Build a Middleman site and commit it to an orphan master branch, see the related blog post for the setup: http://tommaso.pavese.me/2016/05/22/how-to-deploy-a-middleman-website-to-github-pages/

middleman_build.sh

#!/bin/bash

middleman build &&
echo "--- middleman build complete"

git checkout master &&

echo "--- cleaning old build"
(ls -1 | grep -v 'build' | xargs rm -rf ) &&

echo "--- copying new build to the root level"
cp -R build/* ./ &&
rm -rf build &&

echo "--- committing"
git add . &&
git commit --message "Automated commit at $(date +"%Y-%m-%d %H:%M:%S %Z")" &&

echo "--- done"
exit 0