Simply paste the following code into your functions.php file.
function custom_body_class($classes){
if(is_singular()){
$myvar = "myparam";
} else {
$myvar = "anotherparam";
}
global $post;
array_push($classes, $myvar);
return $classes;
}
add_filter('body_class', 'custom_body_class');
Of course, feel free to adapt the code to fit your needs. For example, a great use can be in multi-language sites: The custom parameter can be used to output the current language in the body class.
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Add custom parameters into the body_class() function