Introduction to Timelines

What Is a Timeline?

On Monday we explored how pulse, beat, division, and metrical structure work together to create meter. Today we turn to a different organizing structure found in many musical cultures around the world: the timeline.

Timelines are not just any ostinatos. They are memorable, easily recognized patterns that function as the "reference line" of the music. In many traditions they serve as a regulator or heartbeat, signaling the underlying cycle to the ensemble.

Because timelines repeat cyclically, they can be described very simply by:

• The total number of pulses in the cycle
• The onset positions—the pulses where attacks occur

This makes timelines ideal for geometric representations (such as circles) and mathematical descriptions (such as inter-onset intervals), which we will explore today.

Three Ways to Represent a Timeline

1. Binary Representation (X . . X . X … / 1 0 1 0 …)

A timeline can be written as a simple row of symbols—one for each pulse in the cycle. There are two equivalent ways to do this:

• X = an onset (a sounded pulse)
• . = a silence

Example (16 pulses): X . X . . X . . . X . . X . . .

The same pattern can also be written using numbers:

• 1 = an onset
• 0 = a silence

Binary form (same 16-pulse example): 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0

This representation is compact, unambiguous, and useful when we connect rhythmic structure to geometry or later mathematical ideas.

2. Onset List

The same pattern can be represented simply by listing the pulse numbers with attacks:

[0, 2, 5, 9, 12]

3. Circle Representation (Geometry)

We can place each pulse evenly around a circle. This makes it easy to see symmetry, spacing, and operations like rotation.

The Cuban Tresillo

The Cuban tresillo is one of the most well-known timelines. It consists of 3 onsets in a cycle of 8 pulses.

The pattern can be notated as:

• Binary: X . . X . . X .
• Onset list: [0, 3, 6]
• Interval notation: [3-3-2] (the spaces between onsets)

Here it is on a circle:

This timeline is common

This timeline is common in music around the world and inspired a lot of 20th century music.

It is still popular today.

Long Timelines

Some timelines can be quite long. Do you recognize this one?

How Do You Fit 5 Into 16?

So far, we've mostly dealt with timelines where the onset-number divides the pulse-number neatly. For example, a waltz in 3/4, and a hemiola in 6/8 (6÷3=2 and 6÷2=3).

What happens when the onset-number does not divide the pulse-number neatly?

Here are six common timelines, all within a 16-pulse cycle:

As Circle Diagrams:

Show in Standard Notation

Traditional notation of these patterns (collapsed by default - students can read notation but complex polyrhythms are challenging to notate):

Listen to Each Timeline:

Example 1: Son Timeline

Pattern: [3-3-4-2-4]

Example 2: Shiko Timeline

Pattern: [4-2-4-2-4]

Example 3: Rumba Timeline

Pattern: [3-4-3-2-4]

Example 4: Soukous Timeline

Pattern: [3-3-4-1-5]

Example 5: Gahu Timeline

Pattern: [3-3-4-4-2]

Example 6: Bossa Nova Timeline

Pattern: [3-3-4-3-3]

Operations on Timelines

Because a timeline is a pattern on a cycle, we can transform it in simple and musically meaningful ways:

Rotation

Shift every onset forward by the same number of pulses. This creates a new pattern with the same spacing.

Complement

The complement fills in every rest where there was no attack. If the original timeline has 5 attacks in 16 pulses, the complement has 11.

Interactive Timeline Sequencer