Periodic frequent pattern mining (PFPM) with temporal regularity is an emerging field in data mining. The user-defined maximum periodicity threshold restricts most of the existing PFPM approaches in mining valuable patterns. The scenario is not good for real world applications. Even a pattern having all the periods below the threshold value except the one becomes irregular. In addition, the patterns with all the periods higher than the threshold value are out of consideration. Hence, there is a high chance of missing out valuable patterns in the existing approaches. To solve the problem, this paper introduces rhythmus period (RP) for PFPM. In real life applications, patterns occur with uneven temporal intervals or periods. However, uneven periods of a pattern often display some sort of consistency. Interestingly, occurrence of a pattern with consistent periods also exhibit high regularity in the database. The periods of a pattern that follow some sort of consistency are called rhythmus periods. Understanding the rhythmus periods of the patterns is of high interest in the fields of targeted marketing, targeted advertisement, intrusion detection etc. This paper introduces a new interestingness measure called rhythmus period ratio (RPR) based on the rhythmus periods of the patterns. Accordingly, a new approach termed as rhythmus periodic frequent pattern mining (RPFPM) is proposed for discovering the periodic frequent patterns without periodicity threshold. The outcomes of the comprehensive experiments on both of the synthetic and real world datasets show the effectiveness of the proposed approach.