Interlock and Nesting: Gamelan

Companion to Chapter 5: Gamelan. This page states the interlocking and nesting rules explicitly, and is the theoretical background for Poly’s Kotekan parameter. Everything below is summarised from the published scholarship listed under Sources — prior research restated in Poly’s terms, not original theory. See About This Guide for what this guide is, what it is not, and what it leaves out.

The System

Gamelan offers two distinct counterpoint systems that Poly models separately. Balinese kotekan is micro-level interlock: two parts (polos and sangsih) divide a rapid figuration between them so that their composite is a continuous stream neither player could sustain alone (Vitale 1990; Tenzer 2000). Javanese colotomic structure is macro-level nesting: instruments mark points in a long cycle at stroke rates related by powers of two, producing a temporal hierarchy in which the largest gong subsumes all smaller cycles (Sumarsam 1995) ^{18, 19}.

Both systems share one deep property: the cycle is end-weighted. The gong stroke and the kotekan cadence tone fall on the completion of the cycle, which is simultaneously the start of the next — arrival, not departure. This inverts the Western downbeat instinct and governs where every part places its weight.

The Rules

Kotekan (Bali)

1. The composite must be continuous. At the interlock’s subdivision rate, (almost) every pulse is struck by exactly one of the pair. Gaps in the composite are errors; the whole point is a stream faster than one player’s hand.

2. Each part alone must be playable and idiomatic. Parts avoid long same-hand runs at maximum speed; each is a sparse, syncopated figure with its own kinetic logic. If one “part” of your pair is an unplayable near-continuous stream, you have written a melody plus an echo, not kotekan.

3. Polos leans onbeat, sangsih leans offbeat. The division of labour is not arbitrary: polos (“basic”) carries more of the beat-coincident strokes; sangsih (“differing”) carries the off-positions and the higher notes where the parts differ in pitch (Vitale 1990). This division is style-dependent, not a law: in norot the relationship is effectively reversed, with sangsih taking the beat-coincident tones. Treat it as the common case rather than the general one.

4. The parts overlap at structural tones. Strict complementation is only the textbook case. In practice both players strike together at cadence points, phrase joins, and angsel (break) figures — the overlap marks structure (Tenzer 2000). A pair with empty intersection everywhere sounds mechanical. Poly’s kotekan derivation takes an interlock style and a structural-overlap count, so the doubling is a setting on the pair rather than something added around it.

5. The style of interlock is a named choice. Norot oscillates around neighbouring tones; kotekan telu shares three-pulse cells; kotekan empat four; nyog cag alternates strictly. Each has a different composite texture. Choosing one and staying with it is the reliable default, and the safest starting discipline — but it is a discipline, not a rule of the tradition: Tenzer documents stylistic mixing within a single kebyar performance (Tenzer 2000). Nor need every added part interlock: a third part may double the pokok tones instead, sitting outside the pair rather than completing it (Rule 6) — the Pokok lane in Construction below. What Poly models: three of these four are settings on the interlocking pair — nyog cag, telu and empat. Poly models only the rhythmic dimension of telu and empat, the cell length the interlock repeats on, and not the pitch content those terms also carry; for that dimension read Tenzer 2000, the standard analysis of kotekan varieties, and Vitale 1990, which shows real kotekan is not a pure set complement. Norot is not expressible in Poly at all: it is defined by pitch oscillation around neighbouring tones, and a Poly lane carries one note. And because the derivation fills any pulse a cell would otherwise leave unstruck (Rule 1), a cell mode adds strikes to the strict complement rather than moving them — so at cycles where the cell index never disagrees with the source, telu and nyog cag coincide.

6. The interlock serves a melody. Kotekan elaborates a slower core melody (pokok). Its accents must land on the pokok tones at the pokok’s rate — the fast surface is an ornamentation system, not free figuration.

Colotomy (Java, and the Balinese gong cycle)

7. Stroke rates halve as instruments deepen. If the ketuk marks every unit, the kempul marks every 2, kenong every 4, gong every 8 (or deeper). Ratios are powers of two; a 3:1 layer belongs to a different system.

8. Weight accrues to coincidence, and the gong takes all. The more layers coincide on a stroke, the heavier it is; the gong stroke — where everything coincides — is the heaviest event and falls at the cycle’s end/beginning. Nothing competes with it: texture typically thins just before it and re-blooms after.

9. Density scales with register, inversely. The lowest instruments play slowest, the highest fastest (the kotekan sits at the top of this pyramid). A low, fast voice or a high, slow voice inverts the pyramid and reads as foreign.

10. Tempo and density trade off (irama). When the beat slows, elaborating parts double their subdivision so surface density stays roughly constant. In Poly: halving tempo should be paired with doubling elaborating lanes’ step counts or subdivision — the surface stream is the invariant.

Construction

1. Colotomic frame. Four lanes, one hit each, steps 4/8/16/32 at 1/4 (Rule 7), velocity increasing with depth (Rule 8), rotations aligned so all coincide at the cycle boundary.
2. Pokok. A mid-register lane, 8 steps, 4–8 hits, even and calm (Rule 6’s melody proxy).
3. Kotekan pair. Polos: 8 or 16 steps, 5 hits, biased onbeat (Rule 3). Sangsih: Kotekan L{polos} for the strict complement (Rule 1). Check polos alone for playability (Rule 2).
4. Structural overlap. Add doubled strokes at the cycle boundary — accent masks on both pair lanes, or a sparse third lane striking with both at the gong point (Rule 4).
5. Feel. No swing, no humanize: gamelan ensembles prize unison precision. Dynamics terraced by register, not contoured within parts.

Rule-Checked Kotekan Over Colotomy

Lane	Role	Steps	Hits	Rotation	Subdivision	Note	Velocity	Kotekan	Interlock	Overlap
1	Gong (cycle)	32	1	0	1/4	36	115	off	—	0
2	Kenong	16	1	0	1/4	43	95	off	—	0
3	Kempul	8	1	0	1/4	48	85	off	—	0
4	Ketuk	4	1	0	1/4	53	75	off	—	0
5	Pokok melody	8	4	0	1/4	60	75	off	—	0
6	Polos	8	5	0	1/16	72	80	off	—	0
7	Sangsih	8	3	0	1/16	72	75	L6	empat	1

What Breaks the Idiom

• Gaps in the kotekan composite (Rule 1) — usually caused by editing polos after setting the complement; re-derive sangsih after any polos change.
• An unplayable polos. Dense polos + sparse sangsih is a melody with decoration, not interlock (Rule 2).
• Front-weighted cycles. Accenting pulse 0 as a Western downbeat instead of weighting the cycle’s completion (Rule 8’s end-weighting).
• Non-binary colotomic ratios (Rule 7) — a 3-layer belongs to the African/Cuban pages, not here.
• Swing or humanize. Gamelan’s precision is the aesthetic; looseness reads as error, not warmth.

Sources

Primary: Tenzer 2000 (kotekan typology, kebyar structure), Vitale 1990 (kotekan mechanics from a performer-composer), Sumarsam 1995 (Javanese colotomy and irama). See also refs 18, 19, 20.

Attribution: the kotekan typology, overlap-at-structure, and onbeat/offbeat division (Rules 3–6) summarise Tenzer 2000 and Vitale 1990; the colotomic hierarchy (Rules 7–8, 10) summarises Sumarsam 1995. Rules 1–2 and 9 are this guide’s compressions of performance constraints those sources describe at length rather than rules they state in this form. All patch values are ours.