Xenharmonic Wiki

Module:Infobox ET: Difference between revisions

← Older editNewer edit →
Plumtree (talk | contribs)
autopatrolled, emailconfirmed
1,976 edits
mNo edit summary
Plumtree (talk | contribs)
autopatrolled, emailconfirmed
1,976 edits
Refactoring
Line 4: Line 4:
local rat = require('Module:Rational')
local rat = require('Module:Rational')
local l = require('Module:Limits')
local l = require('Module:Limits')
local ET = require('Module:ET')


-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximate(size, equave, interval, towards)
local function approximation(et, interval, towards, precomputed_approx)
if size == 0 then
local approx = ET.approximate(et, interval, towards or 0)
return 0
end
towards = towards or 0
local exact = math.log(interval) / math.log(rat.as_float(equave)) * size
local approx = nil
if towards < 0 then
approx = math.floor(exact)
elseif towards > 0 then
approx = math.ceil(exact)
else
approx = math.floor(exact + 0.5)
end
return approx
end
 
-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximation(suffix, size, equave, interval, towards, precomputed_approx)
local approx = approximate(size, equave, interval, towards or 0)
if precomputed_approx then
if precomputed_approx then
approx = precomputed_approx
approx = precomputed_approx
end
end
local tuning = size
local tuning = et.size
if not rat.eq(equave, 2) then
if not rat.eq(et.equave, 2) then
tuning = tuning .. suffix
tuning = tuning .. et.suffix
end
end
local ratio = rat.new(approx, size)
local ratio = rat.new(approx, et.size)
if rat.as_table(ratio)[1] ~= approx then
if rat.as_table(ratio)[1] ~= approx then
local link = rat.as_table(ratio)[2] .. suffix
local link = rat.as_table(ratio)[2] .. et.suffix
ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
if not rat.eq(equave, 2) then
if not rat.eq(et.equave, 2) then
ratio = ratio .. suffix
ratio = ratio .. et.suffix
end
end
ratio = ratio .. ']])'
ratio = ratio .. ']])'
Line 44: Line 27:
ratio = ''
ratio = ''
end
end
local cents = i._to_cents(i._backslash_ratio(approx .. '\\' .. tuning), 6)
local cents = u._round(ET.cents(et, approx), 6)
return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio
return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio
end
end
Line 50: Line 33:
function p.infobox_ET(frame)
function p.infobox_ET(frame)
local tuning = frame.args['tuning']
local tuning = frame.args['tuning']
local size, equave = i.parse_ET(tuning)
local et = ET.parse(tuning) or ET.parse('12edo')
local prime = ""
local prime = ""
if u.is_prime(size) then
if u.is_prime(et.size) then
prime = " (prime)"
prime = " (prime)"
end
end
local suffix = tuning:match('%d+(ed.+)')
local prev_one = ''
local prev_one = ''
if size > 0 then
if et.size > 0 then
prev_one = '[[' .. (size - 1) .. suffix .. '|← ' .. (size - 1) .. suffix .. ']]'
prev_one = '[[' .. (et.size - 1) .. et.suffix .. '|← ' .. (et.size - 1) .. et.suffix .. ']]'
end
end
local next_one = '[[' .. (size + 1) .. suffix .. '|' .. (size + 1) .. suffix .. ' →]]'
local next_one = '[[' .. (et.size + 1) .. et.suffix .. '|' .. (et.size + 1) .. et.suffix .. ' →]]'
local step_size = i._backslash_ratio('1\\' .. tuning)
local step_size = ET.cents(et, 1)
local fifth = approximate(size, equave, 3/2)
local fifth = ET.approximate(et, 3/2)
local fifth_error = i._to_cents(i._backslash_ratio(fifth .. '\\' .. tuning)) - i._to_cents(3/2)
local fifth_error = ET.cents(et, fifth) - i._to_cents(3/2)
local dual_fifth = math.abs(fifth_error) > i._to_cents(step_size) / 3
local dual_fifth = math.abs(fifth_error) > step_size / 3


local note_12edo = ''
local note_12edo = ''
if rat.eq(equave, 2) and size == 12 then
if rat.eq(et.equave, 2) and et.size == 12 then
note_12edo = '<sup>by definition</sup>'
note_12edo = '<sup>by definition</sup>'
end
end
local octave = approximate(size, equave, 2)
local octave = ET.approximate(et, 2)
local A1 = 7 * fifth - 4 * octave
local A1 = 7 * fifth - 4 * octave
local m2 = 3 * octave - 5 * fifth
local m2 = 3 * octave - 5 * fifth
local A1_cents = i._to_cents(i._backslash_ratio(A1 .. '\\' .. tuning), 4)
local A1_cents = u._round(ET.cents(et, A1), 4)
local m2_cents = i._to_cents(i._backslash_ratio(m2 .. '\\' .. tuning), 4)
local m2_cents = u._round(ET.cents(et, m2), 4)


local infobox_data = {}
local infobox_data = {}
table.insert(infobox_data, {
table.insert(infobox_data, {
'Prime factorization',
'Prime factorization',
u._prime_factorization(size) .. prime
u._prime_factorization(et.size) .. prime
})
})
table.insert(infobox_data, {
table.insert(infobox_data, {
'Step size',
'Step size',
i._to_cents(step_size, 6) .. '¢' .. note_12edo
u._round(step_size, 6) .. '¢' .. note_12edo
})
})
if not rat.eq(equave, rat.new(3, 2)) then
if not rat.eq(et.equave, rat.new(3, 2)) then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Fifth',
'Fifth',
approximation(suffix, size, equave, 3/2)
approximation(et, 3/2)
})
})
end
end
if not rat.eq(equave, 2) then
if not rat.eq(et.equave, 2) then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Octave',
'Octave',
approximation(suffix, size, equave, 2)
approximation(et, 2)
})
})
end
end
Line 104: Line 86:
A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
})
})
if dual_fifth and size > 0 then
if dual_fifth and et.size > 0 then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Sharp fifth',
'Sharp fifth',
approximation(suffix, size, equave, 3/2, 1)
approximation(et, 3/2, 1)
})
})
table.insert(infobox_data, {
table.insert(infobox_data, {
'Flat fifth',
'Flat fifth',
approximation(suffix, size, equave, 3/2, -1)
approximation(et, 3/2, -1)
})
})
local sharp = approximate(size, equave, 3/2, 1)
local sharp = ET.approximate(et, 3/2, 1)
local flat = approximate(size, equave, 3/2, -1)
local flat = ET.approximate(et, 3/2, -1)
table.insert(infobox_data, {
table.insert(infobox_data, {
'Major 2nd',
'Major 2nd',
approximation(suffix, size, equave, 9/8, 0, sharp + flat - octave)
approximation(et, 9/8, 0, sharp + flat - octave)
})
})
end
end
Line 123: Line 105:
local consistency = tonumber(frame.args['Consistency'])
local consistency = tonumber(frame.args['Consistency'])
if consistency == nil then
if consistency == nil then
consistency = l.consistency_limit(size, equave, false, 43)
consistency = l.consistency_limit(et.size, et.equave, false, 43)
end
end
if consistency == nil then
if consistency == nil then
Line 136: Line 118:
local distinct_consistency = tonumber(frame.args['Distinct consistency'])
local distinct_consistency = tonumber(frame.args['Distinct consistency'])
if distinct_consistency == nil then
if distinct_consistency == nil then
distinct_consistency = l.consistency_limit(size, equave, true, 43)
distinct_consistency = l.consistency_limit(et.size, et.equave, true, 43)
end
end
if distinct_consistency == nil then
if distinct_consistency == nil then
Line 153: Line 135:
.. '</td>'
.. '</td>'
.. '<td style="width: 70%; padding-left: 1em; padding-right: 1em; text-align: center">'
.. '<td style="width: 70%; padding-left: 1em; padding-right: 1em; text-align: center">'
.. frame.args['tuning']
.. tuning
.. '</td>'
.. '</td>'
.. '<td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">'
.. '<td style="width: 15%; text-align: right; white-space: nowrap; font-size: smaller">'
Retrieved from "https://en.xen.wiki/w/Module:Infobox_ET"