99,80},{85,27},{18,17},{35,17},{52,17},{88,63},{98,55},{52,33},{85,33},{8,7},{15,7},{22,7},{39,28},{36,7},{51,14},{65,14},{81,28},{85,56},{99,56},{64,39},{64,55},{36,25},{25,18},{17,9},{26,9},{35,9},{44,9},{77,36},{88,85},{91,72},{75,49},{64,51},{17,11},{28,11},{39,11},{45,22},{50,11},{66,35},{18,13},{49,26},{44,13},{75,26},{70,13},{85,52},{17,15},{32,15},{49,30},{96,77},{77,15},{75,68},{63,34},{40,17},{91,17},{50,21},{99,50},{44,27},{98,27},{50,33},{44,39},{64,49},{72,55},{88,75},{48,35},{49,33},{64,27},{51,50},{81,77},{63,25},{88,25},{91,27},{34,21},{55,21},{28,17},{39,34},{45,17},{96,17},{28,15},{88,15},{21,13},{34,13},{55,26},{60,13},{81,26},{39,35},{16,11},{27,11},{65,22},{49,11},{60,11},{75,44},{91,75},{72,49},{10,9},{49,36},{28,9},{65,18},{85,36},{39,25},{64,25},{72,65},{45,28},{13,7},{20,7},{27,7},{33,14},{34,7},{75,14},{80,33},{88,65},{81,68},{33,17},{49,34},{50,17},{84,17},{50,27},{77,27},{11,10},{8,5},{13,5},{18,5},{21,10},{27,20},{28,5},{49,40},{51,10},{77,20},{81,80},{85,63},{80,49},{35,26},{24,13},{50,13},{63,13},{44,21},{65,21},{70,27},{50,49},{99,49},{15,11},{26,11},{49,44},{48,11},{63,22},{85,22},{66,25},{85,78},{91,25},{49,45},{21,17},{55,17},{72,17},{99,91},{96,55},{49,48},{4,3},{7,3},{10,3},{11,6},{13,3},{13,12},{16,3},{17,6},{25,12},{35,6},{35,24},{49,12},{65,24},{77,24},{85,48},{88,49},{91,48},{55,12},{42,25},{68,63},{64,35},{99,35},{90,77},{14,13},{27,13},{40,13},{77,75},{66,13},{85,54},{56,27},{35,34},{26,17},{60,17},{77,17},{15,14},{11,7},{18,7},{25,7},{32,7},{39,7},{51,28},{65,28},{81,56},{68,25},{14,11},{25,11},{36,11},{39,22},{45,44},{16,15},{77,30},{96,49},{49,27},{81,35},{88,51},{91,55},{99,85},{66,49},{63,50},{44,25},{55,42},{80,21},{45,34},{48,17},{65,17},{99,17},{17,13},{30,13},{55,52},{56,13},{81,52},{72,35},{99,26},{85,49},{14,9},{55,18},{32,9},{65,36},{50,9},{85,72},{91,18},{96,91},{78,55},{98,51},{40,33},{80,39},{55,49},{13,10},{9,5},{14,5},{21,20},{24,5},{33,10},{51,20},{77,40},{52,51},{81,20},{91,20},{91,80},{99,40},{22,21},{65,42},{64,21},{85,21},{35,27},{68,65},{99,98},{13,11},{24,11},{35,11},{63,44},{81,22},{85,44},{70,39},{36,17},{55,34},{70,17},{98,81},{54,35},{84,65},{91,81},{96,25},{27,26},{20,13},{33,13},{72,13},{28,27},{55,27},{9,7},{16,7},{25,14},{30,7},{39,14},{65,56},{81,14},{85,28},{99,28},{77,60},{91,30},{68,15},{50,39},{65,63},{70,33},{72,25},{24,17},{65,34},{99,34},{75,17},{36,35},{55,36},{16,9},{25,9},{34,9},{77,18},{52,9},{91,36},{91,85},{40,39},{52,49},{77,51},{32,21},{85,42},{91,64},{99,64},{99,65},{12,11},{35,22},{34,11},{45,11},{56,11},{81,44},{91,45},{48,25},{80,63},{98,25},{33,26},{36,13},{49,13},{85,26},{75,13},{55,54},{68,27},{81,55},{91,60},{34,15},{49,15},{64,15},{64,63},{66,65},{35,33},{68,33},{90,49},{99,68},{75,34},{63,17},{80,17},{88,35},{98,39},{85,84},{91,90},{68,45},{60,49},{49,25},{99,25},{34,27},{68,55},{88,27},{34,33},{98,65},{44,35},{98,75},{49,39},{88,39},{88,81}}
local function gcd(a, b)
return b==0 and a or gcd(b,a%b)
end
local function table_contains(tbl, x)
found = false
for _, v in pairs(tbl) do
if v == x then
found = true
end
end
return found
end
-- Utility fuunction to get specific note name with ud.get_note_names_table
-- (this is essentially what "Template:Ups and downs note name" does)
local function ud_note(et, fifth, step)
return table.concat(ud.get_note_names_table(et, fifth)[step], ", "):sub(0, -1)
end
function p.interval_table(frame)
local tuning = frame.args['tuning']
local et = ET.parse(tuning) or ET.parse('12edo')
local wikitext = '{|class="wikitable"\n'
local octave = ET.approximate(et, 2)
local fifth = ET.approximate(et, 3/2)
local fifth_error = ET.cents(et, fifth) - iv._to_cents(3/2)
local dual_fifth = math.abs(fifth_error) > (400 / et.size)
local dual_flat_fifth = ET.approximate(et, 3/2, -1)
local dual_sharp_fifth = ET.approximate(et, 3/2, 1)
wikitext = wikitext .. '!Steps\n'
wikitext = wikitext .. '!Cents\n'
if rat.eq(et.equave, 2) then
if dual_fifth then
wikitext = wikitext .. '![[Ups and downs notation]]<br>(dual flat fifth ' .. dual_flat_fifth .. '\\' .. et.size .. ')\n'
wikitext = wikitext .. '![[Ups and downs notation]]<br>(dual sharp fifth ' .. dual_sharp_fifth .. '\\' .. et.size .. ')\n'
else
wikitext = wikitext .. '![[Ups and downs notation]]\n'
end
end
wikitext = wikitext .. '!Approximate ratios\n'
for i=0,et.size do
wikitext = wikitext .. '|-\n'
wikitext = wikitext .. '|' .. i .. '\n'
wikitext = wikitext .. '|' .. u._round(ET.cents(et, i), 6) .. '\n'
if rat.eq(et.equave, 2) then
if dual_fifth then
wikitext = wikitext .. '|' .. ud_note(et, dual_flat_fifth, i) .. '\n'
wikitext = wikitext .. '|' .. ud_note(et, dual_sharp_fifth, i) .. '\n'
else
wikitext = wikitext .. '|' .. ud_note(et, fifth, i) .. '\n'
end
end
wikitext = wikitext .. '|'
for j=1,#ratios_list do
local n = ratios_list[j][1]
local d = ratios_list[j][2]
-- In approximate ratios column, show all ratios in the list that are within 1/3 of ET size (33.3 relative cents)
if math.abs(ET.cents(et, i) - (math.log(n/d)/math.log(2)) * 1200) <= (400 / et.size) then
wikitext = wikitext .. '[[' .. n .. '/' .. d .. ']]' .. ' '
end
end
wikitext = wikitext .. '\n'
end
wikitext = wikitext .. '|}'
return wikitext
end
return p
.svg){kind=icon}