Module:Chord consistency: Difference between revisions

← Older edit

@@ Line 1: / Line 1: @@
+local ET = require('Module:ET')
 local rat = require('Module:Rational')
 local utils = require("Module:Utils")
-local ET = require('Module:ET')
 local p = {}
@@ Line 83: / Line 83: @@
 	end
 	return true
+end
+-- determine maximum error
+function p.max_error(et, ratios)
+	local maxe = 0.0
+	for a_key, a in pairs(ratios) do
+		local a_approx = ET.approximate(et, rat.as_float(a))
+		local e = math.abs((ET.cents(et, a_approx) - rat.cents(a)) / ET.cents(et, 1))
+		if (e > maxe) then
+			maxe = e
+		end
+	end
+	return maxe
+end
+function p.consistent_edos(harmonics, distance, ed, maxlen)
+	distance = distance or 1.0
+	ed = ed or 'edo'
+	local max_n = 72
+	maxlen = maxlen or max_n
+	if max_n < maxlen then max_n = maxlen end
+	local all_interval = {}
+	for i, h in ipairs(harmonics) do
+		-- compute all ratio
+		for j, g in ipairs(harmonics) do
+			if j > i then
+				local a = rat.new(g, h)
+				all_interval[rat.as_ratio(a)] = a
+			end
+		end
+	end
+	local vals = {}
+	for i = 1, max_n do
+		local et = ET.parse('' .. i .. ed)
+		local consistent = p.additively_consistent_int(et, all_interval, false, nil)
+		if consistent then
+			local maxe = p.max_error(et, all_interval)
+			if maxe <= 5.0e-11 then
+				table.insert(vals, "[[" .. i .. ed .. "]]" .. "(just)")
+				break
+			end
+			local dist = 0.5/maxe
+			local up = (dist >= distance)
+			local llevel = 0
+			while (dist >= 2) do
+				llevel = llevel + 1
+				dist = dist / 2
+			end
+			if up then
+				if #vals >= maxlen then
+					table.insert(vals, "&hellip;")
+					break
+				end
+				table.insert(vals, "[[" .. i .. ed .. "]]" .. string.rep("*", llevel))
+			end
+		end
+	end
+	return table.concat(vals, ", ")
 end
 function p.noinfobox_chord(frame)
-	local page_name = frame:preprocess("{{PAGENAME}}")
+	local distance = tonumber(frame.args["Distance"])
 	local debug_data = ""
 	local infobox_data = {}
@@ Line 98: / Line 158: @@
 			assert(h > 0, "invalid harmonic")
 			table.insert(harmonics, h)
+		end
+		if distance == nil then
+			if #harmonics >= 5 then
+				distance = 1.5
+			elseif #harmonics >= 3 then
+				distance = 2.0
+			else
+				distance = 3.0
+			end
 		end
@@ Line 116: / Line 186: @@
 		local root_interval_links = {}
 		local step_interval_links = {}
-		local all_interval = {}
 		for i, h in ipairs(harmonics) do
 			-- compute ratio of this harmonic relative to the root
@@ Line 131: / Line 200: @@
 				local step_denom = prev / step_gcd
 				table.insert(step_interval_links, "[[" .. step_numer .. "/" .. step_denom .. "]]")
-			end
-			-- compute all ratio
-			for j, g in ipairs(harmonics) do
-				if j > i then
-					local step_gcd = utils._gcd(g, h)
-					local step_numer = g / step_gcd
-					local step_denom = h / step_gcd
-					local a = rat.new(g, h)
-					all_interval[rat.as_ratio(a)] = a
-				end
-			end
-		end
-		local vals = {}
-		for i = 1, 50 do
-			local et = ET.parse('' .. i .. 'edo')
-			local consistent = p.additively_consistent_int(et, all_interval, false, previous)
-			if consistent then
-				table.insert(vals, "[[" .. i .. "edo]]")
 			end
 		end
+		cat = "(d >= " .. distance .. ") " .. p.consistent_edos(harmonics, distance, 'edo', 4)
 	--end
-	cat = table.concat(vals, ", ")
 	return cat