How does the bottom number of a time signature identify the note value used for a beat?

In musical notation, a time signature is typically written as two vertically aligned numbers. While the top number indicates the number of beats in each measure, the bottom number identifies the specific note value that receives one beat.12

The bottom number functions as a denominator representing the rhythmic unit of measurement. For example, in a time signature of 4/4, the bottom "4" signifies that the quarter note is the unit of time that receives one beat. Similarly, a bottom number of "2" indicates a half note, "8" indicates an eighth note, and "16" indicates a sixteenth note. Essentially, this value establishes the fundamental rhythmic pulse for the composition, allowing performers to interpret the duration of each beat within the measure.1324