Using case for a range of numbers in Bash

In bash, you can use the arithmetic expression: ((...))

if ((461<=X && X<=660))
then
    echo "480p"
elif ((661<=X && X<=890))
then
    echo "720p"
elif ((891<=X && X<=1200))
then
    echo "1080p"
else
    echo "DVD"
fi >> moviefinal