Module:Infobox ET

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Infobox ET.

This module depends on the following other modules: Module: ET Module: Infobox Module: Limits Module: Rational Module: Utils

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')

-- towards is one of: -1 (floor), 0 (nearest), 1 (ceil)
local function approximate(size, equave, interval, towards)
	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
		approx = precomputed_approx
	end
	local tuning = size
	if not rat.eq(equave, 2) then
		tuning = tuning .. suffix
	end
	local ratio = rat.new(approx, size)
	if rat.as_table(ratio)[1] ~= approx then
		local link = rat.as_table(ratio)[2] .. suffix
		ratio = ' (→[[' .. link .. '|' .. rat.as_ratio(ratio, '\\')
		if not rat.eq(equave, 2) then
			ratio = ratio .. suffix
		end
		ratio = ratio .. ']])'
	else
		ratio = ''
	end
	local cents = i._to_cents(i._backslash_ratio(approx .. '\\' .. tuning), 6)
	return approx .. '\\' .. tuning .. ' (' .. cents .. '¢)' .. ratio
end

function p.infobox_ET(frame)
	local tuning = frame.args['tuning']
	local size, equave = i.parse_ET(tuning)
	local prime = ""
	if u.is_prime(size) then
		prime = " (prime)"
	end
	local suffix = tuning:match('%d+(ed.+)')
	
	local step_size = i._backslash_ratio('1\\' .. tuning)
	local fifth = approximate(size, equave, 3/2)
	local fifth_error = i._to_cents(i._backslash_ratio(fifth .. '\\' .. tuning)) - i._to_cents(3/2)
	local dual_fifth = math.abs(fifth_error) > i._to_cents(step_size) / 3

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

	local infobox_data = {}
	table.insert(infobox_data, {
		'Prime factorization',
		u._prime_factorization(size) .. prime
	})
	table.insert(infobox_data, {
		'Step size',
		i._to_cents(step_size, 6) .. '¢' .. note_12edo
	})
	table.insert(infobox_data, {
		'Fifth',
		approximation(suffix, size, equave, 3/2)
	})
	table.insert(infobox_data, {
		'Semitones (A1:m2)',
		A1 .. ':' .. m2 .. ' (' .. A1_cents .. '¢ : ' .. m2_cents .. '¢)'
	})
	if dual_fifth then
		table.insert(infobox_data, {
			'Sharp fifth',
			approximation(suffix, size, equave, 3/2, 1)
		})
		table.insert(infobox_data, {
			'Flat fifth',
			approximation(suffix, size, equave, 3/2, -1)
		})
		local sharp = approximate(size, equave, 3/2, 1)
		local flat = approximate(size, equave, 3/2, -1)
		table.insert(infobox_data, {
			'Major 2nd',
			approximation(suffix, size, equave, 9/8, 0, sharp + flat - octave)
		})
	end
	
	local consistency = tonumber(frame.args['Consistency'])
	-- 1. When an equave is too close to 1, large powers of this equave explode computations
	-- 2. When an equave has too many factors, the number of those factors explode computations
	-- 3. When an equave has too large factors, computations explode
	if rat.geq(equave, rat.new(3, 2)) and rat.is_prime_ratio(equave) and rat.max_prime(equave) <= 47 then
		if consistency == nil then
			consistency = l.consistency_limit(size, equave, false, 17)
		end
		if consistency == nil then
			consistency = 'at least 17'
		end
	end
	if consistency ~= nil then
		table.insert(infobox_data, {
			'Consistency limit',
			consistency
		})
	end
	local distinct_consistency = tonumber(frame.args['Distinct consistency'])
	if rat.geq(equave, rat.new(3, 2)) and rat.is_prime_ratio(equave) and rat.max_prime(equave) <= 47 then
		if distinct_consistency == nil then
			distinct_consistency = l.consistency_limit(size, equave, true, 29)
		end
		if distinct_consistency == nil then
			distinct_consistency = 'at least 29'
		end
	end
	if distinct_consistency ~= nil then
		table.insert(infobox_data, {
			'Distinct consistency limit',
			distinct_consistency
		})
	end

	local s = '<div style="\n' ..
		'border: 1px solid #999;\n' ..
		'margin: 0;\n' ..
		'margin-left: 1em;\n' ..
		'margin-bottom: 0.5em;\n' ..
		'padding: 0.5em;\n' ..
		'background-color: #f0f0f0;\n' ..
		'min-width: 15em;\n' ..
		'float: right;\n' ..
		'">\n' ..
		'{| width="100%" style="border-collapse: collapse;"\n' ..
		'|+ style="font-weight: bold" | ' .. frame.args['tuning'] .. '\n'
	for i, entry in ipairs(infobox_data) do
		local caption = entry[1]
		local text = entry[2]
		s = s .. '|-\n' ..
			'| style="text-align:right; padding-right: 0.25em" | ' .. caption .. '\n' ..
			'| style="background-color: white; padding-left: 0.25em; font-weight: bold" | ' .. text .. '\n'
	end
	s = s .. '|}</div>'
	return s
end

return p