It's exactly the opposite.
We can think of Tension = length x mass x pitch
This is greatly oversimplified, and doesn't actually work for calculations - the actual math can be reviewed here: https://davidvanooijen.wordpress.com/calculating-string-tensions/
But for this question we can use a simplified understanding.
For tension to remain the same, if length is reduced either mass or pitch have to be increased.
Assuming we are keeping tension and pitch the same, the mass of the string must be increased—i.e., a heavier string if the scale is shorter.
So all else equal:
Heavier strings produce more tension, lighter strings have less tension (pitch, scale length remain the same)
Longer scale lengths have more tension, shorter scale lengths have less tension (pitch and string mass remain the same)
High pitch has more tension, low pitch has less tension (length and mass remain the same)
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