1/7 twist 5.56: does it reduce velocity vs 1/9 or 1/12

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It's physics. All else being equal, the faster twist will be slower and wear a bit more. Neither will be enough to worry about. The higher RPM will also stabilize the bullet better and give more consistent groups. It's all a compromise
 
The only reason to select a 1/7 twist over the slower twist is to stabilize a longer and heavier bullet. The 1/7 will allow the use of 80 grain bullets and the longer length tracer rounds.

The slower twists will not stabilize the longer, heavier bullets and thus the point of velocity is made moot. The 1/9 twist is a good compromise for all but the heaviest bullets, the one in 12 is adequate for 55 grain and lower weights.

Stability of flight is the selectiion criteria, not velocity.
 
Stability of the bullet is dependent on RPM which is determined by twist and velocity.

Sierra has found that the 69 gr MK stabilizes best with a 1/7 twist. You'll have to look the article up in their reloading manual for the details
 
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