Establish a good daily warm-up and routine if you don't already have one. If you need one, I have a warm-up packet that I'll send to you. Email me at: email@example.com and ask for it. Every trombonist has a slightly different way of going about their routine, but most routines have these commonalities: long tones, lip slurs, and tonguing.
Long tones: play relaxed and non-metered long tones every day. Focus on your sound. Have a sound in mind that you want to emulate (from your teacher, a recording, a trombone performance you attended, etc...), and chase that sound, every day. I like to think of long tones as the most relaxing thing I do, all day, and I believe that your sound is the most important thing about you, as a musician. Without a beautiful core sound, it is difficult to do much else. I like to play my Remington series with a floated first note (only air to start the first note, no tongue), and a relaxed glissando to the second note (then, breathe before the next note). I also play slow scales, using as little tongue as possible, while playing legato or glissed.
Lip slurs: play these to develop flexibility on your instrument, learning to navigate the harmonic series, without using your tongue. Start with easy slurs (4th-line F down to low Bb, and then back up), and work your way up to adding more partials and playing faster (while staying relaxed). Always play these slowly to start. A relaxed accuracy is key, in the beginning, but even after you feel you have more control, still keep things as tension-free as possible.
Tonguing: after you have gotten some air moving through the instrument while playing long tones and lip slurs, *then* work on tonguing, while keeping the same sound that you've been producing, previously. Don't allow the notes in this part of your routine to not sound as good as everything else. Practice tonguing repeated notes (static, or non-moving slide), and also practice tonguing moving notes (dynamic, or moving slide). Make sure to move your slide quickly between notes, avoiding any unnecessary glissandos (while at the same time making sure that your right arm stays as relaxed as possible). Scales are a great thing to practice here, varying your articulations.
Finally, when learning these etudes, take the time to practice slowly and accurately. Make sure that you are being attentive to every detail in the music, first.
Junior Trombone: Audition Solo 1E, Animato
-Practice the dynamic and articulation contrasts - the composer is very specific about these things. Be exact in your performance, while staying within the "Animato” marking.
-In m.7 decide where you are going to switch slide direction, and practice making it as smooth as possible, utilizing a quick slide in that direction switch. On the recording, I play the F in 6th position, coming back to play the E in 2nd, then continuing the descending chromatic scale.
-Also in m.7 - don't try to play the p softer than you can physically sound good. Contrast is more important than playing so soft that you might risk having a note not speak
during your performance. On the other end of the dynamic spectrum, don't play the
ff in m.15 louder than you can still produce a full and controlled sound.
-m.1, 3, 6, and 17: make sure that your dotted rhythm is precise and exact. Don't
clip either note, and make sure that the 16th note leads into the note that follows.
-m.18: be precise with your triplets, and in m.20, same thing with the eighth notes. Also, note that
the triplets are not slurred, but the eighths are. Contrast is important here.
-For both endings, make sure that your high Eb's are not sharp. Bring them down slightly and listen to your pitch
Clinic Trombone: Audition Solo 2E, Andante
-Practice the dynamic, articulation, and rhythmic contrasts - the composer is very
specific about these things.
-Make sure to stay within the 2 marked tempos - practice both the Andante and also Allegro sections with a metronome and also practice switching back and forth accurately, from one tempo to another.
-Rhythmic contrasts: this solo switches between duple and triple rhythmic subdivisions often. Pay close attention to these, and make sure that you are subdividing internally, when you approach each rhythmic switch.
-m.5-7: note that the dynamic remains f until the decrescendo in m.8. Be aware, however, that as you ascend from the low F (played f), the notes you are playing becomes more naturally "brighter" as you get into the 5th and 6th partial notes...so, avoid playing too loud when you are in m.8, and make sure to adhere to the phrase marking in that measure.
-Allegro: to prepare for playing this section, perhaps practice your Ab major scale in varying patterns, as a "cross-training" exercise.
-m.19: make sure to crescendo all the way to the f at the beginning of the chromatic scale in m.22. The dynamic there shouldn't be a surprise to the listener, rather, a logical arrival point from the previous two measures' worth of crescendo. On the other hand, make sure to play more terraced dynamics in the next few measures following the chromatic scale, and then contrast the f to mf terrace with the decrescendo and rit.
-Finally, whether playing the "a" or "b" ending, practice taking a nice and musical breath into the Andante ending (don't hurry into it). At the end, make sure to practice/play long tones in the low register daily, as to help to facilitate a clean last measure, with straight and still-beautiful tone.
Senior Trombone: Audition Solo 3E, Allegro giocoso / Andante con amore / Allegro giocoso
-Practice the dynamic, articulation, and rhythmic contrasts - the composer is very specific about these things.
-Make sure to stay within the 2 marked tempos - practice both the Allegro giocoso and also Andante con amore sections with a metronome and also practice switching back and forth accurately, from one tempo to another. The general impulse, if not careful enough, will be to take the Andante con amore too fast, and when returning to it, the Allegro giocoso too slow.
-While on the subject of time, or pulse, use your metronome to practice coming in exactly in time on the second 16th note - this happens often (m.2, 5, 10, 23, 24, and 27). Do the same for coming in on the second triplet note (m. 3, 4, 5, 6, 22, and 28).
-Practicing your A major scale in various patterns will help you to prepare to play this solo. Be diligent in playing your 5th position F# far enough out (right where it belongs in the scale), as well as making the appropriate finite adjustments for the upper F#, in a raised 3rd position.
-In the Andante con amore section, m.9 & 13, you have to make a decision about whether to play the E# in 1st or 6th position. If you play it in 1st position, you must make the movement to F# clean and smooth, and avoid the bump that crossing partials gives you (i.e.: don't take away from your phrase). In the recordings, I chose to play the E# in 6th position for the simple reason that it eliminates that bump that I just mentioned. In this case, you have a smooth transition from 6th to 5th position, and your only "challenge" is putting your 6th position E# far enough out (in my opinion, as trombonists, we should always be working on staying precise on our 5th, 6th, and 7th position notes - what a wonderful opportunity in this etude to practice just that!).
-Dynamics: remember that you are the soloist...and dynamics are relative. Be careful to not play louder than you can comfortably sound beautiful, when playing f and ff, and at the opposite end of the dynamic spectrum, don't try to play p softer than you can still play beautifully and with smooth and fluid legato.
-The "stinger" note in both endings: be careful that your sforzando here isn't more than it needs to be. Be full and accented, but not gross and over-the-top. Don't do anything with the note that will take away from everything else that you played, previously.
Download these trombone performance notes [pdf].