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