Fireworks images from a T2i and a Tamron 18-200mm lens, handheld.
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Focal Length: 38.0mm
Aperture: f/4.0
Exposure Time: 0.0050 s (1/200)
ISO equiv: 4000
Exposure Bias: none
Metering Mode: Matrix
Exposure: shutter priority (semi-auto)
White Balance: Auto
Flash Fired: No (enforced)
Orientation: Normal
Color Space: sRGB
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Focal Length: 80.0mm
Aperture: f/5.6
Exposure Time: 0.0040 s (1/250)
ISO equiv: 400
Exposure Bias: none
Metering Mode: Matrix
Exposure: shutter priority (semi-auto)
White Balance: Auto
Flash Fired: No (enforced)
Orientation: Normal
Color Space: sRGB
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Focal Length: 60.0mm
Aperture: f/5.0
Exposure Time: 0.0040 s (1/250)
ISO equiv: 5000
Exposure Bias: none
Metering Mode: Matrix
Exposure: shutter priority (semi-auto)
White Balance: Auto
Flash Fired: No (enforced)
Orientation: Normal
Color Space: sRGB
The technique used here is to choose a shutter speed and let the camera figure out everything else. There's no reason to worry about background because it's going to be black, regardless of everything else.