es) and shorter notes (semi-breves). These groups could be subdivided variously into groups of two and three, giving far more variety of rhythmic development. Furthermore, different voices could be under different mensurations at the same time, allowing some voices to move at slower rates and while some move at faster rates.
Figure 7: Below is a video and transcription of an isorhythmic motet from the "Mass of Tournai" from the 14th century. Notice how the lower voices is moving at a much slower pace than the middle voice, which itself is moving at a pace both faster than the lower voice but slower than the top voice. Franconian Notation allowed composers to notate the stratification of musical lines for the first time.
Idiomatic to this isorhythmic style was the stark independence of each musical stratum. Rather than all voices having equal rates of temporal progression, voices would be intentionally set at three different rates, or mensurations. As music would continue to develop into the 14th, 15th, and 16th centuries, this rhythmic stratification would continually decrease and return to relative equality, albeit with greater rhythmic variety than found in the 13th century Notre Dame School. While the early 15th century would see the popularity of Cantus Firmus masses and motets, which utilizes a similar form of rhythmic stratification, this would decline in popularity over this century, and ultimately loose favor in the 16th century, only resurfacing in the 17th and 18th centuries, in some, mostly German, contrapuntal organ and choral works, such as in Johann Pachelbel’s and Georg Bohm’s chorale fantasias for the organ and Johann Sebastian Bach’s later cantus firmus based organ works and vocal chorale fantasias, as found in his cantatas BWV-4 and BWV-80.
In the 20th century, such stark rhythmic stratification has returned prominently in the experimental music of the rhythmic avant-garde. Composers like Olivier Messiaen, in pieces like Visions de la Amen, and Conlon Nancarrow, in works like Study No. 17 for player piano, returned to the idea of measured or “mensural” rhythmic stratification (see Figure 8 and 9). Our modern system of musical notation, while allowing for such extreme rhythmic layering, does not suggest it obviously, generally requiring all instruments within a work to share the same time signature and barlines. Furthermore, most conventional uses of our modern system require barlines at all times, and these barlines should typically be relatively short, usually 2 to 7 beats long with 7 being rather exceptional. It is nothing new to note, but an understanding of a system of music that operates without barlines, under stratified rather than homogenous rhythmic hierarchies would allow for different modes of music composition, as demonstrated in the works of the two above composers as well as Karlheinz Stockhausen, John Cage, George Crumb, and many others. Many young music students, so arbitrarily entrenched in the modern metric system, are totally ignorant of these possibilities.
Figure 8: Messiaen's "Vision de la Amen" (see my post on this piece for further information on its isorhythmic structuring.
Figure 9: Nancarrow's "Study No. 17" for player piano, which has three musical strata in canon under the temporal proportions 12/15/20, realized as the three contrasting tempos of 138, 172.5. and 230 beats per minute. The three musical lines contain all the same pitch and rhythmic content (albeit different octave transpositions), however each voice is moving at a different rate according to the three above tempos.
The second profound development in Western music notation, which has perhaps given us more than it has taken, is the proliferation of “score” notation, that is, the notation of all polyphonic parts in music such that they all visually appear meaningfully juxtaposed (usually in a vertical list) according to their progression over time. Typically, this “meaningful juxtaposition” is the precise, concordant, periodic ordering of their rhythmic events from the shortest to the longest durations within any