The sawtooth f(t) = t/π on (−π, π), repeated every 2π, is a sum of sines: f(t) = (2/π) ∑ (−1)ᵏ⁺¹ sin(kt)/k. Term k is a circle of radius proportional to 1/k turning k times as fast as the first. With N = 1, 5, 10, 25 and 100 terms the ramps straighten and the tone brightens