Pailiaq

Joined 24 September 2024

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+-- EDO Approximations Module
+-- Calculates EDO approximations for just intervals
+-- Usage: {{#invoke:EDO_Approximations|main|interval=3/2|tolerance=9|min_edo=10|max_edo=60}}
+local p = {}
+-- Convert a frequency ratio to cents
+local function cents(ratio)
+    return 1200 * math.log(ratio, 2)
+end
+-- Parse a ratio string like '3/2' into a number
+local function parse_ratio(ratio_str)
+    local num, denom = ratio_str:match("^(%d+)/(%d+)$")
+    if not num or not denom then
+        return nil
+    end
+    return tonumber(num) / tonumber(denom)
+end
+-- Find the best approximation of an interval in a given EDO
+local function find_best_approximation(ratio_cents, edo)
+    local edostep = 1200 / edo
+    -- Find the nearest step
+    local best_step = math.floor(ratio_cents / edostep + 0.5)
+    local approximation_cents = best_step * edostep
+    local absolute_error = approximation_cents - ratio_cents
+    local relative_error = (absolute_error / edostep) * 100
+    return best_step, absolute_error, relative_error
+end
+-- Calculate all EDO approximations within tolerance for a given ratio
+local function calculate_edo_approximations(ratio, tolerance, min_edo, max_edo)
+    local ratio_cents = cents(ratio)
+    local results = {}
+    for edo = min_edo, max_edo do
+        local steps, abs_error, rel_error = find_best_approximation(ratio_cents, edo)
+        if math.abs(rel_error) <= tolerance then
+            table.insert(results, {
+                edo = edo,
+                steps = steps,
+                abs_error = abs_error,
+                rel_error = rel_error
+            })
+        end
+    end
+    return results
+end
+-- Format a number with sign and 2 decimal places
+local function format_error(value)
+    if value >= 0 then
+        return string.format("+%.2f", value)
+    else
+        return string.format("%.2f", value)
+    end
+end
+-- Main function to generate the wikitable
+function p.main(frame)
+    -- Get parameters from template invocation
+    local args = frame.args
+    local interval_str = args.interval or args[1]
+    local tolerance = tonumber(args.tolerance) or 9.0
+    local min_edo = tonumber(args.min_edo) or 10
+    local max_edo = tonumber(args.max_edo) or 60
+    -- Validate and parse interval
+    if not interval_str then
+        return "Error: No interval specified"
+    end
+    local ratio = parse_ratio(interval_str)
+    if not ratio then
+        return "Error: Invalid interval format (use format like '3/2')"
+    end
+    -- Calculate approximations
+    local results = calculate_edo_approximations(ratio, tolerance, min_edo, max_edo)
+    if #results == 0 then
+        return "No EDOs found within tolerance of " .. tolerance .. "%"
+    end
+    -- Build the wikitable
+    local output = {}
+    table.insert(output, '{| class="wikitable"')
+    table.insert(output, '|+ EDO Approximations for ' .. interval_str)
+    table.insert(output, '|-')
+    table.insert(output, '! EDO !! Step size !! Absolute Error ([[Cent|¢]]) !! [[Relative_interval_error|Relative Error]] ([[Relative_cent|%]])')
+    for _, result in ipairs(results) do
+        local edo_link = string.format("[[%dedo|%d]]", result.edo, result.edo)
+        local step_size = string.format("%d\\%d", result.steps, result.edo)
+        local abs_err = format_error(result.abs_error)
+        local rel_err = format_error(result.rel_error)
+        table.insert(output, '|-')
+        table.insert(output, string.format('| %s || %s || %s || %s', edo_link, step_size, abs_err, rel_err))
+    end
+    table.insert(output, '|}')
+    return table.concat(output, '\n')
+end
+return p