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Extensio and fractio modi

In a previous video we gave you an overview of the basic technique of transcribing modal notation as well as of the fundamental principles of composition of the Notre Dame organum. Here you will find a short résumé of the two central compositional concepts, extensio modi and fractio modi.

Modal notation does not offer many possibilities for rhythmic variety. Its six patterns can of course be combined and the voices can change modes several times during the course of a composition. Nevertheless modal structure is somehow limited. The modal pattern of a musical phrase could be modified by interpolating single notes in the phrase. In order to bring more variety to the rigid modal structure, two compositional devices were employed, which were able to interrupt the uniformity of the rhythmical flow: the extensio modi and the fractio modi. In both cases, modal notation allows to make some adjustments to the rhythmic framework through the modification of the ligature structure.

The musicologist Willi Apel defines the extensio modi as follows:

This term is used here to denote the occasional omission of a brevis (eighth-note of the transcription). Such a modification of the modal pattern is very frequently used at the end of an ordo. (Apel 1953, p. 234)

Extensio modi from the Transcription of the clausula GoClausula Go. © Firenze, Biblioteca Medicea Laurenziana, Plut. 29.1 fol. 11r

This passage is set in the first mode. In the facsimile you can see a single note at the end of the ordo, which breaks the flow of two-note ligatures. This note causes the interruption of the rhythmic pattern by extending the two last notes.

And here is Willi Apel’s definition of the second compositional practice, the fractio modi:

This term signifies the opposite procedure of extensio modi, that is, the breaking up of the normal pattern of the modal rhythm into smaller values, preferably of the longa into two breves. (Apel 1953, p. 235)

Fractio modi from the Transcription of the clausula GoClausula Go. © Firenze, Biblioteca Medicea Laurenziana, Plut. 29.1 fol. 11r

This excerpt shows an ordo in the first mode, its end indicated with a vertical dash on the right-hand side. Within the pink circle, you see a single note that is followed by a four-note ligature: we are confronted here with some exceptions.

The single note, being situated within the ordo and therefore to be read in the pattern of the mode, corresponds to the value of a quaver. We would need to read it differently if it appeared at the end of the phrase: then it would signal extension (in the sense of extensio modi).

After the single note we would probably expect a unity of three notes, expressing the pairing required by the first mode to be continued. In other words, we would assume that the passage encircled should provide the succession of short-long note values. But the following four-note ligature exceeds the first mode by one note (no such a ligature is foreseen in that mode). As we have an unexpected ‘surplus’ note at the beginning of the ligature, we need to adapt our interpretation. The solution of the puzzle is, that we have to read the first two notes of the four-note-ligature as corresponding to two short note values, followed by a standard short value and a long value that resume the pattern of the mode. Thus, instead of a long note value at the beginning of the four-note ligature we will have two short notes that literally break up the mode: a so called fractio modi occurs.

A plica can also be considered a form of fractio modi, for at the end of the second ligature a smaller note value breaks the pattern of the mode.


Apel, Willi. The Notation of Polyphonic Music 900–1600. Cambridge MA: The Medieval Academy of America, Fifth Edition, 1953.

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This article is from the free online course:

From Ink to Sound: Decoding Musical Manuscripts

University of Basel