Here's the breakdown:

* Temperature: The Earth's internal heat increases with depth. The geothermal gradient, the rate at which temperature increases with depth, is not constant. It varies depending on location and geological factors.

* Pressure: Pressure also increases with depth. The immense pressure from the weight of overlying rock can actually increase the melting point of rocks.

* Composition: Different rock types have different melting points.

The "Zone of Melting"

There's a zone within the Earth called the asthenosphere. This is a partially molten layer within the upper mantle. While not entirely molten, it behaves more like a very viscous fluid. The asthenosphere is where magma is generated, but the depth at which this occurs is variable and depends on the factors mentioned above.

So, in short, there's no single "depth" at which rock melts. It's a complex process influenced by temperature, pressure, and rock composition.