Residents have also objected to Partnerships for Renewables' Cloich Forest scheme near Eddleston.
The company says the project could generate more than 60MW of electricity and up to Â£7m for the local community.
However, the MoD has concerns about its effects on the monitoring station at Eskdalemuir in Dumfries and Galloway.
It is used to monitor for nuclear test ban treaty breaches.
The station is sensitive to turbine noise and a tolerance limit set for all wind farms within a 50km radius of the site has already been reached.
The Cloich Forest project lies just within that zone.
Last month a 10-turbine scheme near Moffat was refused by Dumfries and Galloway Council amid similar concerns.
The Ministry of Defence has opposed plans for an 18-turbine wind farm in the Borders due to fears over its impact on a seismic monitoring station.