This is his particular area of expertise, and he carefully guides us through the field; taking common examples which cannot easily be read in terms of major or minor, he uses concepts propounded by various theorists to argue the necessity of an awareness of modal theory, and in particular the eight church modes
The sixteenth-century Magnificat, with its idiosyncratic ties to the Catholic liturgy's declining but persistent medieval system of eight church modes
, reveals tonal relationships particularly in the Magnificats of Tone Seven - that help illuminate the faceted polyphonic application of the still incompletely understood modal system.
The correspondences listed on page 17 correspond to the graph only if one corrects its mistake with regard to the Pentateuch modes, but lets stand all of the errors with regard to the church modes
Given Mathieu's advocacy of purely intoned harmony, it is curious that he explains the origin and distinction of major and minor tonalities through the concept of church modes
, a scalar system that is incongruent, if not inconsistent, with his own idea of the harmonic lattice.
Unfortunately, his nomenclature is that of the much later medieval church modes
, which applies the same and similar Greek names in quite a different way from the Greeks - the Greek Dorian scale is the Phrygian of medieval plainchant, and so on.
Take the attempt to show that the famous "songs" of the planets display between them all eight church modes
Each composition is presented in two parts: first, music and text, which includes incipit, beginning section of transcription and corresponding initial text; second, references providing location information to existing editions, length of composition expressed in number of measures, modus in reference to church modes
, number of choruses, number of voice parts, ensemble classification (such as ad voces mixtas, ad aequales, alternatim), and text and text sources.
An intermediate stage between the church modes
and major-minor tonality is evident in pieces with bifocal and migratory harmonies (see Jan LaRue, "Bifocal Tonality: An Explanation for Ambiguous Baroque Cadences," in Essays on Music in Honor of Archibald Thompson Davison [Cambridge, Mass.