As with all instruments, learning the trumpet requires patience and practice.

Holding the Instrument

The left hand holds the trumpet, while the right hand plays (pushes the valves).  The thumb of the left hand is placed in the ring of the 1st valve slide (if there is one).  The rest of the fingers wrap around the three valves, leaving a finger to go inside the 3rd valve ring (if there is one).  The thumb of the right hand is placed in between the 1st & 2nd valves under the lead pipe (what the mouthpiece is put into).  The 2nd, 3rd, & 4th fingers are rounded and placed on the three valves accordingly.  The last finger rests on the ring (if there is one) on the lead pipe.  It is very important that this finger does not hook into the ring because it will push the trumpet into the mouth, causing unnecessary pressure and increasing the chances of injury to the mouth.

Breathing

This may seem like the part that is the easiest, but it is so important that should be reviewed in depth.  When inhaling, make sure that the air is entering the stomach, not the chest.  The shoulders should not raise.  When this happens, unnecessary strain is eventually applied to the neck, which chokes the air supply.  Place a hand on your stomach and practice concentrated breathing while having only the stomach expand, and keeping shoulders relaxed.

When exhaling, keep the same relaxation through the whole body.  Don't let the air just pass through the mouth.  Actively push the air through until absolutely no air can be pushed.  Near the end of the air stream, the abdominal muscles should be tight because it is the stomach area that is pushing.  Lung supply can be built through exercises like running and swimming.  Try maintaining a steady air flow, while you are panting.  This will help build lung capacity and make it easier to play.

Buzzing

The source of sound from wind instruments is vibration.  The vibration that is produced for brass instruments is called a buzz, which comes from the lips.  Without the mouthpiece, form the mouth into an embouchure (basic formation of the muscles of the mouth) that can spit seeds as fast as possible.  Make sure the aperture (hole) is small enough and the lip muscles on the side are tight to maintain the pressure.  Now, blow air forcefully through the aperture.  As this is being done, slowly close the mouth even further to create vibration between the lips.  This is called a buzz.  A good buzz will result in a pure sound.  Now, apply this method to the mouthpiece, which amplifies the buzz.  Once a good buzz is attained, the mouthpiece can be put in the instrument.

Creating the Sound

With the mouthpiece in the horn, apply the same techniques used above.  Try and maintain a steady tone, which can be applied through a steady push from the abdominal muscles.  To practice this, use a tuner and try to make the ticker move as minimal as possible.  Do not worry about tuning as much as keeping the tone steady.  Practice holding a note as steady as possible for as long as possible, making the sound at the beginning as good as the sound at the end.

The Tongue

The tongue is used for attacking and releasing notes, based on the articulation provided in the music.  To attack a note, simply interrupt the vibration between the lips by inserting the tongue in the aperture.  Once this has been done, quickly withdraw the tongue.  A small interruption has been made in the sound, which causes an attack of another note.  Now try to start the sound with the tongue.  Place the tongue in the aperture as air is being blown.  Good coordination between the air and the tongue will result in accurate and tight tonguing technique.

To release notes with a tongue (although notes can also be released by stopping air), follow the same procedure.  Don't be very aggressive and only use this technique when the music says so.  It will not sound very graceful when legato notes are being halted by a heavy tongue.  To stop the note, keep the tongue in place while you stop the air from being pushed.

Finally, do not force the tongue outside the mouth.  This cause the sound to get sloppy and will delay the time of the sound.  Always maintain the same embouchure, regardless of the intensity of the tongue.

Obtaining the Different Range of Notes

EMBOUCHURE DOES NOT CHANGE! APERTURE DOES!  Always remember that the embouchure is set for any note.  Of course, it may seem easier to change the embouchure altogether, but it reduces the quickness of the change between notes in different ranges.  Professional players can be distinguished by the way that their mouth is set for all the notes.  They do not need to take the trumpet off their mouth to reset their mouth for a different note.  When seeing high screaming trumpet playing, you may see an embouchure change, but that is usually because the trumpet is not even meant to register that high and those notes are not common in music.

For high notes, it is not the amount of air, but the speed of the air.  Create more pressure in the mouth by closing the aperture as small as needs to be, allowing the air to pass quicker.  For low notes, it is the opposite.  There needs to be less pressure and a great amount of air to support the low notes because the vibration is much slower.  Slow vibration is very easy to fall apart if there is not enough air.
 
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