How is a minor interval altered to become diminished?

To transform a minor interval into a diminished interval, you lower the top note of the interval by a half step. This alteration reduces the interval more than a minor interval’s already diminished size and creates a diminished interval.

For example, if you have a minor third (which consists of three half steps), lowering the top note by a half step gives you two half steps, thereby resulting in a diminished third, which consists of only two half steps. This concept is foundational in understanding how intervals are built and modified within music theory, helping with the broader comprehension of voice leading and harmonic structure.