Book excerpt: This book shows teachers and students how meter fundamentals are taught through Ski-hill Graph Pedagogy, the three-step psychoacoustic mathematical music theory approach developed by music educator-researcher Andrea M. Calilhanna, inspired by contemporary meter theory of Battell Professor of the Theory of Music, Yale University, Richard Cohn. The ski-hill graph enables students to visually represent meter fundamentals mathematics through a soundbased approach experienced from listening to music in the first lessons! Students taught the meter as time signatures and beats grouped in measures understand meter as the notation. However, the ski-hill graph is a solution for understanding meter because music is acoustics (sound) and listening is central to Cohn’s sound-based theories. To apply accurate meter mathematics from the ski-hill graph to music preparation means students save time later in rehearsals from a solid start to decode their work. Visualising meter through the ski-hill layout as a summary of all pulses and all meters from listening assists students to understand their meter experiences and its mathematical aspects. Students listen, clap, tap and map with mathematics: meter beat-class, first through the ski-hill, then they apply the ski-hill mathematics to annotate, practice and compose music through other representations such as linear and circle graphs. In this way, students not only become aware of new information, but they also understand their new knowledge. Knowing and understanding mathematical elements of meter means the theory can apply to performance to improve timing, inform expression, sight-reading and much more! Without skills to analyse meter from listening to music, many important details are left out because they are hidden by notation-based understandings of music analysis. Cohn’s theories of meter, however, offer solutions to understand each pulse and meter as cycles to decode music performed and listened to. The book works through small cycles to grow listeners’ awareness of mathematical aspects of meter: mathematical music theory. The Ski-hill Graph Pedagogy approach provides students with several benefits for meter fundamentals pedagogy, including development of mathematical knowledge and practical skills to understand musical timing and expression, and increased performance confidence through more secure performances from critical thinking and metacognitive processes. Ski-hill Graph Pedagogy is suitable for most teaching styles, and provides inclusive, ethical music theory for diverse music education. Suitable for teaching meter fundamentals with students of all ages.