Todoroki is a valley you count your way up. The recommended month is November, the middle of it. The main fall drops fifty-eight metres — it is on the national list of a hundred notable waterfalls — and above it smaller falls continue up the valley in a long sequence known as the ninety-nine falls. Ninety-nine is not a count. It is an old way of saying many, and the valley spends two hours proving the point.

The path climbs about fifteen hundred metres to Nabewari, the highest of them, and the round trip takes roughly two hours. The higher you go, the shorter the gaps between falls become, until the sound of falling water simply stops breaking. Red leaves stand beside white water the whole way up.

The valley is narrow and takes direct light for only part of the day, so the colour burns brightest close to midday. Time it that way if you can. The rock stays damp on the lower steps even in dry weather, and the way down asks for more attention than the way up.

Beside the main fall stands Todoroki Shrine, and the path passes through its grounds rather than around them. Stop there once, with the water loud behind you. Then keep climbing. You came to count uncountable things, and the valley is glad to keep you at it.