Module:JI ratios: Difference between revisions

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@@ Line 7: / Line 7: @@
 p = {}
--- SEARCH_MAX is hardcoded to limit the size of output.
+-- TODO
+-- - Allow option to search by Tenney height first or int limit first?
+-- INT_LIMIT_MAX is hardcoded to limit the size of output.
 -- 400 -> ~24000 ratios
 -- 300 -> ~14000 ratios
@@ Line 14: / Line 17: @@
 -- 128 -> ~2500 ratios
 -- 100 -> ~1500 ratios
-local SEARCH_MAX = 150
+local INT_LIMIT_MAX = 150
+local DEFAULT_INT_LIMIT = 50
-local DEFAULT_INT_LIMIT = 50
+-- TENNEY_HEIGHT_MAX is hardcoded to limit size of output.
+local TENNEY_HEIGHT_MAX = 16
+local DEFAULT_TENNEY_HEIGHT = 10
 --------------------------------------------------------------------------------
@@ Line 29: / Line 35: @@
 	local integer_limit = integer_limit or DEFAULT_INT_LIMIT
-	integer_limit = math.max(0, math.min(SEARCH_MAX, integer_limit))
+	integer_limit = math.max(0, math.min(INT_LIMIT_MAX, integer_limit))
 	local ratios = {{1,1}, {2,1}}
@@ Line 43: / Line 49: @@
 			local ratio_2 = ratios[i+1]
 			local mediant = {ratio_1[1]+ratio_2[1], ratio_1[2]+ratio_2[2]}
-			local int_max = math.max(mediant[1], mediant[2])
+			local INT_LIMIT_MAX = math.max(mediant[1], mediant[2])
 			table.insert(new_ratios, ratios[i])
-			if int_max <= integer_limit then
+			if INT_LIMIT_MAX <= integer_limit then
+				new_ratios_added = true
+				table.insert(new_ratios, mediant)
+			end
+		end
+		table.insert(new_ratios, ratios[#ratios])
+		ratios = new_ratios
+	end
+	-- If the max cents is greater than the octave, duplicate all existing
+	-- ratios and raise them by the required number of octaves.
+	if max_cents > 1200 then
+		local new_ratios = {}
+		local num_octaves_up = math.ceil(max_cents / 1200)
+		for j = 1, num_octaves_up do
+			for i = 2, #ratios do
+				local num = ratios[i][1] * math.pow(2, j)
+				local den = ratios[i][2]
+				local gcd = utils._gcd(num, den)
+				num = num / gcd
+				den = den / gcd
+				if math.max(num, den) <= integer_limit then
+					table.insert(new_ratios, {num, den})
+				end
+			end
+		end
+		for i = 1, #new_ratios do
+			table.insert(ratios, new_ratios[i])
+		end
+	end
+	-- Remove any ratios that exceed the max cents
+	-- Convert to ratios that Module:Rational can work with
+	for i = 1, #ratios do
+		ratios[i] = rat.new(ratios[i][1], ratios[i][2])
+	end
+	return ratios
+end
+-- Find JI ratios up to a max Tenney height within the octave by finding mediants.
+-- A cent value can be passed in to either exclude ratios that are above an
+-- interval below the octave or include ratios above the octave.
+function p.search_by_tenney_height(tenney_height, max_cents)
+	local max_cents = max_cents or 1200
+	local tenney_height = tenney_height or DEFAULT_TENNEY_HEIGHT
+	tenney_height = math.max(0, math.min(TENNEY_HEIGHT_MAX, tenney_height))
+	local ratios = {{1,1}, {2,1}}
+	-- Find ratios by finding the mediants between existing ratios, only adding
+	-- those that do not exceed the integer limit.
+	local new_ratios_added = true
+	while new_ratios_added do
+		new_ratios_added = false
+		local new_ratios = {}
+		for i = 1, #ratios-1 do
+			local ratio_1 = ratios[i]
+			local ratio_2 = ratios[i+1]
+			local mediant = {ratio_1[1]+ratio_2[1], ratio_1[2]+ratio_2[2]}
+			local curr_height = utils.log2(mediant[1]*mediant[2])
+			table.insert(new_ratios, ratios[i])
+			if curr_height <= tenney_height then
 				new_ratios_added = true
 				table.insert(new_ratios, mediant)
@@ Line 239: / Line 314: @@
 function p.tester()
-	local params = p.parse_search_params("Prime Limit: 7; Tenney Height: 11")
+	--local params = p.parse_search_params("Prime Limit: 7; Tenney Height: 11")
-	ratios = p.search_by_params(params)
+	--ratios = p.search_by_params(params)
-	ratios = p.sort_by_closeness_to_cent_values(ratios, {0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200}, 15)
+	--ratios = p.sort_by_closeness_to_cent_values(ratios, {0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200}, 15)
+	--return p.ratios_as_texts(ratios)
-	return p.ratios_as_texts(ratios)
+	local ratios = p.search_by_tenney_height(15)
+	--local ratios = p.search_by_int_limit(150)
+	return #ratios
 end
 return p