Pythagoras is often associated with the discovery of the relationship between musical harmony and mathematical ratios. When he reportedly heard the sounds made by blacksmiths hammering metal, he noticed that the pitch of the sounds (or musical notes) produced varied according to the weight of the hammers and the way they struck the anvils.
From this observation, he understood that pleasant musical combinations arise from specific numerical ratios of string lengths or weights, which can create harmonious tones. For example, if one hammer had a certain weight and produced a sound at a specific frequency, a second hammer of a different weight that created a sound at a different frequency would also form a mathematical ratio with the first, leading to harmonious intervals.
Therefore, among the options provided, the most pertinent idea would be that "Pleasant musical combinations are caused by the weight of different hammers." This aligns with Pythagorean theory, emphasizing the relationship between music and mathematical ratios.