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The thirteen stroke roll is a less common rudiment that is based around double strokes. As with the five stroke roll, seven stroke roll, nine stroke roll, and eleven stroke roll - this rudiment uses one single stroke to end the odd-number group. It's best incorporated into drum fills and drum solo patterns. Here is it written out:
If you've already practiced the similar rudiments listed above, you'll have no difficulty working through this pattern. Just focus on keeping all the double strokes at an even volume, and practice with a metronome to stay in perfect time. You can work through it using both right and left hand leads.
Here is a drum beat using the thirteen stroke roll in a real playing situation:
This last exercise uses the thirteen stroke roll within the context of a simple drum fill: