IX. Beams and Tuplet Notation
Beams may be extended over any number of eighth, sixteenth, or thirty-second notes. Beams are used to show note groupings equivalent to a single longer note, as shown below.
While beaming is common in instrumental music, in vocal music eighths and shorter values often appear unconnected, with flags, when each note carries a single text syllable. Beams are used more often when one syllable is sung across a group of notes.
Repeating Example 16 A and B, we recall that triplet notation can be used to show the division of a quarter note into three eighth notes.
Ex. 40 repeat of example 22 A and B
As determined earlier, the slur and number are required to indicate divisions that cannot otherwise be indicated in basic binary notation. Example 41 shows how beaming is used to indicate divisions of the quarter note. Divisions of eighth, sixteenth, and thirty-second notes can be beamed with no slurs, since these divisions fall into the normal binary system. Other divisions will require slurs and numbers.
The convention is to keep adding the same note value to a natural group until the next natural group comes up. In Ex.41, four 16ths is a natural group and needs no modifying number. 16ths are added to form 5-, 6-, and 7-note groupings (quintuplets, sextuplets, and septuplets, respectively); the 8-note grouping can be expressed naturally with thirty-second notes. This means that groupings of 9, 10, 11, 12, 13, 14, and 15 would all be expressed in thirty-second notes with slurs and numbers; of these, only the 9 grouping is shown in the example above. Example 42 shows the same grouping principle applied to a dotted quarter note.
Three eighths is a natural grouping of the dotted quarter note and needs no clarification. This is true also for the 6 grouping. Groupings of 7, 8, 9, 10 and 11 can be beamed using sixteenth-notes with slurs. A grouping of 12 notes is a natural division of the dotted quarter note and can be beamed as 32nd notes as can groupings up to 23 in number.
Tuplet notation and beaming conventions are not always applied simultaneously to make as clear as possible groupings that are often quite difficult to perform. [See Burkhart, 6th ed., p. 229 and 231 (Beethoven), p. 325 (Chopin), p. 352 (Schumann), and p. 535 (Saylor) for examples.] The term simile may be placed after a few tuplets are identified. If a note in another part, say a quarter note, is aligned consistently with groups of three beamed eighth notes there may be no slurs and numbers at all. In such a case the piece may have a signature of 4/4, with twelve 8th notes grouped in threes.