For many musicians, especially those more familiar with other styles, a fundamental early question concerns the chords of medieval music. While a description of chords can become rather technical, the interested amateur will find it fascinating when supplemented by recorded examples, and when considered in small pieces. The following discussion is written in an open and inclusive manner, and should remain approachable for the careful reader.
The use of chords, or what we might call "vertical structure" to distinguish it from the "horizontal structure" defined principally by melody, is a topic which is both crucial for understanding the music itself and illustrative of general conclusions about polyphonic music. First it is important to understand that medieval composers did not use "harmony" in a sense which classical composers would have understood. This is perhaps most easily grasped by realizing that the lowest voice of many of the most elaborate polyphonic works of the period consists of a pre-existing melody, often plainchant. Other melodies were added to these, and each layer would have its own horizontal concerns. Of course, in the greatest masterpieces, the vertical elements add something tangible to this mix, without sacrificing the horizontal beauty.
Cadential motion, i.e. the way in which individual phrases are brought to a close, is crucial for understanding this structure, and so must play a major role in subsequent discussion. Such ending motion is crucial to horizontal ideas as well, just as the "final" (or last note) of a mode is fundamental to defining it. Of course modality is a theoretical idea specifically developed for application to the system of Gregorian plainchant which underlies medieval polyphony, and so is never too far removed from polyphonic music. Nonetheless, it is generally not possible to assign modality to polyphonic music of this period, unless it is notionally assigned based on that of the lowest voice, a common technique. Ideas to let this modality dictate chord structure, and thus accidentals in other voices, are frequently flawed.
Much of Early Music history can be viewed as a series of changes to cadential formulas & combinations. For instance, the earliest Western polyphony generally cadences on the unison. Shortly afterward (by epochal standards, anyway) composers start cadencing on octaves & fifth combinations. Eventually this gives way to more frequent use of the third, and then to fully third-based cadences in the high Renaissance. At this point, cadential formulas become more evidently analogous to the triadic system which today we call "common practice" harmony. Nonetheless, the differing idioms of these intervening centuries provide many stimulating ideas on chord construction & combination. A developing set of articles here, most by Margo Schulter, will hopefully provide a glimpse of some of this richness.
This article provides a fine orientation to the general context in which discussions on chord structure in medieval music will take place, illustrating examples from what is perhaps the most dynamic & exciting period in the history of the development of polyphony.
This article is even more extensive, surveying what is known about medieval approaches to tuning, the Pythagorean system in particular, as well as a broader history of Western tuning in general. It provides a wide range of informative discussion on tuning issues in polyphony.
This extensive article discusses the role of hexachords & solmization in medieval music, how they affect musica ficta choices, and how they interact with other concerns of the era.
The articles on hexachords & Pythagorean tuning serve to illuminate underlying concepts which frame the idea of medieval chord structure per se. In many ways, issues of tuning and solmization are sufficiently different from the modern reader's intuition that without these discussions, it can be difficult to appraise the medieval approach to vertical structure.
With some luck, and some interest from readers, other articles of this type can be developed.