In Medieval and Renaissance times, large instrumental ensembles were unusual. When a piece did include parts for more than one instrument, the parts were not even necessarily for specific instruments. (For example, the same music for four players might be played by either four string or four recorder players.)
But writing for specific instruments allows a composer to take advantage of the specific timbre and abilities of that instrument, in effect giving the artist more colors and textures to work with. Baroque and Classical composers became adept at using this expanding pallette, writing works for specific sets of instruments. These composers particularly had to take into account the limitations of the instruments, which were sometimes (especially for many wind instruments) quite severe. A typical Classical symphony would rely heavily on the strings, with pairs of flutes, oboes, clarinets, bassoons, trumpets, horns, and tympani added for color and interest.
At the same time, composers were also experimenting with writing for specific instruments in smaller ensembles. Here is a short list of some of the most popular instrument combinations for chamber music. Writing for a common instrumentation will make it much easier for you to find a group interested in playing your arrangement.
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Piano and one wind or string instrument
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String quartet (2 violins, viola, and cello)
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String quartet with a piano or a wind instrument
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Woodwind quintet (normally flute, oboe, clarinet, bassoon, and French horn)
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Brass quintet (normally two trumpets, one French horn, and either two trombones, or one trombone and one tuba)
Throughout the Romantic, post-Romantic, and Modern eras, the basic playing abilities of wind instruments improved greatly, and composers also continued to be interested in experimenting with new sounds and colors. A typical late Romantic symphony would need more of all the wind instruments found in the Classical group (3, 4 or more of each instead of 2) as well as a piccolo, some trombones, and a tuba. It might also need a harp, English horn, bass clarinet, euphonium, piano, or saxophone, and almost certainly would call for a variety of percussion.
Improvements in wind instruments also led in the nineteenth and twentieth centuries to a blossoming of band music. Previously used mostly for military music, by the twentieth century, the band - a large group of winds and percussion - became a common vehicle for both art ("classical") and popular (especially dance and jazz) music, as well as for instructing young musicians. The typical modern "wind ensemble" includes expanded sections of all the winds found in the modern orchestra and a varied percussion section, as well as a saxophone section and a baritone/euphonium section.
But, for many arrangers, the most important development of the twentieth century was electronic amplification. Using both electric instruments and microphone-amplified acoustic instruments (including the voice) allows a much greater variety of groups that can get a big enough sound to entertain in a large hall or noisy setting.
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Traditional jazz - Cornet or trumpet, trombone, clarinet, double bass, drums, keyboard, and banjo
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Big band jazz - cornet/trumpet section, trombone section, saxophone section (including altos, tenors, and baritones, and maybe soprano and/or clarinet), and rhythm section (including drums, guitar, keyboard, and double bass or bass guitar). Some big bands also include a violin section. Any jazz group may also include a vocalist.
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Modern jazz "combo" - trumpet or cornet, trombone, saxophone, guitar, keyboard, and double bass or bass guitar
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Rock or pop band - drums, keyboard, lead guitar, rhythm guitar, bass guitar, and vocals