Pagination not working on homepage

This is my working pagination query. I’ve updated it to use the parameters in your question:

<?php 
if ( get_query_var('paged') ) {
    $paged = get_query_var('paged');
} else if ( get_query_var('page') ) {
    $paged = get_query_var('page');
} else {
    $paged = 1;
}

$args = array(
    'post_type'      => array('post', 'music', 'videos'),
    'post_status'    => 'publish',
    'posts_per_page' => 10,
    'orderby'        => 'date',
    'order'          => 'DESC',
    'paged'          => $paged 
);

// Create new query
$temp = $wp_query; 
$wp_query = null; 
$wp_query = new WP_Query(); 
$wp_query->query( $args );
while ($wp_query->have_posts()) : $wp_query->the_post(); 
?>

<!-- add your content -->

<?php 
    // End the custom loop    
    endwhile; ?>

<?php 
    // This is where I put my pagination, included from another file
    echo get_template_part( 'pagination' ); ?>

<?php
    // Need this to reset the query
    $wp_query = null; 
    $wp_query = $temp;  // Reset
?>

I see you’re using numbered pagination, while I am using the default wordpress next and previous pagination. I don’t think there will be a problem using this code for either type.

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