Module:Infobox ET

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This module should not be invoked directly; use its corresponding template instead: Template:Infobox ET.

This module automatically fills in information about a specified equal temperament tuning.

Introspection summary for Module:Infobox ET
Functions provided (1) Line Function Params 43 infobox_ET (invokable) (frame)	Lua modules required (6) Variable Module Functions used ET Module:ET approximate cents parse is_zeta is_highly_composite why_zeta infobox Module:Infobox build i Module:Interval _to_cents l Module:Limits consistency_limit rat Module:Rational eq new converges as_float as_table as_ratio u Module:Utils _round is_prime _prime_factorization

No function descriptions were provided. The Lua code may have further information.

---

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
	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