Module:Infobox ET
Note: Do not invoke this module directly; use the corresponding template instead: Template:Infobox ET.
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This module depends on the following other modules: |
This module automatically fills in information about a specified equal temperament tuning.
local p = {}
local i = require('Module:Interval')
local u = require('Module:Utils')
local rat = require('Module:Rational')
local l = require('Module:Limits')
local ET = require('Module:ET')
local infobox = require('Module:Infobox')
-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximation(et, interval, towards, precomputed_approx)
local approx = precomputed_approx or ET.approximate(et, interval, towards or 0)
local tuning = et.size
if not rat.eq(et.equave, 2) then
tuning = tuning .. et.suffix
end
local ratio = rat.new(approx, et.size)
local convergement_notice = ''
local converges = rat.converges(ratio, math.log(interval) / math.log(rat.as_float(et.equave)))
if converges then
convergement_notice = '<br/>(' .. converges .. ')'
end
if rat.as_table(ratio)[1] ~= approx then
convergement_notice = ''
local link = rat.as_table(ratio)[2] .. et.suffix
ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
if not rat.eq(et.equave, 2) then
ratio = ratio .. et.suffix
end
ratio = ratio .. ']])'
else
ratio = ''
end
local cents = u._round(ET.cents(et, approx), 6)
return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio .. convergement_notice
end
function p.infobox_ET(frame)
-- debug mode will disable the categories
local debug_mode = frame.args['debug'] ~= nil
local categories = ''
local tuning = frame.args['tuning']
local et = ET.parse(tuning) or ET.parse('12edo')
-- category of the main article
categories = categories .. '[[Category:' .. tuning .. '| ]]'
-- category of the equal division
if rat.eq(et.equave, 2) then
categories = categories .. '[[Category:Equal divisions of the octave|' .. string.rep ('#', string.len (et.size)) .. ']]'
else
categories = categories .. '[[Category:' .. et.suffix .. '|' .. string.rep ('#', string.len (et.size)) .. ']]'
end
-- prime test
local prime = ""
if u.is_prime(et.size) then
prime = " (prime)"
if rat.eq(et.equave, 2) then
categories = categories .. '[[Category:Prime EDO|' .. string.rep ('#', string.len (et.size)) .. ']]'
end
end
-- zeta test
local zeta_override = frame.args['Zeta']
local zeta_switch = nil
if type(zeta_override) == 'string' and #zeta_override > 0 then
zeta_switch = not zeta_override:match('^[Nn][Oo]$')
else
zeta_switch = rat.eq(et.equave, 2) and ET.is_zeta(et)
end
local prev_one = ''
if et.size > 0 then
prev_one = '[[' .. (et.size - 1) .. et.suffix .. '|← ' .. (et.size - 1) .. et.suffix .. ']]'
end
local next_one = '[[' .. (et.size + 1) .. et.suffix .. '|' .. (et.size + 1) .. et.suffix .. ' →]]'
local step_size = ET.cents(et, 1)
local note_12edo = ''
if rat.eq(et.equave, 2) and et.size == 12 then
note_12edo = '<sup>by definition</sup>'
end
local octave = ET.approximate(et, 2)
local twelfth = ET.approximate(et, 3)
local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth_error = ET.cents(et, fifth) - i._to_cents(3/2)
local dual_fifth = math.abs(fifth_error) > step_size / 3
local A1 = -11 * octave + 7 * twelfth -- 2187/2048 = [-11 7>
local m2 = 8 * octave - 5 * twelfth -- 256/243 = [8 -5>
local A1_cents = u._round(ET.cents(et, A1), 4)
local m2_cents = u._round(ET.cents(et, m2), 4)
local infobox_data = {}
table.insert(infobox_data, {
'Prime factorization',
u._prime_factorization(et.size) .. prime
})
table.insert(infobox_data, {
'Step size',
u._round(step_size, 6) .. '¢' .. note_12edo
})
if not rat.eq(et.equave, 2) then
table.insert(infobox_data, {
'Octave',
approximation(et, 2)
})
end
if not rat.eq(et.equave, rat.new(3, 2)) then
table.insert(infobox_data, {
'Fifth',
approximation(et, 3/2)
})
end
table.insert(infobox_data, {
'Semitones (A1:m2)',
A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
})
if dual_fifth and et.size > 0 then
table.insert(infobox_data, {
'Dual sharp fifth',
approximation(et, 3/2, 1)
})
table.insert(infobox_data, {
'Dual flat fifth',
approximation(et, 3/2, -1)
})
local sharp = ET.approximate(et, 3/2, 1)
local flat = ET.approximate(et, 3/2, -1)
table.insert(infobox_data, {
'Dual major 2nd',
approximation(et, 9/8, 0, sharp + flat - octave)
})
end
local consistency = tonumber(frame.args['Consistency'])
if consistency == nil then
consistency = l.consistency_limit(et, false, 43)
end
if consistency == nil then
consistency = 'at least 43'
end
if consistency ~= nil then
table.insert(infobox_data, {
'Consistency limit',
consistency
})
end
local distinct_consistency = tonumber(frame.args['Distinct consistency'])
if distinct_consistency == nil then
distinct_consistency = l.consistency_limit(et, consistency or true, 43)
end
if distinct_consistency == nil then
distinct_consistency = 'at least 43'
end
if distinct_consistency ~= nil then
table.insert(infobox_data, {
'Distinct consistency limit',
distinct_consistency
})
end
-- special properties
if ET.is_highly_composite(et) or zeta_switch then
local text = ''
if ET.is_highly_composite(et) then
text = text .. '[[Highly composite equal division|highly composite]]'
if rat.eq(et.equave, 2) then
categories = categories .. '[[Category:Highly composite EDO|' .. string.rep ('#', string.len (et.size)) .. ']]'
end
end
if zeta_switch then
if #text > 0 then text = text .. '<br>' end
if not (type(zeta_override) == 'string' and #zeta_override > 0) then
text = text .. ET.why_zeta(et)
else
text = text .. zeta_override
end
categories = categories .. '[[Category:Zeta|' .. string.rep ('#', string.len (et.size)) .. ']]'
end
table.insert(infobox_data, {
'Special properties',
'<div style="max-width: 270px;">' .. text .. '</div>'
})
end
result = infobox.build(
'[[' .. et.suffix .. '|' .. tuning .. ']]',
infobox_data,
prev_one,
next_one
)
if not debug_mode then
result = result .. categories
end
return result
end
return p