Module:Infobox ET: Difference between revisions

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@@ Line 4: / Line 4: @@
 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(tuning, size, equave, interval, towards)
+	local approx = approximate(size, equave, interval, towards or 0)
+	local ratio = rat.new(approx, size)
+	if rat.as_table(ratio)[1] ~= approx then
+		ratio = ' (→' .. rat.as_ratio(ratio, '\\') .. ')'
+	else
+		ratio = ''
+	end
+	return string.format("%d", approx) .. '\\' .. tuning
+		.. ' (' .. i._to_cents(i._backslash_ratio(approx .. '\\' .. tuning), 6) .. '¢)'
+		.. ratio
+end
 function p.infobox_ET(frame)
@@ Line 16: / Line 45: @@
 	end
 	local step_size = i._backslash_ratio('1\\' .. tuning)
-	local fifth = math.floor(math.log(1.5)/math.log(rat.as_float(equave))*size+0.5)
-	local fifth_ratio = rat.new(fifth, size)
-	if rat.as_table(fifth_ratio)[1] ~= fifth then
-		fifth_ratio = ' (→' .. rat.as_ratio(fifth_ratio, '\\') .. ')'
-	else
-		fifth_ratio = ''
-	end
 	local infobox_data = {}
@@ Line 35: / Line 57: @@
 	table.insert(infobox_data, {
 		'Fifth',
-		string.format("%d", fifth) .. '\\' .. tuning .. ' (' .. i._to_cents(i._backslash_ratio(fifth .. '\\' .. tuning), 6) .. '¢)' .. fifth_ratio
+		approximation(tuning, size, equave, 3/2)
 	})
 	table.insert(infobox_data, {