It’s one of those things that weren’t invented in China but took off in China: 简谱 is a way of writing down music using numbers and dots and dashes. It was invented because the standard notation can be difficult to read, especially to beginners:

But this is (arguably) more accessible:

Wikipedia (en, zh) says this notation was invented in France in the 1700s and came to China by way of Germany and Japan in the early 1900s. I haven’t seen it used anywhere outside of China, though — which is a shame, because it’s such a handy tool.
The Notes
简谱 uses the numbers 1 through 7 to denote the seven notes on a major scale — that is, do, re, mi, fa, so, la, si (ti) — and uses a 0 to denote a pause. Very often, this translates to 1 = C, 2 = D, …, 6 = A, 7 = B.
