What is an interval that is a half step smaller than the corresponding minor/perfect interval called?

An interval that is a half step smaller than the corresponding minor or perfect interval is known as a diminished interval. In music theory, intervals are categorized based on their size, and when you lower a minor or perfect interval by a half step, you create what is termed a diminished interval.

For instance, if you have a perfect fifth interval, the diminished fifth is formed by lowering the perfect fifth by a half step. Similarly, if you take a minor third and lower it by a half step, it becomes a diminished third. This concept is foundational in understanding how intervals function within scales and harmonies.

The other types of intervals mentioned, such as augmented, major, and minor intervals, refer to different alterations or sizes. An augmented interval is one that is a half step larger than a major or perfect interval, while a major interval is already a specific size that does not involve further lowering. A minor interval is also a defined size that is slightly smaller than its corresponding major interval but is not diminished. Understanding these distinctions is crucial for deepening your knowledge of harmony and interval relationships in music.