Asynchronous Academy

Polyrhythms & Cross-Tempos

Suggested Duration: 2.5 Hours

"Two times heartbeat, three times breathing—polyrhythm is the body's natural state."

Polyrhythmic Drumming Proverb

Polyrhythms & Cross-Tempos

In standard pop and classical music, every instrument plays in the same time signature (e.g., everyone plays in 4/4). But in African percussion, jazz, and advanced electronic music, we often overlay different rhythmic meters at the same time. This is called a polyrhythm.

Core Music Theory & Sound Concepts

1. Polyrhythm vs. Polymeter

  • Polymeter: Different instruments play in different meters (loop lengths) but share the same beat speed. For example, a Synth plays a 5-step loop, while the Kick plays a 4-step loop. Over time, the downbeats shift out of sync, only realigning after a set mathematical cycle.
  • Polyrhythm: Two different beat subdivisions are played simultaneously within the same space of time. For example, playing "3 against 4" (triplets against sixteenth notes).

2. The 3:4 Polyrhythm

  • This represents playing 3 equal beats in the exact same time span as 4 equal beats.
  • How it sounds: "Pass the golden butter" is a classic mnemonic to feel a 3:4 polyrhythm.
  • Sequencer Grid Alignment: If you divide a bar into 12 steps:
    • The 4-Beat Track hits every 3 steps (steps 1, 4, 7, 10).
    • The 3-Beat Track hits every 4 steps (steps 1, 5, 9).
    • They align perfectly on step 1, split apart, and resolve back together on the next bar.

3. The Least Common Multiple (LCM)

  • To find out when two polymetric tracks will align, you calculate their Least Common Multiple.
  • If Track A is a 5-step loop and Track B is a 16-step loop:
    • $\text{LCM}(5, 16) = 80\text{ steps}$.
    • The pattern will take 5 full bars of 16 steps before both tracks hit step 1 at the exact same millisecond.
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Polymeter Tip: Change the Loop Length dropdown of your melody sequencer track to 12 steps or 5 steps, while keeping the kick drum track at 16 steps. Press play. You will hear the melody shift its starting accent across the drum beats on each cycle!

Your Assignment Task

  1. Experiment in the Synth Sandbox:
    • Set the Kick Sequencer loop length to 16 steps (standard 4/4). Program kicks on steps 1, 5, 9, 13.
    • Set the Synth Bass Sequencer loop length to 12 steps (3/4). Program notes on steps 1, 4, 7, 10.
    • Press Play. Listen to how the melody shifts position relative to the kick drum on each repeat.
    • Now, set the Synth Melodic Sequencer to a 5-step loop (kicking on step 1). Press play and count the measures until the melody note overlaps with the kick drum.
  2. Write and Submit your Analysis:
    • Alignment Calculation: Calculate the mathematical cycle length (in steps and bars) for:
      • A 3-step polymeter against a 16-step loop.
      • A 7-step polymeter against a 16-step loop.
    • Grid Diagram: Draw a grid mapping the 3:4 polyrhythm across a 12-step bar, highlighting where the beats conflict and where they resolve.
    • Groove Evaluation: How does polymetric overlapping prevent a repetitive electronic loop from sounding boring or predictable over a long period?
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Polyrhythms & Cross-Tempos Analysis

Submit your completed polyrhythmic grid diagram and timing analysis as a Markdown (.md) file using the course app submission portal.

Assessment

Pre-Submission

Before you submit, please complete the Pre-Submission Self-Assessment.

What to Turn In

  • 📤

    Polyrhythmic grid diagram and timing analysis (Google Doc or Markdown)

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Learning Goals

We are learning to:

  • 🎯

    Analyze the mathematical properties of polyrhythms, specifically the 3:4 and 3:2 ratios.

  • 🎯

    Program overlapping sequencer tracks of varying lengths to construct polyrhythmic loops.

Success Criteria

I can:

  • ✅

    Program a 3:4 polyrhythm in the sandbox by setting drum and synth tracks to different loop lengths.

    Expectations Covered: A1.1, C1.2
  • ✅

    Calculate the alignment cycle of complex meters.

    Expectations Covered: C2.1
  • ✅

    Contrast polyrhythm with polymeter.

    Expectations Covered: C1.1

Rubric

Category Level 4 Level 3 Level 2 Level 1
Knowledge/Understanding
Knowledge of polyrhythmic ratios (3:4, etc.), polymeter, and alignment cycles.
 Demonstrates precise mathematical and musical understanding of polyrhythms and cycles. Demonstrates considerable understanding of polyrhythms and cycles. Demonstrates basic understanding of polyrhythms and cycles. Demonstrates limited understanding of polyrhythms and cycles.
Application
Creating distinct overlapping polyrhythmic tracks in the sandbox.
 Loops are highly complex, polyrhythmically accurate, and demonstrate excellent rhythmic resolution. Loops show clear polyrhythmic structures. Loops show basic polymetric overlapping attempts. Loops lack coordination or timing alignment.
Knowledge/Understanding
Criteria: Knowledge of polyrhythmic ratios (3:4, etc.), polymeter, and alignment cycles.
Level 4

Demonstrates precise mathematical and musical understanding of polyrhythms and cycles.

Level 3

Demonstrates considerable understanding of polyrhythms and cycles.

Level 2

Demonstrates basic understanding of polyrhythms and cycles.

Level 1

Demonstrates limited understanding of polyrhythms and cycles.

Application
Criteria: Creating distinct overlapping polyrhythmic tracks in the sandbox.
Level 4

Loops are highly complex, polyrhythmically accurate, and demonstrate excellent rhythmic resolution.

Level 3

Loops show clear polyrhythmic structures.

Level 2

Loops show basic polymetric overlapping attempts.

Level 1

Loops lack coordination or timing alignment.