Logs are crucial for analyzing large-scale software systems, offering insights into system health, performance, security threats, potential bugs, etc. However, their chaotic nature$\unicode{x2013}$characterized by sheer volume, lack of standards, and variability$\unicode{x2013}$makes manual analysis complex. The use of clustering algorithms can assist by grouping logs into a smaller set of templates, but lose the temporal and relational context in doing so. On the contrary, Large Language Models (LLMs) can provide meaningful explanations but struggle with processing large collections efficiently. Moreover, representation techniques for both approaches are typically limited to either plain text or traditional charting, especially when dealing with large-scale systems. In this paper, we combine clustering and LLM summarization with event detection and Multidimensional Scaling through the use of Time Curves to produce a holistic pipeline that enables efficient and automatic summarization of vast collections of software system logs. The core of our approach is the proposal of a semimetric distance that effectively measures similarity between events, thus enabling a meaningful representation. We show that our method can explain the main events of logs collected from different applications without prior knowledge. We also show how the approach can be used to detect general trends as well as outliers in parallel and distributed systems by overlapping multiple projections. As a result, we expect a significant reduction of the time required to analyze and resolve system-wide issues, identify performance bottlenecks and security risks, debug applications, etc.