Notation Used

Rhythms are normally described in musical notation, like the following Clave Son:

Figure 1: Clave Son in standard Musical Notation

There are a number of things you should notice here:

• Time signature: This is the 4/4 at the beginning of the figure. The numerator tells you how many beats there are per measure (each measure is separated by the vertical lines). In our example we have 4 beats per measure and the denominator tells you the duration of each of these beats. This duration is defined as some number which is a power of two. A '1' would stand for a whole note, a '2' for a half-note, a '4' for a quarter note, an '8' for an eigth-note, a '16' for a sixteenth-note, etc.
  There are 2 half-notes in one whole note; there are 2 quarter notes in one half-note and 4 quarter notes in one whole note; there are 2 eigth notes in one quarter note, etc. The following figure displays how these different types of notes are written in standard notation:

  
  Figure 2: 1 Whole note, 2 half notes, 4 quarter notes, 4 eigth notes, and 8 sixteenth notes

  So in Figure 1 we defined each measure as having 4 quarter notes.

• The dot after the first note means "plus a half". In other words, if you put a dot next to a quarter note, it means you add half of a quarter note to the duration of that beat. So our first note lasts 1 quarter note + 1 eigth note. (If you had a dot next to an eigth note, that note would last 1 eigth note + 1 sixteenth note).
• The arc joining the second and third notes is a tie. This means that the second note ties into the third note (i.e. the third is not played). So our second "pulse" has a duration of two eigth notes (since the first eigth note is tied to the second eigth note).
• The squiggly lines at the beginning and end of the second measure are quarter note rests (there are also eighth note, sixteenth note rests, etc., but we will not explain that here, it is not necessary). In our analysis we will consider pulses lasting until the start of the next pulse, so in this case our third and fifth notes will have a duration of two quarter notes, or 4 eigth notes.
• Notice that although we have defined each measure as having 4 quarter beats per bar, we are not limited to only use quarter notes (otherwise we'd have pretty boring rhythms!). In our example we can see that there are some eigth notes being used. Also, the first note in our measure (the dotted quarter note) has a duration of 1 and a half quarter notes, but it's easier to say it has a duration of 3 eigth notes. The second and third notes (which are tied together, so count as one "pulse") also have a duration of three eigth notes.
  What we need to consider for our analysis is: What is the smallest subdivision by which we can define all the duration of all our pulses? In our case we saw that it is an eigth note.

So we can alternatively define the two measures in Figure 1 as a line with 16 evenly spaced marks (so each mark would constitute as one eight-note beat), and place 'x's where each "pulse" is played. So Figure 1 would translate to the following "timeline":

Figure 3: Clave Son timeline

The following is an example of a traditional Latin-American rhythm in 6/8:

Figure 4: 6/8 Clave in standard Musical Notation

In Figure 4 we can see that the smallest subdivision is sixteenth notes, so we can define our rhythm as a timeline of 12 intervals:

Figure 5: 6/8 Clave timeline

Finally, for the purposes of the analysis, we will join the ends of these timelines to form a circle, with the first pulse in the "north pole" of these circles. This actually makes more sense, since the rhythms we will analyze are cyclic (they repeat constantly throughout the piece). So the timelines in Figure 3 and Figure 5 would translate to:

Figure 6: Clave Son and 6/8 circle representations