In musical notation, “moto perpetuo” doesn’t so much describe a physical impossibility but rather a state of uninterrupted, uniformly moving notes—as realized by various composers in their own distinctive manners. Paganini’s Moto perpetuo for solo violin (with or without boom-chick accompaniment, or even in the vocal form called “I’m a Little Busy Body” that Jerry Lewis made famous) may be the best-known piece to carry the name, although we also know the “Perpetuum mobile” finale of Ravel’s Violin Sonata. But plenty of other pieces, such as piano etudes, have the moto perpetuo characteristics. Chopin’s Etude in A Minor, op. 10 no. 2, is a good example with its famous Bucephalus for the right hand to boom-chick accompaniment. But there are well-defined earlier examples too. Here is the Prelude from Bach’s Partita in E Major for solo violin; all but the first two bars (not shown here) consist of uninterrupted 16ths. You can surmise how the very nature of fiddling conduces to moto perpetuo practice. The shape of the melody itself implies accents in a hidden rhythm. (You don’t even have to imagine some rhythms concealed in the melody when Bach exposes them plainly in an arrangement, as the Sinfonia at the beginning of Cantata no. 29 (for concertante organ, three trumpets, drums, two oboes, and strings).
The idea of moto perpetuo applies specifically to melody — not necessarily to the principal melody in a texture. Here is an example of an interior melody in an otherwise well-defined rhythmic texture, well-shaped but subordinate to the melody above it:
This mostly harmonic interior melody (second violins) runs partly stepwise, and somewhat lacks what one would call melodic individuality, but it adds energy, in the form of steady motion, to the texture. It has a valid function that some of us irreverently call noodling, which gives instrumentalists something to do, not only to pass the time, but to do it in an animating manner — especially for strings, and often for pianists.
Motion in constant note-values is a characteristic of concertante styles from the Baroque to the 20th century; one thinks of Vivaldi’s violin concertos and their steady up-and-down bowing style that we describe as “mechanical” when repeated in patterns. Keyboard concertos begin with J. S. Bach. The first movement of Bach’s great D Minor Clavier Concerto, BWV 1052, has a vigorously rhythmic ritornello (“little returning thing”) as a main theme in various keys. In this movement of 190 bars, the various appearances of the ritornello are separated by constant-value passage work, nearly all of it in the keyboard, in episodes of 18, 11, 29, 9, 18, and 36 bars respectively — 121 bars in all, but showing dazzling variety and melodic inspiration. (This includes an unforgettably energetic moment, the solo cadenza over a tonic pedal from m. 145 to 161.)
The energy component of a texture is reducible to the smallest steady note-value, even moving between different parts, as though the total energy of the texture as a whole. I call it kinesis; it represents the sum of the smallest note-values operating together. It’s not the same thing as pulse, which has to be a unit of measure that is perceptible and countable. Think of kinesis as analogous to the enthalpy (I may well be misusing this term from physical chemistry, but I like the way it sounds) of a closed system: it encompasses all the notes that move the music ahead in time.
Chopin’s Etude in E-flat Minor, op. 10, no. 6, illustrates all of these motional types. It is a slow moto perpetuo, 3/8 in steady 16ths in an inner part; it makes use of a motivic noodle in six 16ths, with considerable chromaticism. With the kinesis mobilizing the 16th notes from beginning to end, it offers them in an accompanimental texture supporting a slow and beautifully cantabile upper melody.
The Sacrificial Dance in The Rite of Spring, provides more dramatic illustration of kinesis in a whole texture, “which I could play,” Stravinsky wrote later, “but did not, at first, know how to write.” (Get out your scores. That he had lasting difficulties with writing down the Danse sacrale can be measured by several revisions that he made over the years.) The dance is in several sections, beginning at No. 142 with a “D major” section, a basic measurement in 16ths, and an underlying irregular eighth-note pulse of constantly changing meters: 3/16, 2/16, 3/16, 3/16, 2/8, 2/16, 3/16, etc. The underlying pulse, M. M. = 126, is maintained to the very end of the work, whether notated in eighths (through no. 173) or quarters (174-185); the time signatures are often indicated in sixteenths, as just mentioned. The overall motion feels rhythmically jagged because of fermatas and breath rests, and because of the rhythmically varied melodic line.
The final section of the Sacrificial Dance begins at No. 186 (“The Chosen One dances alone while the others watch,” M. M. 126 to the eighth). In contrast to the earlier parts of the Dance, this passage (mm. 483-555 in constantly-changing meters) proceeds, with one exception, in uninterrupted sixteenths through the texture, until the last three bars of the work. This is an example of a textural kinesis: a moto perpetuo affecting all parts of the texture, which basically alternates in irregular bursts from the bottom register (bassoons, tuba, low strings, timpani, bass drum) to middle-high register (everything else). It is easy to imagine how Stravinsky discovered this kind of non-mechanistic alternation of left and right hand at the piano. The bass is always A alternating with C, separated in time by one, two, or three 16th rests (occasionally, no rest). The single exception to the uninterrupted 16ths, noted above, is at the crucial second bar after No. 197, a 2/8 bar; the downbeat of that bar is a single 16th rest in all parts — a hiccup in time that shatters the kinesis, catastrophically, for an instant before it resumes.
Other factors also drive this relentless virginal sacrifice, of course: the two-note ostinato bass that isn’t even rhythmically regular (until the next-to-last page of the score); the melodic accumulation to higher and higher points; the increasingly thicker texture. But more than any of these, it is the kinesis that propels everything, to propitiate the violent gods of spring, “like the whole earth cracking,” as Stravinsky wrote later about springtime in Russia.