diff --git a/Library/Homebrew/download_strategy.rb b/Library/Homebrew/download_strategy.rb
index f2c34437d9..7c08865607 100644
--- a/Library/Homebrew/download_strategy.rb
+++ b/Library/Homebrew/download_strategy.rb
@@ -897,10 +897,16 @@ class GitDownloadStrategy < VCSDownloadStrategy
     case @ref_type
     when :branch then "+refs/heads/#{@ref}:refs/remotes/origin/#{@ref}"
     when :tag    then "+refs/tags/#{@ref}:refs/tags/#{@ref}"
-    else              "+refs/heads/master:refs/remotes/origin/master"
+    else              default_refspec
     end
   end
 
+  sig { returns(String) }
+  def default_refspec
+    # https://git-scm.com/book/en/v2/Git-Internals-The-Refspec
+    "+refs/heads/*:refs/remotes/origin/*"
+  end
+
   sig { void }
   def config_repo
     command! "git",
@@ -1069,6 +1075,30 @@ class GitHubGitDownloadStrategy < GitDownloadStrategy
       super
     end
   end
+
+  sig { returns(String) }
+  def default_refspec
+    if default_branch
+      "+refs/heads/#{default_branch}:refs/remotes/origin/#{default_branch}"
+    else
+      super
+    end
+  end
+
+  sig { returns(String) }
+  def default_branch
+    return @default_branch if defined?(@default_branch)
+
+    command! "git",
+             args:  ["remote", "set-head", "origin", "--auto"],
+             chdir: cached_location
+
+    result = command! "git",
+                      args:  ["symbolic-ref", "refs/remotes/origin/HEAD"],
+                      chdir: cached_location
+
+    @default_branch = result.stdout[%r{^refs/remotes/origin/(.*)$}, 1]
+  end
 end
 
 # Strategy for downloading a CVS repository.