MODI

MODI. — The term m. in music is used both in rhythm and in harmony.

1) In a rhythmic sense it refers, in the music of the 12th and 13th centuries, to the six metrical schemes taken from classical prosody (trochaic, iambic, dactylic, anapestic; less frequent, spondean and tribrachic) on which the *vagantes* modelled their songs. It is also applied to the chosen duration value as a unit: *modus maior*, graphically represented by the *maxima*; *modus minor* by the *longa* (both completely blackened); *modus perfectus*, ternary; *modus imperfectus*, binary. Often the key signature indicates (closed circle for the perfect m., semicircle for the imperfect m.) the nature of the chosen measure. This system applies to the music of the 15th and 16th centuries, written according to proportional notation.

2) In a harmonic sense, modern music knows two m.: major and minor, distinguished by the placement of the two semitones in the eight-note scale: for the major, the first semitone is two whole tones from the tonic; for the minor, it is one and a half tones away. The tones are nothing but transpositions of the two modal successions, major and minor.

3) By confusion, one speaks of “ecclesiastical” or “Gregorian tones,” whereas correct terminology adheres to the word “m.” for the harmonic systems that underlie the monodic compositions of both Greek music and Western medieval liturgical and secular music.

Until the first decades of the 20th century, the question of Gregorian modes seemed resolved with the explanation of “complete and homogeneous” scales of three tones. Discussion concerned only the number of these scales, their Greek or Eastern origin, whether they had a proper expressive character, and from which modal scale the modern major and minor had developed. Gregorian studies undertaken by the Solesmes school have highlighted far more complex problems and proposed objective solutions that are not negligible, even if not entirely definitive. The first aspect of the modal question is summarized under the generic term traditional theory (classical theory or theory of the *octoechos*); the questions that have arisen since about 1920, on the other hand, generally fall within the framework of the modern theory or exochordal theory.

I. TRADITIONAL THEORY

The theory of the eight modes, as can be gathered from the writings of medieval authors, is based on a few points. Although it is possible to construct a scale of tones using only four fundamentals—the famous tetrachord of finals: D, E, F, G, respectively for the protus, deuterus, tritus, and tetrardus—each of the scales results from the pairing of a fixed pentachord and a mobile tetrachord: D–A + A–D in the protus. The mobility of the tetrachord above or below the pentachord makes possible the double form, authentic and plagal, of each of the four scales, which always preserve the same final or fundamental; thus the authentic protus, 1st mode, extends from low D to high D, while the plagal protus, 2nd mode, goes from low A to high A. These are not two different scales, but two forms of the same scale, since the final is identical in both cases, namely D; the difference is that a plagal melody unfolds in the lower part of this scale, while an authentic melody prefers the upper part. Ancient theorists did not have as clear a concept as moderns do of the existence and function of a dominant; modern followers of the traditional system have considered the eight reciting tones (*tenores*) of the psalmody formulas—la, fa, la, do, la, re, do—as constructive data; they have introduced new elements by affirming the presence of the harmonic dominant (the fifth) not only in authentic modes but also in plagal ones; they have applied to the repetition of the final in the upper octave of the authentics the same property of repose of the final as at the base of the scale, so that in Gregorian melodies a double law would be verified: 1) attraction toward the extreme notes as centers of repose (tonic-final-fundamental) in authentic modes; 2) repulsion from the extremes toward the center in plagal modes.

Although the final notes are D, E, F, G, some melodies in the current editions, and many more in the diastematic manuscripts, cadence, definitively or provisionally, on the other three higher notes, namely A, B, C. Perhaps, in order not to multiply the psalmody formulas, but above all because the determination of the mode of a melody was made solely by considering the species of the fixed pentachord (or tetrachord), theorists did not hesitate to classify melodies ending on A, B, C as protus, deuterus, and tritus, despite the difference in harmonic structure from the modes on D, E, F.

The greater importance recognized for the basic tetrachord is confirmed by the few examples of modal analysis left by Ubaldo (Gerbert, *Scriptores ecclesiastici de musica sacra*, I, St-Blasien 1784, p. 140) and by Regino of Prüm (ibid., I, p. 231), who identify modulations by referring to modal formulas: these characteristic formulas of the mode never reach the span of an octave, generally content themselves with a single semitone, and exceed the limits of the tetrachord only slightly.

The name *octoechos* given to the theory of the eight modes, together with other terms and particularities, suggests a Byzantine importation into the Western system. Both the Byzantine and Western modal systems, as well as the traditional and modern theories, owe a debt to Greek musical modes, at least insofar as they share the same foundation, namely the tetrachord. In Gregorian chant itself, the melodies of deuterus (3rd and 4th modes with final E and harmonic division fourth plus fourth, with A, the ancient *mese*, as the central pivot) can, without too much daring, be relocated with the Greek Dorian mode.

Table of the eight modes according to traditional theory.

| Protus authenticus | 1st mode |
| Deuterus plagalis | 4th mode |
| Tritus authenticus | 5th mode |
| Tetrardus plagalis | 8th mode |
| Assimilated modes | |
| Protus authenticus | 1st mode |
| Deuterus plagalis | 4th mode |
| Tritus authenticus | 5th mode |

II. MODERN THEORY OF THE THREE EXACHORDS

Based exclusively on the analysis of the melodies published in the Vatican edition of 1905 and 1907, Fr. J. H. Desroquettes, a monk of Solesmes, was the first to affirm the existence of three groups of modal cadences in which the ancient melodist chose the harmonic material for his compositions.

He was followed in the development of the new theory by Prof. H. Potiron, organist, composer, and theorist, and by Abbot Suñol. The justification and explanation of the new system rests primarily on the observation that medieval copyists supported the cadences of the *protus* on D, G (with B♭), and A; the cadences of the *deuterus* on E, A (with B♮); the cadences of the *tritus* on F, B♭, and C; and the cadences of the *tetrardus* on G and C. A single cadential note with a few intervals above and below suffices to define one of the four modes, which will then be either authentic or plagal, taking into account the greater development above or below the fundamental. In a modal system understood in this sense, there exists only one semitone: the appearance of a new semitone almost automatically determines a modulation—tonal if, in the new hexachord, one remains in the same mode; tonal and modal if, in the new hexachord, one also changes the mode. For example, if one leaves the *protus* in D (natural hexachord) and modulates to a cadence on A at the fifth with B♮, one passes into the hard hexachord and remains in the *protus*; if one cadences on natural B, the modulation is tonal (from the natural to the hard hexachord) and modal (from the *protus* to the *deuterus*). In addition to the appearance of a new semitone, the insistence on intervals characteristic of a mode and cadences outside the tetrachord of the modal notes also determine modulations.

The essential difference between this system and the traditional system lies in the abandonment of the classic pentachord-plus-tetrachord structure, i.e., the seven-note scale of consecutive tones. The traditional theory was at first nothing more than an easy method of classification; the modern hexachordal theory claims more: it seeks to discover the modal principle of Gregorian melodic composition. While the traditional theory still distinguishes, like the Greeks, the various species of tetrachords (Dorian, Phrygian, Lydian), the modern theory, though speaking always of tetrachords, practically overlooks the ancient distinction, since the tetrachord of the modal notes is not organic: indeed, any one of the four notes can be a final; but E (A in the soft hexachord, B in the hard hexachord), even if it is a final, will not be considered a fundamental. Moreover, the other three finals and fundamentals are not the starting point of a tetrachordal system that can then be recognized in the melodies. Thus, the three tetrachords C–D–E–F, D–E–F–G, and E–F–G–A are not distinguished; rather, it is the single tetrachord C–D–E–F that is repeated three times in the sound diagram.

The importance of the modern theory is highlighted by the ease and coherence it provides in the analysis of Gregorian melodies; on the other hand, it is believed that this system does not distort the modal character of the melodies one wishes to accompany: the accompaniment must and can thus better follow the continuous ebb and flow of the melody, which is rarely fixed in either a mode or a tone. The traditional theory is less aware of this.

**Schema of the 4 modal cadences in the 3 hexachords**

| Mode Tetrardus | Protus | Deuterus | Tritus | Complementary hexachord notes |
|----------------|--------|----------|--------|-------------------------------|
| C | D | E | F | G A (natural hexachord) |
| F | G | A | B | C D (soft hexachord) |
| G | A | B | C | D E (hard hexachord) |

The *ethos*, that is, the expressive character of the individual Gregorian modes, cannot be determined a priori: ancient and modern theorists do not agree on the psychological effect to be attributed, for example, to a second or a fifth mode. The most varied texts and the most opposing sentiments can be musically expressed in any of the eight modes. Joy is not always and only illustrated with melodies of the fifth mode, nor sadness with melodies of the second mode. It is true that a well-defined modal system modifies the expression of a given sentiment and paints it with its own colors, but in Gregorian melodies, even in their most archaic form, frequent modulations mitigate at every moment the dominant impression that would result from the prevalence of one mode over the others.

**