There are multiple classifications.
Ancient System
Stringed Instruments - Instruments played with strings.
Percussion Instruments - Played by beating/hitting/shaking the instrument.
Woodwind Instruments - Played by blowing and wrought from wood.
Brass Wind Instruments - Played by blowing and wrought from brass.
Sachs - Hornbostel
Chordophones - Played using strings.
Membranophones - Percussion instruments previously made with animal skin.
Idiophones - Played by the use of its body.
Aerophones - Played by the use of wind.
Schaeffner
Instruments with solid, vibrating bodies.
Instruments with air.
Range
Soprano
Alto
Tenor
Baritone
Bass
Contrabass
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Saxophones are reed instruments not normally found in a symphony orchestra.
then its called an orchestra
A normal full orchestra would have all instruments except for saxophone and bass clarinets.
The organization of an orchestra is hundreds of years old and fairly universal. Clarinets sit with similar instruments (like the oboe, bassoon and flute) in the center of the orchestra.
Violins! I am a keen violinist, and violins are the main instruments played in an orchestra closely followed by cellos and violas.