In your bartik theme
folder there is a function
named bartik_process_page(&$variables)
.But I have to say try copying your theme
to the sites/themes
folder if you have to change or alter any theme
.Inside this function place the $variables['theme_hook_suggestions'][]
and specify the required tpl.php file
for your purpose.For example
function bartik_process_page(&$variables) {
$variables['theme_hook_suggestions'][] = 'html__test'; //Place your code here
I have a file named html--test.tpl.php
in my bartik
folder.Try clearing the cache
and run. :)