Gallery of Interesting Music Notation

Music Notation and Music Representation

Below is a little "gallery" of unusual music notation from the works of respectable composers and publishers, most of them very well-known. I also present examples of unusual music notation, and discuss the issues of music notation and representation and their relation to knowledge representation in general, on the IU Music Informatics website, as well as in a talk entitled "Music Notation, Representation, and Intelligence" that page links to. The commentary on the current page is intended more for the casual observer, but its gallery of notation examples is considerably larger.

To clarify the difference between notation (essentially, graphical) issues and representation issues, this extraordinary slur, by far the most complex I know of, is from Sorabji's Opus Clavicembalisticum (1930), IX [Interludium B] (Curwen ed., pp. 175-176). It has a total of 10(!) inflection points; it spans three systems, repeatedly crosses three staves (this is also the most staves in a single system for any slur I know of), and goes slightly backwards--i.e., from right to left--several times. However, the complexity is almost entirely graphical: its implications for representation are minimal.

 

A phenomenon that -- in terms of music representation -- is much deeper appears in a passage from a Chopin Nocturne (Op. 15 no. 2) in which one notehead is a triplet in one voice, but normal duration in another. Consider the last note of the measure, and notice that both "versions" of the note end at the barline; therefore, in the upstemmed voice, it begins earlier than in the downstemmed one! But surely Chopin didn't intend it to be sounded twice, and pianists never play it that way. How should it be represented? It's not easy to say. And this "impossible" rhythm, where a single notehead that's part of two voices has interpretations in the voices that are inconsistent, isn't as rare as you might think: Julian Hook has found dozens of examples in the works of Brahms, Chopin, Rachmaninov, etc.

The Brahms Capriccio for piano, Op. 76 no. 1, is in 6/8. A dotted half note lasts a full measure of 6 eighths, or 12 16ths; but this passage has a a dotted half note that lasts only eleven 16ths (on the top staff, in the second measure of the excerpt). Why? Notating a duration of 11 16ths "correctly" would have required four tied notes, but the fact that the dotted half note actually used really lasts to the end of the measure and no longer is obvious -- so obvious that, surely, few people even notice the inconsistency. Clearly, it's written the "shorthand" way it is to avoid the clutter of four notes and three ties.

This notation is much like the well-known "variable dot" of Baroque music: a dot may increase the duration of a note by more or less than the standard amount. For example, the D-major Fugue in Book I of the Well-Tempered Clavier has several instances of a quarter-note duration filled by a dotted eighth and three 32nds. Either the 32nds form an unmarked triplet, or the dotted eighth is short for an eighth tied to a 32nd; all experts agree on the latter interpretation. (Cf. Rastall (1982), p. 214.)

This passage from Debussy's La Danse de Puck has a clef in mid-air, applying only to the note to its immediate right, while a different clef appears on the staff they belong to. Thus, it's bizarrely obvious that two clefs are simultaneously active on the staff. On the other hand, a subtle way to have two simultaneous clefs on a staff appears in the fourth measure on the lower staff of this excerpt, from Scarbo in Ravel's Gaspard de la Nuit. The passage is in 3/8 time, so the bass and treble clefs are both in effect for this entire measure! The obvious reason in these and other cases of two clefs simultaneously active on a staff (in music by Brahms and others, as well as other works of Debussy) is simply to save space by avoiding a third staff.

A passage from J.S. Bach's Goldberg Variations, no. 26, changes time signature in the middle of a measure (at the beginning of the excerpt, the lower staff is in 3/4, the upper in 18/16). Since a time signature describes the total duration of the measure, what could this possibly mean? Actually, a time signature describes the metric structure of the measure as well as its duration; this change occurs on a beat, and it goes from a simple triple (3/4) to a compound triple meter (18/16), while the other change in the excerpt does the opposite. The only reasonable interpretation is that -- with each meter change -- an equivalent tempo change keeps beats the same (real-time) duration, and what's happening is simply a change from duple to triple subdivision of the beat. Indeed, the passage is invariably performed that way. So Bach (or his editor) could just have written the 18/16 parts in 3/4, but with continuous sextuplets.

 

Other Examples

Briefly, here are a few more examples. All are interesting as examples of notation, but most aren't of much interest in terms of representation except to suggest the lengths to which composers and publishers have pushed every parameter.

Bach's Jesu, Joy of Man's Desiring, in the well-known piano arrangement by Dame Myra Hess (Oxford), has single notes (not part of a chord) on the "wrong" side of the stem almost from beginning to end. Why? Simply to show three independent voices on one staff.

By far the shortest notated duration I know of appears in this page of Anthony Phillip Heinrich's Toccata Grande Cromatica from The Sylviad, Set 2, m. 16 (c. 1825). At the very end of the page--the end of the last measure on the lower staff of the bottom system--there are some 1024th and even two 2048th(!) notes. However, the context shows clearly that these notes have one beam more than intended, so they should really be 512th and 1024th notes, respectively. The passage--in 2/4, marked "Grave"--also contains many 256th notes. (How reasonable these durations are can be inferred from the fact that even at a tempo as slow as M.M. eighth = 40 (quarter = 20), a 1024th note would last about 1/85 sec. The next shortest notated durations seem to be 256ths in works of several composers going back as far as Vivaldi.)

Here's a passage from Marcello's Stravaganze in which inconsistent note spellings are carried to an extreme. The passage is actually rather simple, but it begins with the voice in the bizarre key of A-sharp minor while the keyboard part is in its (far more normal) enharmonic equivalent, B-flat minor! By measure 3, the two parts have swapped keys; then they repeatedly swap back and forth.

Double sharps and double flats aren't too unusual, especially in passages in "remote keys" with many sharps or flats in the key signature. But -- while they're very rare -- triple sharps and flats have appeared in print! One example is this F triple-sharp (used as a lower neighbor between two G double-sharps) near the end of the last movement of Reger's Clarinet Sonata, Op. 49 no. 2, piano part (1904; Universal ed.); it's in the right hand, in the last measure of the excerpt.

Finally, this passage from a keyboard piece by Johann Kuhnau illustrates a very unusual way to notate unison (dotted) whole notes in two voices on a staff: one note is inside of the other! It's on the downbeat of the 2nd measure of the 2nd system, top staff. This is largely a curiosity, but notice that the standard way of notating this, namely two dotted whole notes side-by-side, presents the problem of where to put the second augmentation dot.

Last updated: 16 April 2008
Comments to: donbyrd(at)indiana.edu
Copyright 2006-08, Donald Byrd