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Families of Instruments: E.g., The Saxophone Family
Any given musical instrument is constructed so that it can handle only a certain range of pitches. The guitar, for instance, only has a certain number of frets, limiting the upper and lower range of the instrument.
This applies to wind instruments, like any other. So it’s common to have “families” of wind instruments—families of clarinets, flutes, and saxophones, for instance—of varying sizes. The smaller-sized instruments handle higher pitches, the larger ones, lower pitches.
For instance, each of the four common sizes in the saxophone family—soprano, alto, tenor, and baritone—is good for a certain range of pitches, from a high-pitched range (soprano sax) to a low-pitched range (baritone sax).
All saxophones use the same fingering for a particular written note. So, if you learn to play, say, alto sax, and you decide to switch to another sax in the same family, you don’t have to learn a whole different way of fingering.
Problem is, because each instrument is built for a different pitch range, when you finger the alto sax to play, say, the written note C, the note you actually hear coming out of your horn is E♭, 9 semitones below C. On the tenor sax, when you finger the instrument to play C, the note that comes out is B♭, more than an octave below the C written on the page.
Therefore, composers and orchestrators must notate the music so that it accounts for the difference between the notes that come out of the transposing instrument and the notes on the page.