Transposing Instruments. (The New Oxford Companion to Music)

Instruments for which the music is written higher or lower than it sounds by a known or stated interval. (Should the interval always be an octave - as an octave higher with guitar and double bass - then the instrument need not be considered a transposing one.)
Stringed instruments are rarely transposing (an exception is the violino piccolo). Practically all the regular transposers are wind instruments. With these the operative interval in most cases stated in the instrument's designation, e.g. 'Bb clarinet' or 'clarinets in Bb'. The rule is that the named note, in this example Bb, is that which the instrument will sound when the player reads or composer writes the note C. All the other written notes correspondingly sound a tone lower. There are, however, some cases where knowledge of the transposing instrument is assumed, as with the cor anglais (English horn), the interval (a fifth lower than written) here being always the same, whereas on clarinet, horn, trumpet, saxophone, etc. this is far from being the case.
These transpositions are for the benefits of the performer, in that they allow a woodwind player, for example, to react to any given note written on paper always with the same fingering when required to change to a deeper or higher instrument of the same kind, irrespective of the different sounds produced; and correspondingly with brass instruments. The composer or arranger obligingly arranges for this with the appropriate transposition, to which he is so accustomed thatwhen writing a part for cor anglais or for horn in F, and wanting the sound of F, he writes the C above, without having to stop to think. A conductor or other experienced score-reader then does the opposite, seeing (in this example) C but mentally 'hearing' the F below, having quickly noted the various different designations at the beginning of the score. Only in more complex instances might he have to pause for an instant on a first on the first reading of the score, to see what the harmony of the wind instruments actually amounts to. Schoenberg held that these transpositions should be abolished, in full scores at least, but they are so ingrained among musicians that to write all wind parts at sounding pitch has been found to make things harder, not easier.
Tables 1 and 2 below are laid out from the score-reading point of view. In Table 1, wherever the key is stated in parentheses, it is, or can be, omitted from the designation of the instrument in score and part. A part 'in C' (sounding as written or an octave lower) needs to be specified as such in cases where (as with clarinet, trumpet, etc.) the instrument can be in other keys also. With the brass in Table 2, the note headings do not necessarily refer to different actual instruments as they do in Table 1, for in older times a horn or trumpet was put in different keys by inserting crooks and the heading tells which crook to insert; players today, no longer using crooks, make as needed their own transpositions at sight, but this is no concern of the score-reader.
Bass clef when used for low notes of horn (also basset horn, Table 1) and occasionally trumpet; the older practice is to write the notes an octave lower than they would be if in the treble clef. The preferred modern practice is to continue into the bass clef logically. The context usually makes it quite clear which method is adopted.

Cornet transpositions: as horn from 'in Bb' (alto) downwards; but 'in C' sounds as written.

Bass trumpet: as horn in Eb, D, C, and Bb 'basso'.

Wagner tubas: Wagner himself changed his method for these in the full scores of the Ring.
( i ) In the prelude to Götterdammerung: tenor tubas in Bb, something a ninth lower; bass tubas in F, sounding
an octave and a fifth lower. Bruckner follows this method in his Seventh Symphony, but in the Eighth partly the
next ( ii ).
( ii ) Das Rheingold: sounding respectively a tone and a fifth lower than written.
( iii ) For the rest of the cycle the scores have (tenor) 'in Eb', sounding a sixth lower (but in bass clef a third
higher); and (bass) 'in Bb', sounding a ninth lower (but when in bass clef, a tone lower).

 Table 1

WOODWIND TRANSPOSITIONS 
 Parts as written  Actual sound
 Alto flute (in G)  Fourth lower
 Oboe d'amore (in A)  Minor third lower
 Cor anglais (in F)  Fifth lower
 Bass oboe or Heckelphone (in C)  Octave higher
 Clarinet in Eb  Minor third higher
 Clarinet in D  Tone higher
 Clarinet in C  As written
 Clarinet in Bb  Tone lower
 Clarinet in A  Minor third lower
 Basset horn (in F)  Fifth lower (see Note I below for notes written in bass clef)
 Alto clarinet in Eb  Major sixth lower
Bass clarinet (normally assumed to be in Bb)  Here are two notations:
( i ) normal, in treble clef: a minor lower
( ii ) Wagner and some others: a tone lower, using bass clef freely. The
part then looks more 'bass' but infringes the purpose of transposing
since it makes the player 'rethink' while fingering
 Bass clarinet in A  Similarly two notations:
( i ) tenth lower
( ii ) minor third lower
 Saxophone, Bb soprano  Tone lower
 Saxophone, Eb alto  Major sixth lower
 Saxophone, Bb tenor  Ninth lower
 Saxophone, Eb baritone  Octave and sixth lower ( as that by imagining bass clef instead of
treble, one can read the actual sounds, but remembering to add three
flats to the key signature.

Table 2 

BRASS TRANSPOSITIONS 
 Designation  Sounds above/below the written notes
   HORN  TRUMPET
 In Bb  'Bb alto': tone lower  Tone lower
 In Bb  'Bb basso': ninth lower (see Note 1)  Tone lower
 In A  Minor third lower  Minor third lower
 In Ab  Major third lower  Minor sixth higher (see Note 3)
 In G  Fourth lower  Fifth higher
 In F  Fifth lower  Fourth higher (see Note 4)
 In E or Eb  Sixth lower (minor or major)  Third higher (major or minor)
 In D or Db  Seventh lower (similarly)  Tone or semitone higher
 In C  Octave lower (see Note 2)  As written
Notes to Table 2
1. Horn in Bb. Parts in older music frequently fail to specify 'alto' or 'basso', in which case the matter has to be decided as best one can by context (if with many high notes, 'basso'). 'Horn in A', or 'Ab', is occasionally 'basso' in later music, e.g. Verdi, then sounding a tenth lower.
2. 'In C'. Occasionally in the earlier Viennese classics this is 'C alto', sounding as written.
3. The octave difference between 'in A' and 'in Ab': in early 19th-century music, usually 'in A' means trumpets crooked down in A; 'in Ab', crooked up to Ab. Should in either case the transposition listed above make nonsense of the music, then try the other! In the same period 'in Bb' occasionally reads a seventh higher.
4. 'Tromba contralta' in F in Russian works, e.g. Rimsky-Korsakov, sounds a fifth lower than written.


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