The Aztec Calendar, also renowned as the Tonalpohualli, is an intricate representation of the Mesoamerican understanding of time, which is not merely a linear progression of days but a complex interplay of cycles that informs agricultural activities, ceremonial rituals, and daily life. The calendar’s depiction on a large stone monolith, often referred to as the Sun Stone, is a profound testament to the cosmology of the Aztecs. This monumental artwork, segmented into intricate designs, encapsulates the essence of their timekeeping methodology and underscores their sophisticated comprehension of cosmic cycles.

Central to the Aztec Calendar is the Tonalpohualli, which consists of 260 days categorized into 20 periods of 13 days each. Each of these periods is ascribed a specific deity and significant symbolic meaning, integrating the spiritual with the temporal. The alignment of this calendar with the agricultural cycles particularly enhances its importance, as the Aztecs relied heavily on the seasons for planting and harvesting maize, the staple of their diet. This correlation demonstrates a harmony between man and nature that governed life in the Aztec civilization.

In contrast, the Mayan Calendar, often revered for its complexity as well, operates on a dual calendar system. The Mayans employed the Tzolk'in, similar to the Tonalpohualli as it too consists of a 260-day cycle comprising 20 periods of 13 days, resembling the Aztec system in structure but differing in cultural significance and application. Alongside the Tzolk'in, the Mayans used the Haab', a solar calendar consisting of 365 days and divided into 18 months of 20 days each, plus an additional short month of 5 days known as Wayeb, which was considered a time devoid of distinct energies—a liminal moment on the time continuum. The coupling of these two calendars formed the Calendar Round, which is intrinsically aligned with agricultural practices and the cyclical understanding of life and death embraced by the Mayans.

The mutual reliance on a sacred and cyclical comprehension of time reflects a broader Mesoamerican cultural paradigm, indicating a rich tapestry of interaction and adaptation between the Aztec and the Mayan civilizations. It is notable that while both calendars share similarities in the structure and significance of their cycles, their interpretations diverge significantly, influenced by their respective mythologies, rituals, and historical experiences. This stark differentiation is underscored when we examine their respective cosmologies, guiding their understanding of existence, and the divine interplay with earthly matters.

One significant differentiation lies in the interpretation of time. For the Aztecs, the Tonalpohualli was not merely a chronological system, but a reflection of their religious beliefs. Each day was imbued with specific attributes and gods, serving as direct reflections of their worldviews. This belief system is further manifested in their rituals and ceremonies, which were often scheduled according to this calendar. These rituals could include agricultural ceremonies, warfare initiation, and even individual life events such as birth and marriage, thus interweaving the fabric of daily life with the divine.

On the other hand, the Mayan interpretative framework manifested in a more complex system of long-count markings for greater calendrical analysis. The Mayan calendar, with its Long Count, not only tracked days but encompassed larger temporal cycles, marking significant dates with an intricate combination of numerology and astrology. This enables the Mayan civilization to document historical events with remarkable accuracy, evidenced through their inscriptions on monumental architecture and Codices that have survived the passage of time.

Moreover, the Long Count calendar measures time in units of 20, which allows for a vast recording of historical chronology that reflects a deeper understanding of cycles spanning millennia. The Mayans believed that the world underwent cycles of creation and destruction, which revolved around both the material and the spiritual. Such a belief system urged their societies to frame historical events within the mythological backdrop of their creation stories, giving historical events a cosmic significance that was arguably different from the more immediate, agrarian focus of the Aztec calendar.

The overlapping cultural milieu of these two civilizations followed a shared historical trajectory wherein their calendars influenced one another across centuries. There exists an abundance of evidence indicating a degree of cultural interaction, ranging from trade networks to artistic exchanges that facilitated the blending and evolution of Mesoamerican practices. The migration waves and the subsequent ascension of the Aztec Empire certainly played a role in shaping their interpretation of time, borrowing from established traditions of their predecessors, including aspects of the Mayan Calendar.

When investigating their respective mythologies, we delve into the symbolism associated with their calendars that further accounts for differences in application and significance. For instance, while the Aztec calendar is heavily laced in warrior culture and entwined with concepts of duality, such as night and day, their celestial orientation propels them towards a more direct association with concepts of duality and balance. The belief that the sun required human sacrifice to rise each day underscores their perspective of time being a cycle of renewal and sacrifice, directly influencing subsequent societal behaviors and norms.

Conversely, the Mayans viewed time as a more cyclical passage, which embraced continuity, eternity, and the natural transitions between light and darkness. The sacredness of time in Mayan culture manifested in their poetic traditions and elaborate oral histories, which showcased the relationship they perceived between celestial bodies and cyclical events in the natural world. Consequently, the understanding of time as eternal fosters a unique interaction with their earthly existence. This philosophical distinction gives rise to a multitude of interpretations, as certain periods for the Mayans are associated with auspicious times for planting or harvesting, while others might be indicated as times of caution.

The advent of modern scholarly interpretation into both the Aztec and Mayan systems reveals the complexities that have been intertwined through language, history, and mythology. Currently, extensive archaeological and linguistic analyses provide insights into the calendars as synchronous cultural frameworks, assisting historians and archaeologists in piecing together the fragmented legacies of these ancient peoples. The significant similarities and contrasts found in their calendars not only reflect their respective positions within the Mesoamerican landscape but also highlight the shared spirit of an enduring legacy that encapsulates historical human understanding.

As we examine the cosmologies that informed these societies, it also draws attention to the overarching themes of nature, existence, sacrifice, and rebirth that are common across Mesoamerican civilizations. The calendars are more than just methodologies of timekeeping; they are a sophisticated manifestation of how humanity has attempted to derive meaning from existence, navigate the complexities of life, and ultimately find balance within the cosmos. The calendars of the Aztecs and Mayans speak to the intrinsic need for order, harmony, and understanding in the face of chaos and uncertainty, which is remarkably relevant even in contemporary times.

In conclusion, the Aztec and Mayan Calendars reveal the rich tapestry of Mesoamerican civilization that goes beyond mere chronology. Their respective interpretations of time are not mere echoes of one another but reflections of cultural identities that demonstrate a complex interplay of mythology, agriculture, spirituality, and societal norms. Through the lens of these calendars, we gain a profound understanding of the ways in which ancient societies structured their lives and rituals, offering a glimpse into the human condition that transcends historical boundaries, capturing the essence of time and existence through the eyes of two remarkable civilizations. This intricate relationship between the Aztec and Mayan calendars emphasizes not only their distinct identities but also their shared legacy as vital chapters in the story of Mesoamerican history.