Research on drone swarms has gained traction in recent times due to their ability to outperform single drones in various tasks. In order for autonomous drone swarms to carry out tasks effectively, it is crucial that the tasks are distributed among the drones. This poses a considerable challenge that must be addressed in the advancement of drone swarm technology. The assignment problem is basically defined as the process of assigning M tasks to N drones in a way that minimizes the total cost. This paper presents an auction-based distributed task allocation algorithm called Harmony DTA (Drone Task Allocation) for heterogeneous drone swarms. Prior research primarily focuses on minimizing overall costs associated with assignments. In contrast, Harmony DTA not only minimizes total costs through an enhanced cost calculation function, but also ensures equitable distribution of workload among drones. Additionally, the proposed two-stage auction process reduces the total message size utilized during communication. Matlab simulations and field tests were conducted to assess the effectiveness of the proposed algorithm. Moreover, the algorithm's performance was evaluated in comparison to the CBBA (Consensus Based Bundle Algorithm). The results obtained indicated that the proposed algorithm is capable of assigning tasks with high efficiency, without encountering conflicts.