Creating a formula field to capture time intervals

Since your field is a Time of Day type, you should be able to then use the minute() and within the if just check for less than 30. Assuming this field where you want the interval to display is Text: 

var text hr = toText( hour( [Time of Day] ) );

var text firstInterval = $hr & ":00 - " & $hr & ":29";

var text secondInterval = $hr & ":30 - " & $hr & ":59";

If(

  Minute( [Time of Day] ) < 30, $firstInterval,

  $secondInterval

)

*replace [Time of Day ] with your actual field name.