Polymetric Patterns

Polymetric patterns let groups of different lengths play at different rates within the same cycle. This creates textures where voices phase against each other — the same notes cycling at different speeds over a shared grid.

Curly Brace Syntax

Use {...} for polymetric groups. Without a subdivision modifier, each element takes one step, so the group spans as many cycles as it has elements:

{C4 D4 E4}            // One note per cycle across 3 cycles

Compare with [] which fits all notes into one cycle:

[C4 D4 E4]            // All three in one cycle

The %N Subdivision Modifier

The %N modifier controls how many steps a polymetric group spans per cycle. The fundamental formula is:

speed_factor = N / L

where N is the subdivision count and L is the number of elements in the group.

The N/L Ratio

When N equals L, the group plays at normal speed — identical to a regular sequence. When N exceeds L, the group plays faster. When N is less than L, it plays slower:

Pattern	N	L	Factor	Effect	Events/cycle	Duration each
{C4 D4 E4}	1	3	1/3	Slow: spans 3 cycles	1	1 cycle
{C4 D4 E4}%3	3	3	1	Normal: = [C4 D4 E4]	3	1/3 cycle
{C4 D4 E4}%6	6	3	2	Fast: 2x speed	6	1/6 cycle
{C4 D4 E4}%9	9	3	3	Very fast: 3x speed	9	1/9 cycle

Without %N on a single group, N defaults to 1 — the group produces one event per cycle, taking L cycles to complete.

Note

Resonon uses rational arithmetic for the N/L ratio, so subdivisions are always exact. {C4 D4}%3 produces a factor of exactly 3/2, not 1.5 — no floating-point drift accumulates.

Non-Divisible Ratios

When N doesn’t divide evenly by L, the content wraps within the cycle. For example, {C4 D4}%3 has factor 3/2:

• 2 elements sped up by 3/2 → 3 onsets per cycle
• Onset times: 0, 1/3, 2/3
• Cycle 1 content: C4, D4, C4 (wraps back to start)
• Cycle 2 content: D4, C4, D4

The content shifts by one position each cycle, creating a phasing effect. After 2 cycles, the content realigns — the phase period equals L cycles for a factor of N/L.

Single Element with %N

A single element with %N simply repeats it N times per cycle:

{C4}%4                 // C4 four times per cycle (= [C4 C4 C4 C4])
{bd}%8                 // Eighth-note pulse

Multi-Group Polymetric

When you separate groups with commas inside {}, all voices play on the same onset grid but their content cycles at different rates. This is the core of polymetric patterns.

Default N for Multi-Group

Without %N, N defaults to the first group’s length. These are equivalent:

{C4 D4 E4, F4 G4}     // N = 3 (first group's length)
{C4 D4 E4, F4 G4}%3   // Explicitly N = 3

Both voices are wrapped as Fast(N/L, Sequence(group)):

• Voice 1: 3 elements, factor = 3/3 = 1 → normal speed, 3 events per cycle
• Voice 2: 2 elements, factor = 3/2 → sped up, also 3 events per cycle

Both voices produce events at the same times — they share one grid:

Time	Voice 1 (3 elements, factor 1)	Voice 2 (2 elements, factor 3/2)
0	C4	F4
1/3	D4	G4
2/3	E4	F4 (content wraps)

Voice 1 completes its content once per cycle. Voice 2’s 2-element content repeats every 2/3 of a cycle, so it completes 1.5 times per master cycle. Over 2 cycles, Voice 1 plays its content 2 times while Voice 2 plays its content 3 times — the content realigns every 2 cycles.

With Explicit %N

An explicit %N overrides the default, setting the grid size for all voices:

{C4 D4 E4, F4 G4}%6   // Both voices produce 6 events per cycle

• Voice 1: factor = 6/3 = 2, cycles through C-D-E twice
• Voice 2: factor = 6/2 = 3, cycles through F-G three times

The larger N creates a denser shared grid while maintaining the same content-phasing relationship.

Polymetric vs Parallel

The {} and [,] syntaxes both layer voices, but they produce fundamentally different rhythmic structures.

Musical Definitions

• Polymetric: different meters running simultaneously — voices share a pulse grid but their content cycles at different rates, creating content phasing
• Polyrhythm: different subdivisions of the same time span — voices have independent onset grids, creating rhythmic conflict

In Resonon

Polymetric {} forces all voices onto one N-step grid. Each voice’s content is sped up by N/L so that every voice produces exactly N onsets per cycle. The “poly” effect comes from content repeating at different rates:

{C4 D4 E4, F4 G4}     // Both voices: onsets at 0, 1/3, 2/3
                       // Voice 2's content phases against Voice 1

Parallel [,] gives each voice its own grid based on its element count. Voices can have different numbers of onsets per cycle:

[C4 D4 E4, F4 G4]     // Voice 1: onsets at 0, 1/3, 2/3
                       // Voice 2: onsets at 0, 1/2

The comparison:

	Polymetric {a b c, d e}	Parallel [a b c, d e]
Voice 1 onsets	0, 1/3, 2/3	0, 1/3, 2/3
Voice 2 onsets	0, 1/3, 2/3	0, 1/2
Grid	Shared (3-step)	Independent
Effect	Content phasing	Onset conflict

Tip

Use {} when you want content to phase against itself over multiple cycles. Use [,] when you want onset rhythms to interlock within each cycle.

Musical Examples

3 Against 2

The classic polymetric relationship:

{C4 E4 G4, F4 A4}     // N = 3, both voices on 3-step grid

Time	Voice 1	Voice 2
0	C4	F4
1/3	E4	A4
2/3	G4	F4

Voice 2’s content phases by one position each cycle. After 2 cycles, both voices realign:

Cycle	Voice 1 content	Voice 2 content
1	C4 E4 G4	F4 A4 F4
2	C4 E4 G4	A4 F4 A4

For true 3-against-2 onset polyrhythm (3 onsets vs 2 onsets), use parallel:

[C4 E4 G4, F4 A4]     // Voice 1: 3 onsets, Voice 2: 2 onsets

4 Against 3

{C4 D4 E4 F4, G4 A4 B4}   // N = 4, both voices on 4-step grid

Time	Voice 1 (4 elements)	Voice 2 (3 elements, factor 4/3)
0	C4	G4
1/4	D4	A4
2/4	E4	B4
3/4	F4	G4 (wraps)

Voice 2 completes its 3-element content every 3/4 of a cycle. Over 3 cycles, Voice 1 plays 3 times while Voice 2 plays 4 times — content realigns every 3 cycles.

Practical Drum Pattern

Combine polymetric drums with a regular melodic pattern:

let drums = AudioTrack("drums");
drums.load_instrument(Sampler(Kit("cr78")));

let bass = AudioTrack("bass");
bass.load_instrument(SamplerMelodic(Kit("keys")));

// 4-against-3 polymetric drums
drums << {bd sd bd sd, hh hh hh};

// Steady bass line underneath
bass << [C3 _ G2 _];

PLAY;

Combining with Other Features

Polymetric patterns compose with other modifiers:

// With compact notation modifiers
{bd*2 sd, hh hh hh}       // Fast modifier inside polymetric

// With alternating patterns
{<C4 E4> <D4 F4> G4, A4 B4}  // Alternating elements phase independently

// With weight modifiers
{C4@2 D4 E4, F4 G4}%6    // Weighted elements within polymetric grid

Rests, Nesting, and Combining

Rests work normally inside polymetric groups:

{_ C4 D4}%3           // Rest on beat 1

Other Patterns Inside Polymetric

Sequential and parallel patterns can appear inside polymetric groups as single elements:

{[C4 D4] E4 F4}       // Sequential [C4 D4] is one element, stretched
{<C4 E4> D4 F4}       // Parallel chord is one element
{C4(3,8) D4 E4}       // Euclidean inside polymetric

Polymetric Inside Other Patterns

[{C4 D4 E4}%3 G4]     // Polymetric fills its slot in a sequence

Nested Polymetric

{{C4 D4}%2 E4 F4}     // Inner polymetric cycles at double speed

Methods

All standard pattern methods work on polymetric patterns:

let base = {C4 D4 E4}%3;

base.fast(2)           // Double the speed
base.slow(2)           // Half the speed
base.transpose(7)      // Up a fifth
base.reverse()         // Reverse the sequence

See Also

• Pattern Basics — Cycle theory and fundamental pattern concepts
• Nested & Parallel Patterns — Regular parallel and nested patterns
• Compact Notation — Modifiers like *n and @n
• Euclidean Rhythms — Another approach to polyrhythmic textures