This technical note describes the results of a preliminary investigation into measures for software architecture. It focuses on measures that directly indicate the health of or detect a problem with the software architecture of an up-and-running software system. Defining these architectural measures is very difficult. The software architecture deeply affects the subsequent development and project management decisions, such as the breakdown of the coding tasks and the definition of the development increments. Most existing measures for up-and-running software systems capture the cumulative results of architectural, developmental, and managerial decisions and do not directly address the health of the software architecture. The investigation into measures requires the joint participation of the software architecture and measurement communities. Since the software architecture community has made such rapid progress over the past ten years, this report first describes what the measurement community needs to know about software architecture to understand the difficulty of defining architectural measures. The current relevant literature is then described in terms of its potential contribution to this research. Finally, the report identifies areas for future research into the application of measurement technology to software architectures. The ultimate goal of this body of work is to provide measurement guidance and quantitative decision support to software practitioners, including software architects and project managers.