The differences between jazz performance and notation can perhaps best be explained by comparing the basic cymbal swing pattern common to mainstream jazz drummers. Although it sounds like this, its notation, when given (it is often taken for granted and not notated) is reproduced below:
Note how the notated eighth -note rhythm varies with the near triplets of the performed version!
The history of the cymbal pattern is reflective of the history of jazz, itself. Back in the latter days of the 19th century and during the early 20th century, ragtime composers notated the dotted rhythm yet often played the triplet rhythm as shown below. (An accessible example is Scott Joplin's piano roll of his composition, Maple Leaf Rag, which is readily available in sheet music as well as on the Smithsonian collection of classic jazz recordings.)
Sometime during the Thirties and Forties the notation slowly began to change from the dotted rhythm to the consecutive eighth-note notation as shown in Ex. 1 above. (Keep in mind that the performer played neither!) An interesting illustration of the process of "smoothing" out the eighth notes can be seen in the old, illegal musicians' fake book--still widely used in the Fifties and Sixties. The older tunes invariably used the dotted-eighth and sixteenth rhythm whereas more recent compositions went toward straight eighth notes. Nonetheless, the earlier tunes required performer accents (almost never notated) on the first and third quarter. (Although not used in this example, old standard jazz tunes often use a 2/2 meter.) Meanwhile, a performer might play a cymbal rhythm which resembles Ex. 3. (and the recording above). The notation in the next examples will represent more closely what the performer plays rather than the straight eighth notes of traditional jazz notation.
As time went on, the performer accents moved over to beats 2 and 4. Depending on your instrument, the shift in accents can become more readily apparent. An easy example is the use of the pianist's left hand. Pianists from the ragtime and stride school of the twenties, for example, accented beats 1 and 3 by the use of low octaves while pianists from a few years later emphasized beats 2 and 4 simply by including rests on the "strong" beats.
The shifted cymbal pattern accents might sound a little like the notation in Ex. 5 below
More recently, other performance variations have occurred. One of many possibilities is listed in Ex. 6. It sounds like this.
While overall accents occur in patterns such as listed above, a drummer will vary the accents of cymbal pattern, depending on what is being played by his/her other limbs as well as by other performers in the group, to develop the accent patterns into larger units. Can you hear a development pattern in the cymbal accents in this recording? Except for special effects, none of the accents given in the notation examples above will be added to notation of a cymbal pattern and, remember most cymbal rhythms are not notated at all.
Other jazz rhythm components, such as beat placement, are equally important for swing but impossible to notate. While a bass player often plays slightly "ahead" of the beat, many horn players choose to play "behind" the beat. Although this tradition has something to do with lower and higher frequencies speaking slightly later or earlier, the concept basically allows the widest possible beat within which one has freedom to work. By the way, this idea is especially interesting for piano players: the left and right hands usually don't play precisely at the same time, as in classical music--rather, the left hand plays slightly ahead and the right hand, slightly behind. Ex. 7 can be heard below.