Helmholtz and Ellis established the basis of modern tuning theory, and provide an interesting late-19th century perspective on tuning. On the subject of just intonation, Ellis seems far more cognizant of its limitations than Helmholtz, who glosses over them in his great zeal for pure consonances. Ellis' theory of duodenes [12, 457-66] is suggestive of a two-dimensional representation of pitch class in terms of P5 and M3. This idea partially inspired the notion of triadic pitch class used in this thesis. A duodene is a simple slip-free triad set, an important concept in this thesis' coverage of just intonation.