The aural-mental process which enables the brass player to pick out specific pitches and to play in tune involves an ability to pre-hear the note that is to be played. A pitch signal is sent from the "mental ear" to bring the embouchure and other elements of tone production into a specific adjustment for a note. Tone and style are guided in the same way. Any inaccuracy of note or intonation is caused by the elements not being in optimum adjustment, or an imprecise or hazy pitch

Obviously, valve slides cannot be moved in very rapid passages. What the player looks for are notes that have sufficient duration to make correction practicable. Another approach is to pre-set the slide for a prominent note within a moving passage. This focuses the passage on a corrected pitch center and makes the entire passage sound more in tune. While some players must make greater use of the slides than others, because of variations in tone production, the general tendency is not to use them enough; this results in less-than-accurate intonation. (There is an advantage to a trigger over a ring for the first valve slide in that only one motion is necessary, rather than the double action required by the ring.)

Specific notes needing correction can be identified through the use of an electronic tuner (serious students should purchase one). After the degree of correction has been determined, general intonation can be improved by carefully playing scales, intervals, and arpeggios against a reference pitch sounded by the tuner.

The low F#, G, and G# tend to vary in pitch from player to player. Some must use the third valve slide, while others can play these notes in tune with minimal or no adjustment.

A more complex problem involves the D, Eb, and E, particularly on the C trumpet.

These notes are minimally up to pitch and require an adjustment of embouchure and air stream to bring them into tune. On the C and higher trumpets, alternate fingerings are often used to improve the intonation of these notes, but their use brings on technical (fingering) complications. The problem is aggravated by too high a placement on the third-space C, which has an unusually wide range of possible placements, and by not using the trigger on the F above. These factors cause some players to have fairly severe intonation problems in the C to G range.

The solution is to cultivate a lower placement on the C. This can be accomplished by centering the C between the G below, and E above. As a temporary measure, the C might be fingered 2-3 until the feel of a lower C is established.  (The 2-3 combination should only be used as an exercise since its pitch is too low for actual use. The player should return to the normal open C once a lower placement has been achieved.) When tuning, one should check the D, Eb, and E against the tuning note. If they seem flat, the main tuning slide should be brought inward until these notes form accurate intervals with the reference pitch. In resolving the problem, the player must use the first valve trigger on the top-line F and A above, to bring them into a better pitch relationship with the D, Eb, and E. While this problem is present on the Bb trumpet, and most acute on the C and higher trumpets, for some reason it causes fewer difficulties on rotary valve trumpets.

Playing in tune is, above all, a practical skill which requires careful listening and experience in matching other players in ensembles. Too much analysis often creates further problems. The best plan is to adopt a relaxed, natural approach to intonation, as one would in singing. Playing in small ensembles provides invaluable experience, as do sectional rehearsals. A useful rehearsal procedure is to have two or three parts play alone. In this way, problems in intonation and balance can be clearly heard and corrected.

TRANSPOSITION

The question is often asked as to why transposition is necessary. Would it not be simpler to provide parts already transposed for Bb or C trumpet?

The origin of the problem goes back to the era of the natural trumpet when it was customary for notes of the harmonic series to be read in C. A crook would be inserted to obtain the desired sounding pitch. For example, Mozart notated the trumpet parts to the Prague Symphony (No. 38 in D, K. 504) in the key of C with the instruction that the D crook be used. By keeping the notation of the harmonic series the same, irrespective of the key of the composition, the parts were made easier for the players to read, and performance on a natural instrument was facilitated. The tradition of writing the fundamental and its overtones in C continued into the valve era and persists today. Trumpeters must be prepared to transpose from parts originally written for trumpets in A, D, Eb, E, and F, to name some of the common keys.

Transposed parts are not usually provided for several reasons. Orchestral trumpeters often substitute trumpets on various parts and it would be difficult for publishers to keep up with individual preferences. Also, switching instruments is made easier by the player having learned the part in its original notation. Above all, there is a certain pride in craftsmanship in being able to play the part as the composer wrote it; therefore trumpeters tend to look down on the use of transposed parts. New compositions, however, should be notated at concert pitch, leaving the choice of which trumpet to use to the player. This applies to parts for the piccolo trumpet as well. Band parts are best written for the Bb trumpet.

There are two methods used in transposition: interval and clef. In the interval system, the notes are mentally moved upward or downward the correct distance between the key of the trumpet specified in the part and the trumpet that will be used. The key signature must be altered in the same way. For example, in Strauss's Ein Heldenleben, the part for Eb trumpet must be read up a perfect fourth when played on a Bb trumpet, since the Bb sounds a fourth below the Eb instrument. If the part is to be played on a C trumpet, the notes must be moved upward a minor third:

Trumpet in Eb

Transposed for Bb trumpet

Transposed for C trumpet

When the distance is only a half step, as in transposing A parts on the B trumpet, one of two procedures can be used, depending on the key signature.  If the part is written without key signature or in a sharp key, the passage may be read in the parallel flat key by altering the key signature:
Transposition Table 
In performing Baroque works written for trumpet in D on the piccolo Bb trumpet, the player will find it easier to read a major third higher while fingering an octave lower than to read downward a minor sixth. If the piccolo is used in A, the part should be read a perfect fifth lower. C parts may be read on the A piccolo by using the bass clef.  
Ultimately, it is the time that can be given to the study of transposition that is important, rather than the method used. Not all of the study time must be with the instrument. Although some daily instrumental work is necessary to orient the ear to different pitch levels, eye and finger coordination may be developed by reading silently and pretending to operate the valves. In this way, non-practice hours can be used to further transposition skills. Simple materials, such as familiar etudes and melodies, should be used at first, gradually progressing to studies specifically designed for transposition.

MUTES

In scores where no specific indication is provided other than that a passage be muted, it is assumed that the straight mute is intended. To achieve a blend in muted sound, it is best if mutes of different materials or makers are not mixed within the same section since they tend to vary in intonation and timbre. The conventional straight mute is usually made from aluminum (although sometimes plastic and other metals are used) and produces a resonantly pungent timbre.  Straight mutes are also constructed from fiber; these have a softer, less cutting sound. It is customary for a composer to specify when a fiber mute is to be used in place of the customary metal type.

Because the bell throats of various trumpets vary in size, it may be necessary to sandpaper a mute's corks to obtain good intonation. A properly adjusted mute will still play slightly sharp; the best method of correcting this is to place a pencil mark on the trumpet's main tuning slide at the beginning of rehearsal. The slide can be extended for muted passages and returned to the mark for open playing.  The amount of correction necessary can be determined by playing open and muted pitches into an electronic tuner. A specially sized mute must be used on the piccolo trumpet due to its small bell.

There is an entire range of specialized mutes, each producing its own specific timbre. Of these, the cup mute and harmon or wa-wa mute are the most common.  The latter incorporates an extendable tube which may be covered and uncovered to create the wa-wa effect. The tube can be adjusted to different lengths for distance effects, or omitted entirely for yet another color. The notation used for the wa-wa effect, and also with hats and plungers, is + (closed), and o (open). Occasionally, a cloth bag is placed over the bell to dull and soften the sound. A useful mute is the whisper mute, which allows the performer to play comfortably, yet produce an extremely soft sound. It is sometimes used as a substitute for the straight mute in very quiet passages. Mutes designed for practicing have appeared recently and are helpful on tours and in other difficult situations.

Recommended Books on the Trumpet and Cornet

D'Ath, Norman W. Cornet Playing. London: Boosey & Hawkes, 1960.

Davidson, Louis. Trumpet Techniques. Rochester: Wind Music, 1970.

Foster, Robert E. Practical Hints on Playing the Trumpet/Cornet. Melville, N.Y.: Belwin-Mills, 1983.

Hanson, Fay. Brass Playing. New York: Carl Fischer, 1975.

Hyatt, Jack H. "The Soprano and Piccolo Trumpets: Their History, Literature, and a Tutor." D.M.A. thesis, Boston University, 1974. UM 74-20, 473.

Johnson, Keith. The Art of Trumpet Playing. Ames, Iowa: Iowa State University Press, 1981.

Lowrey, Alvin. Trumpet Discography. Denver: National Trumpet
Symposium, n.d.

Mathie, Gordon. The Trumpet Teacher's Guide. Cincinatti, Ohio: Queen City Brass Publications, 1984.

Musique pour trompette. 2nd ed. Paris: Alphonse Leduc, n.d.

Sherman, Roger. The Trumpeter's Handbook. Athens, Ohio: Accura
Music,1979.

Smithers, Don. The Music and History of the Baroque Trumpet Before 1721. London: J.M. Dent, 1973.

Webster, Gerald. Method for Piccolo Trumpet. Nashville, Tenn.: Brass Press,1980.

Other Books of Interest to Brass Players (12)

Anderson, Paul G. Brass Solo and Study Material Music Guide. Evanston, Ill. Instrumentalist Co., 1976.

Baines, Anthony. Brass Instruments: Their History and Development. London: Faber & Faber, 1976.

Barbour, J. Murray. Trumpets, Hems, and Music. East Lansing, Mich.: Michigan State University Press, 1964.

Bellamah, Joseph L. Brass Facts. San Antonio, Tex.: Southern Music, 1961.

Brass Anthology. Evanston, Ill.. Instrumentalist Co., 1984.

Brown, Merrill E. Teaching the Successful High School Brass Section. West Nyack, N.Y.: Parker, 1981.

Carse, Adam. Musical Wind Instruments. London: Macmillan, 1940. Reprint: New York: Da Capo Press, 1965.

Devol, John. Brass Music for the Church. Plainview, N.Y.: Harold Branch, 1974.

Eliason, Robert E. Early American Brass Makers. Nashville, Tenn.: Brass Press,1981.

Farkas, Philip. The Art of Brass Playing. Rochester, N.Y.: Wind Music, 1962.

Farkas, Philip. The Art of Musicianship. Bloomington, Ind.: Musical Publications,1976.

Lawrence, Ian. Brass in Your School. London: Oxford University Press, 1975.

Macdonald, Donna. The Odyssey of the Philip Jones Brass Ensemble. Moudon, Switzerland: Editions BIM, 1986.

Mende, Emilie. Pictorial Family Tree of Brass Instruments in Europe. Moudon, Switzerland: Editions BIM, 1978.

Rasmussen, Mary. A Teacher's Guide to the Literature for Brass Instruments. Durham, N.H.: Brass Quarterly, 1968.

Severson, Paul, and McDunn, Mark. Brass Wind Artistry. Athens, Ohio: Accura Music, 1983.

Stewart, Dec. Arnold Jacobs: The Legacy of a Master. Northfield, Ill.. Instrumentalist Publishing Co., 1987.

Taylor, Arthur R. Brass Bands. London: Granada Publishing, 1979.

Brass, and Percussion Instruments of the Orchestra. A Bibliographic Guide (New York: Garland, 1985).

12. A very useful guide to articles, books, and dissertations on brass instruments is Alien B. Skei's Woodwind, Brass, and Percussion Instruments of the Orchestra: A Bibliographic Guide (New York: Garland, 1985).