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Module:Infobox ET: Difference between revisions

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Only show the fifth and the semitones when the equave is the octave; otherwise show the twelfth cuz there's no octave reduction
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local p = {}
local p = {}
local i = require('Module:Interval')
 
local u = require('Module:Utils')
local ET = require("Module:ET")
local rat = require('Module:Rational')
local getArgs = require("Module:Arguments").getArgs
local l = require('Module:Limits')
local infobox = require("Module:Infobox")
local ET = require('Module:ET')
local limits = require("Module:Limits")
local infobox = require('Module:Infobox')
local rat = require("Module:Rational")
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")


-- check whether the input is a non-empty string
-- check whether the input is a non-empty string
local function value_provided(s)
local function value_provided(s)
return type(s) == 'string' and #s > 0
return type(s) == "string" and #s > 0
end
end


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local function approximation(et, interval, towards, precomputed_approx)
local function approximation(et, interval, towards, precomputed_approx)
local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)
local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)
 
-- string for backslash notation
-- "edo" is omitted
local tuning = et.size
local tuning = et.size
if not rat.eq(et.equave, 2) then
if not rat.eq(et.equave, 2) then
tuning = tuning .. et.suffix
tuning = tuning .. et.suffix
end
end
 
local ratio = rat.new(approx, et.size)
local ratio = rat.new(approx, et.size)
 
local convergement_notice = ''
-- convergence notice, suppressed for 1ed's
local convergement_notice = ""
local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
if converges then
if et.size > 1 and converges then
convergement_notice = '<br/>(' .. converges .. ')'
convergement_notice = "<br>(" .. converges .. ")"
end
end
 
if rat.as_table(ratio)[1] ~= approx then
if rat.as_table(ratio)[1] ~= approx then
convergement_notice = ''
convergement_notice = ""
local link = rat.as_table(ratio)[2] .. et.suffix
local link = rat.as_table(ratio)[2] .. et.suffix
ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
ratio = string.format(" (&rarr;&nbsp;[[%s|%s%s]])",
if not rat.eq(et.equave, 2) then
link, rat.as_ratio(ratio, "\\"), (rat.eq(et.equave, 2) == false and et.suffix or ""))
ratio = ratio .. et.suffix
end
ratio = ratio .. ']])'
else
else
ratio = ''
ratio = ""
end
end
 
local cents = u._round(ET.cents(et, approx), 6)
local cents = utils._round(ET.cents(et, approx), 6)
 
return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio .. convergement_notice
return string.format("%s\\%s (%s{{c}})%s%s",
approx, tuning, utils._round(ET.cents(et, approx), 6), ratio, convergement_notice)
end
end


function p.infobox_ET(frame)
function p.infobox_ET(frame)
local args = getArgs(frame)
-- debug mode will disable the categories
-- debug mode will disable the categories
local debug_mode = frame.args['debug']
local debug_mode = yesno(frame.args["debug"] or args["debug"], false)
local categories = ''
local wtext = yesno(frame.args["wtext"] or args["wtext"])
 
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(tuning .. "edo") or ET.parse("12edo")
 
-- category of the main article
-- category of the main article
categories = categories .. '[[Category:' .. tuning .. '| ]]'
local categories = string.format(" {{#ifexist: Category:%s|[[Category:%s| ]]|}}", tuning, tuning)
-- category of the equal division
-- category of the equal division
if rat.eq(et.equave, 2) then
if rat.eq(et.equave, 2) then
categories = categories .. '[[Category:Equal divisions of the octave|' .. string.rep ('#', string.len (et.size)) .. ']]'
categories = categories
.. string.format(" [[Category:Equal divisions of the octave|%s]]",
string.rep("#", string.len(et.size)))
elseif rat.eq(et.equave, 3) then
categories = categories .. string.format(" [[Category:Edts|%s]]",
string.rep("#", string.len(et.size)))
elseif rat.eq(et.equave, rat.new (3, 2)) then
categories = categories .. string.format(" [[Category:Edfs|%s]]",
string.rep("#", string.len(et.size)))
else
else
categories = categories .. '[[Category:' .. et.suffix .. '|' .. string.rep ('#', string.len (et.size)) .. ']]'
categories = categories .. string.format(" [[Category:%s's|%s]]",
et.suffix, string.rep("#", string.len(et.size)))
end
end
 
-- prime test
-- prime factorization
local prime = ""
local prime_factorization_override = frame.args["Prime factorization"]
if u.is_prime(et.size) then
local prime_factorization
prime = " (prime)"
if not value_provided(prime_factorization_override) then
if rat.eq(et.equave, 2) then
prime_factorization = utils._prime_factorization(et.size)
categories = categories .. '[[Category:Prime EDO|' .. string.rep ('#', string.len (et.size)) .. ']]'
if utils.is_prime(et.size) then
prime_factorization = prime_factorization .. " (prime)"
if rat.eq(et.equave, 2) then
categories = categories  
.. string.format(" [[Category:Prime EDOs|%s]]",
string.rep("#", string.len(et.size)))
end
end
if ET.is_highly_composite(et) and et.size > 1 then
prime_factorization = prime_factorization .. " (highly composite)"
if rat.eq(et.equave, 2) then
categories = categories
.. string.format(" [[Category:Highly composite EDOs|%s]]",
string.rep("#", string.len(et.size)))
end
end
end
else
prime_factorization = prime_factorization_override
end
end
 
-- zeta test
-- zeta test
local zeta_override = frame.args['Zeta']
local zeta_override = frame.args["Zeta"]
local zeta_switch = nil
local zeta_switch
if value_provided(zeta_override) then
if value_provided(zeta_override) then
zeta_switch = not zeta_override:match('^[Nn][Oo]$')
zeta_switch = zeta_override:match("^[Yy][Ee][Ss]$") and ET.is_zeta(et)
else
else
zeta_switch = rat.eq(et.equave, 2) and ET.is_zeta(et)
zeta_switch = false
end
end
 
-- navigation arrows
-- navigation arrows
local increment = 1
local increment = 1
if rat.eq(et.equave, 9/4) or rat.eq(et.equave, 4) or rat.eq(et.equave, 9) then
if rat.eq(et.equave, rat.new(9, 4)) or rat.eq(et.equave, 4) or rat.eq(et.equave, 9) then
increment = 2
increment = 2
end
end
local prev_one = ''
local prev_one = ""
if et.size >= increment then
if et.size >= increment then
prev_one = '[[' .. (et.size - increment) .. et.suffix .. '|← ' .. (et.size - increment) .. et.suffix .. ']]'
prev_one = string.format("[[%s|&larr;&nbsp;%s]]",
(et.size - increment) .. et.suffix, (et.size - increment) .. et.suffix)
end
end
local next_one = '[[' .. (et.size + increment) .. et.suffix .. '|' .. (et.size + increment) .. et.suffix .. ' →]]'
local next_one = string.format("[[%s|%s&nbsp;&rarr;]]",
(et.size + increment) .. et.suffix, (et.size + increment) .. et.suffix)


-- step size
-- step size in cents
local step_size = ET.cents(et, 1)
local step_size = ET.cents(et, 1)
local note_12edo = ''
if step_size > 100 then
categories = categories .. string.format(" [[Category:Macrotonal|%s]]",
string.rep("#", string.len(et.size)))
end
local note_12edo = ""
if rat.eq(et.equave, 2) and et.size == 12 then
if rat.eq(et.equave, 2) and et.size == 12 then
note_12edo = '<sup>by definition</sup>'
note_12edo = " (by&nbsp;definition)"
end
end


-- octave, twelfth, and fifth sizes
-- octave, twelfth, and fifth in steps
local octave = ET.approximate(et, 2)
local octave = ET.approximate(et, 2)
local twelfth = ET.approximate(et, 3)
local twelfth = ET.approximate(et, 3)
 
local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth_error = ET.cents(et, fifth) - i._to_cents(3/2)
local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
local dual_fifth = math.abs(fifth_error) > step_size / 3
local is_dual_fifth = math.abs(fifth_error) > step_size / 3


local A1 = -11 * octave + 7 * twelfth -- 2187/2048 = [-11 7>
local A1 = -11 * octave + 7 * twelfth -- 2187/2048 = [-11 7>
local m2 = 8 * octave - 5 * twelfth -- 256/243 = [8 -5>
local m2 = 8 * octave - 5 * twelfth -- 256/243 = [8 -5>
local A1_cents = u._round(ET.cents(et, A1), 4)
local A1_cents = utils._round(ET.cents(et, A1), 4)
local m2_cents = u._round(ET.cents(et, m2), 4)
local m2_cents = utils._round(ET.cents(et, m2), 4)


-- display
-- display
local infobox_data = {}
local infobox_data = {}
table.insert(infobox_data, {
table.insert(infobox_data, {
'Prime factorization',
"Prime factorization",
u._prime_factorization(et.size) .. prime
prime_factorization,
})
})


table.insert(infobox_data, {
table.insert(infobox_data, {
'Step size',
"Step size",
u._round(step_size, 6) .. '¢' .. note_12edo
string.format("%s{{c}}%s&nbsp;",
utils._round(step_size, 6), note_12edo)
})
})


if not rat.eq(et.equave, 2) then
if not rat.eq(et.equave, 2) then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Octave',
"Octave",
approximation(et, 2)
approximation(et, 2),
})
})
if not rat.eq(et.equave, 3) then
if not rat.eq(et.equave, 3) then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Twelfth',
"Twelfth",
approximation(et, 3)
approximation(et, 3),
})
})
end
end
else
else
table.insert(infobox_data, {
table.insert(infobox_data, {
'Fifth',
"Fifth",
approximation(et, 3/2)
approximation(et, 3 / 2),
})
})
table.insert(infobox_data, {
table.insert(infobox_data, {
'Semitones (A1:m2)',
"Semitones (A1:m2)",
A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
string.format("%s:%s (%s{{c}}&nbsp;:&nbsp;%s{{c}})",
A1, m2, A1_cents, m2_cents)
})
})
if dual_fifth and et.size > 0 then
if is_dual_fifth and et.size > 0 then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Dual sharp fifth',
"Dual sharp fifth",
approximation(et, 3/2, 1)
approximation(et, 3 / 2, 1),
})
})
table.insert(infobox_data, {
table.insert(infobox_data, {
'Dual flat fifth',
"Dual flat fifth",
approximation(et, 3/2, -1)
approximation(et, 3 / 2, -1),
})
})
local sharp = ET.approximate(et, 3/2, 1)
local sharp = ET.approximate(et, 3 / 2, 1)
local flat = ET.approximate(et, 3/2, -1)
local flat = ET.approximate(et, 3 / 2, -1)
table.insert(infobox_data, {
table.insert(infobox_data, {
'Dual major 2nd',
"Dual major 2nd",
approximation(et, 9/8, 0, sharp + flat - octave)
approximation(et, 9 / 8, 0, sharp + flat - octave),
})
})
categories = categories
.. string.format(" [[Category:Dual-fifth temperaments|%s]]",
string.rep("#", string.len(et.size)))
end
end
end
end


local consistency = tonumber(frame.args['Consistency'])
-- consistency and distinct consistency
-- max_limit is used to prevent timeout
local consistency = tonumber(frame.args["Consistency"])
local max_limit = rat.eq(et.equave, 2) and 43 or 32
if consistency == nil then
if consistency == nil then
consistency = l.consistency_limit(et, false, 43)
consistency = limits.consistency_limit(et, false, max_limit)
end
end
if consistency == nil then
if consistency == nil then
consistency = 'at least 43'
consistency = "at least " .. max_limit
end
end
if consistency ~= nil then
if consistency ~= nil then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Consistency limit',
"Consistency limit",
consistency
consistency,
})
})
end
end
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(et, consistency or true, 43)
distinct_consistency = limits.consistency_limit(et, consistency or true, max_limit)
end
end
if distinct_consistency == nil then
if distinct_consistency == nil then
distinct_consistency = 'at least 43'
distinct_consistency = "at least " .. max_limit
end
end
if distinct_consistency ~= nil then
if distinct_consistency ~= nil then
table.insert(infobox_data, {
table.insert(infobox_data, {
'Distinct consistency limit',
"Distinct consistency limit",
distinct_consistency
distinct_consistency,
})
})
end
end


-- special properties
-- special properties
if ET.is_highly_composite(et) or zeta_switch then
if ET.is_zeta(et) then
local text = ''
local text = ""
if ET.is_highly_composite(et) then
if rat.eq(et.equave, 2) then
text = text .. '[[Highly composite equal division|highly composite]]'
categories = categories
if rat.eq(et.equave, 2) then
.. string.format(" [[Category:Zeta record EDOs|%s]]",
categories = categories .. '[[Category:Highly composite EDO|' .. string.rep ('#', string.len (et.size)) .. ']]'
string.rep("#", string.len(et.size)))
end
if zeta_switch then
end
if zeta_switch then
if #text > 0 then text = text .. '<br>' end
if not value_provided(zeta_override) then
text = text .. ET.why_zeta(et)
text = text .. ET.why_zeta(et)
else
text = text .. zeta_override
end
end
categories = categories .. '[[Category:Zeta|' .. string.rep ('#', string.len (et.size)) .. ']]'
end
if #text > 0 then
table.insert(infobox_data, {
"Special properties",
"<div style=\"max-width: 300px;\">" .. text .. "</div>",
})
end
end
table.insert(infobox_data, {
'Special properties',
'<div style="max-width: 270px;">' .. text .. '</div>'
})
end
end


result = infobox.build(
local result = infobox.build(string.format("[[%s|%s]]", et.suffix, tuning), infobox_data, prev_one, next_one)
'[[' .. et.suffix .. '|' .. tuning .. ']]',
infobox_data,
if not debug_mode then
prev_one,
next_one
)
if not value_provided(debug_mode) then
result = result .. categories
result = result .. categories
end
end
return result
if wtext 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:Infobox_ET"