This paper introduces a novel annotation framework for the fine-grained modeling of Noun Phrases' (NPs) genericity in natural language. The framework is designed to be simple and intuitive, making it accessible to non-expert annotators and suitable for crowd-sourced tasks. Drawing from theoretical and cognitive literature on genericity, this framework is grounded in established linguistic theory. Through a pilot study, we created a small but crucial annotated dataset of 324 sentences, serving as a foundation for future research. To validate our approach, we conducted an evaluation comparing our continuous annotations with existing binary annotations on the same dataset, demonstrating the framework's effectiveness in capturing nuanced aspects of genericity. Our work offers a practical resource for linguists, providing a first annotated dataset and an annotation scheme designed to build real-language datasets that can be used in studies on the semantics of genericity, and NLP practitioners, contributing to the development of commonsense knowledge repositories valuable in enhancing various NLP applications.