Introduction:
When a hard substance produces a tinkling sound when bent, it indicates that the substance is likely a metal. Metals are known to exhibit this characteristic, which is caused by the movement of the metal ions and the rearrangement of the crystal lattice structure.

Explanation:
1. Non-metal:
Non-metals, such as carbon, sulfur, and phosphorus, do not produce a tinkling sound when bent. They are generally brittle and tend to break or crumble when subjected to bending stress. Non-metals also lack the ability to conduct electricity and heat efficiently, which is another characteristic that distinguishes them from metals.

2. Metal:
Metals are known for their malleability and ductility, which allow them to be bent and shaped without breaking. When a metal is bent, the movement of the metal ions causes a rearrangement of the crystal lattice structure. This movement and rearrangement result in the production of a tinkling sound. The specific sound produced can vary depending on the type of metal and its composition.

Metals also have a high electrical and thermal conductivity, which means they can efficiently transfer heat and electricity. This property is due to the presence of free electrons in the metal's structure, which can move freely and carry electric current or heat energy.

3. Compound:
Compounds are formed by the combination of different elements, including metals and non-metals. While some compounds may exhibit brittleness and produce a sound when broken, the description provided in the question specifically mentions the production of a tinkling sound when bent. This characteristic is primarily associated with metals and not compounds.

Conclusion:
Based on the given information, the hard substance that produces a tinkling sound when bent is most likely a metal. The ability of metals to be bent without breaking, along with their high electrical and thermal conductivity, distinguishes them from non-metals and compounds in this context.