An Unusual Chain of Thirds: The Introit Miserere Mihi, Domine
Mahrt, William, Sacred Music
The chain of thirds is a phenomenon of the basic Gregorian repertory--that body of the Propers of the Mass found in the earliest manuscripts with musical notation. (1) Although no medieval theorist identifies this principle, it is quite clearly observable in the pieces themselves. It consists of a series of strong notes around which the melodies center, conjunct thirds, D-F-a-c-e, with A-C below, as illustrated in example 1. (2) The intervening pitches have relatively weak to strong status, with b being the weakest, then E; G and D then are of intermediate strength. It has a strong affinity with melodies in a pentatonic scales, since such scales consist of the strong and intermediate notes described here. This phenomenon was first described by Curt Sachs (3) for a wide range of melodies, including Gregorian chant, other medieval melodies, and non-Western melodies. Sachs also described the use of "dovetailed" chains of thirds, the basic chain intermixed with an alternate chain, C-E-G-b.
The strong notes of the chain of thirds are the framework of the melodic action of most chants, with the weak notes falling in the position of passing or neighboring notes to those of the chain. This is especially apparent in chants whose finals are themselves strong notes: D and F. The communion for the Midnight Mass of Christmas, In splendoribus sanctorum (example 2), is a good illustration.:
* the first phrase begins with oscillation between F and D and then adds an upper neighboring note, G, to the F;
* the second phrase adds the next higher strong note, a, with passing notes between the a and the F;
* the third and central phrase rises from the F through two notes of the chain F-a-c on the principal accented syllable "ci" forming the peak of the melody, and then descends to the F and D below;
* the fourth moves back from the D to the F, reversing the motion F to D with which the piece began.
This piece is, of course, not quite typical; its disarming simplicity relates to the stillness of the middle of the night on the longest nights of the year and the unpetentious but wondrous context of the birth of the Child. Yet the piece serves to present in the simplest form the chain of thirds in a piece whose final is a strong note.
In chants whose finals are not the strong notes of the chain, that is, E and G, the process of the melody is an intermixture of thirds based upon the final and of the thirds of the chain, a dovetailing of two distinct chains, in Sachs's terms. This can be seen in the simple psalm antiphon for Psalm 109, Dixit Dominus (example 3). This chant begins with notes, b-d, that form thirds with the final, G. It then moves through thirds downward stepwise, c-a, b-G, and finally F-a, which is extended to a full triad, F-a-c, before settling on G. There is thus a shifting between thirds based on the strong notes and those based on the final, with a stronger emphasis upon the strong notes (F-a-c) just before the final (G). This is a very characteristic pattern for pieces in modes seven and eight, on the G final.
Miserere mihi, Domine (example 4) (4) is an instance of an extended use of an alternate chain of thirds for the purpose of an eloquent representation of the text. …