In Disputatio musica tertia (1610) and Synopsis musicae novae (1612), Johannes Lippius (1585-1612) offered a method for teaching composition from the bass voice using triads. Though this approach seems straightforward and intuitive today, Lippius's didactic process was revolutionary in the early seventeenth century for several reasons, most notably: (1) a focus on homophony, (2) an identification of the bass voice as the "fundamental melody," (3) a use of triads to structure verticalities, and (4) an integration of triadic theory and contrapuntal practice. Two decades later Heinrich Baryphonus (1581-1655) and Heinrich Grimm (ca. 1592-1637) were among the first writers to adopt Lippius's triadic approach. They included an extensive passage on triadic composition from the bass in the second edition of Pleiades musicae (1630). Like Lippius, Baryphonus and Grimm focused on homophony, treated the bass voice as a foundation, and combined triadic and contrapuntal approaches, but despite abundant similarities between these texts, subtle differences in methodology emerge. In this paper, I examine the pedagogical approaches of Synopsis musicae novae and Pleiades musicae, teasing out minute, yet significant variations that hint at Baryphonus and Grimm's fundamentally divergent orientation to composition from that of Lippius regarding the primacy of horizontal and vertical elements. In the process, I highlight two possible methods for reconciling the established field of counterpoint with an emerging theory of harmony in the early seventeenth century, a highly developmental period in music-theoretical thought.