Single Tongue Enhancement

Today, we'll discuss the best way I've found to increase single-tongue speed. Happy practicing!Every year I follow a rough schedule that looks something like this: Winter - focus on learning new repertoire for the brass quintet; Spring - focus on brass quintet repertoire; Summer - focus on specific problems in my playing and learn new solo repertoire; Fall - focus on solo recital repertoire. 

A few years ago I decided that the focus for the summer would be my single-tongue speed. I spent some time looking for exercises that would work. I made my own drills, asked colleagues what they did, and spent hours online perusing the various brass forums (yikes, those places can be scary). Ultimately, the exercise that works the best for me came from a blog by an oboist. At this point, I have no idea where it actually came from, otherwise I give the oboist credit.
Single-tongue is something I have to constantly maintain. My default state without maintenance is about quarter = 95 beats per minute. After a few weeks of working with this drill it had increased to about 109 beats per minute (BPM). Here's a link to the exercise. It can also be found at the end of Routine I for euphonium and tuba
Anyway, here's the basic exercise. 

1. Pick a scale that you're comfortable enough with that you can play fast enough to max-out your single-tongue but can just barely stay with the metronome (in this example we'll use 100 BPM for simplicity).
2. Play the scale one octave in straight sixteenth notes at quarter-note = 100
3. Play the scale again using the same scale and rhythm at 50 BPM
4. Again, 100 BPM
5. 60 BPM
6. 100 BPM
7. 70 BPM
8. 100 BPM
9. 80 BPM
10. 100 BPM
11. 90 BPM
12. 100 BPM
13. 105 BPM (this is where the real work start getting done)
14. 100 BPM
15. 105 BPM
16. 100 BPM
17. 105 BPM
18. 100 BPM
19. 105 BPM

The point is to spend time working at your fastest possible single-tongue tempo then speed up another 5%. 
When 100 is easy and you can keep up at stay with the metronome without having trouble, make 101 BPM your new starting tempo. The new sequence should look like this:
101 BPM
51 BPM
101 BPM
etc.
101 BPM
106 BPM
101 BPM
106 BPM
101 BPM
106 BPM
101 BPM
106 BPM
Thank you for reading!