Additive Counterpoint: Balkan

Companion to Chapter 7: Balkan. This page states the rules of additive-meter counterpoint explicitly. 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

Aksak meter — Brăiloiu’s term, from the Turkish for “limping” — builds cycles by concatenating unequal cells of two and three quick pulses rather than dividing a whole into equal beats (Brăiloiu 1951). A rachenitsa is not “7/8” so much as it is the specific sequence 2+2+3; kopanitsa is 2+2+3+2+2; daichovo 2+2+2+3. The cell sequence is the meter’s identity, shared body-deep between musicians and dancers — dance steps map to cells, which is why the sequence is inviolable in a way even a clave is not (Rice 1994). London’s meter theory formalises these as non-isochronous meters: valid, stable metric hierarchies whose beats are unequal by construction (London 2012).

Counterpoint in this system is vertical, not phased: all voices share the same additive grid and the same cycle length, differentiated by density stratum and by which cells they emphasise. The polymetric games of the African and minimalist pages are foreign here — the interest lives in the asymmetry itself, ridden in tight unison at often extreme tempo.

The Rules

1. The cell sequence is fixed and shared by every voice. All lanes agree on where cell boundaries fall for the entire piece. Changing 2+2+3 to 2+3+2 mid-tune changes the dance — it is a different piece, not a variation. (In Poly: one cells definition, reused across lanes; rotation selects the variant before the music starts.)

2. Accents live on cell heads; the long cell’s head is primary. The first pulse of each cell takes the accent, and the three-cell’s head carries the characteristic extra weight (or, in some dances, the stretch — see Rule 8). Accents inside cells are ornamental and light.

3. A continuous quick-pulse stratum runs underneath. Some voice — tambura strum, gadulka bowing, hi-hat — articulates the fast pulse continuously, making the unequal beats countable. Without this stratum, listeners lose the additive grid; with it, even 13/8 feels inevitable.

4. The tupan speaks a two-stroke grammar. The low open stroke (beater hand) marks cell heads — always the long cell, usually the cycle start; the high stick/switch hand fills between with subdivisions and rim strokes. Low = structure, high = motion; inverting this collapses the meter’s audibility.

5. Density strata, same grid. Voices are layered exactly as in the Manding same-cycle model: sparse structural low voice, mid-density response, dense surface — all on the shared additive grid (Rule 1), never on foreign cycle lengths. Cross-cycle polymeter against an aksak frame destroys the dance and is not part of the tradition.

6. No swing. The asymmetry is metric, not micro-timing. Swing applied to an aksak cycle fights the cell structure (Chapter 7 says this; here is the rule’s reason: swing displaces alternate quick pulses, but the quick pulses are the units from which cells are counted — displacing them un-counts the meter).

7. Tight ensemble, minimal humanize. Wedding-band aksak at 200+ BPM is played with near-mechanical unison; timing looseness reads as failure, not feel (Rice 1994). Humanize ≤ 7.5 ms.

8. The long beat is slightly less than 3:2 in practice. Measured performances show three-cells compressed a shade below their notated proportion — a systematic, style-defining tendency, not sloppiness (Goldberg 2015; cf. London 2012 on NI-meter tolerance ranges). Poly expresses this as a subdivision profile over the lane’s cells: the cells keep the bar its notated length, and the profile sets the proportion within it. The shipped Balkan preset runs its three-cells at 2.85:2 rather than 3:2. This is not swing — Rule 6 still holds, and its reason is exactly why: swing would displace the quick pulses the cells are counted from, where this changes the metric proportion itself.

9. Ornaments anticipate the long cell. Grace notes, drags, and melodic turns cluster just before the three-cell’s head, spotlighting the asymmetry. Fills elsewhere are modest.

Construction

1. Define the cells once. E.g. kopanitsa: cells = [2,2,3,2,2], 11 quick pulses at 1/8 or 1/16. Every lane uses this grid (Rule 1).
2. Tupan pair. Low lane: hits on cell heads only (5 hits for kopanitsa), strongest on the three-cell (Rules 2, 4). High lane: dense fill between heads, low velocity, rim timbre.
3. Quick-pulse stratum. A lane with hits on all 11 pulses, quiet, even (Rule 3).
4. Melodic-rhythm proxy. A mid-density lane (E(4,11) or E(7,11)) with rotation aligning its accents to cell heads (Rule 5), mutation 5–10% only.
5. Feel. Swing 0 everywhere (Rule 6); Humanize ≤ 0.15 (Rule 7); ornament lane phrase-gated to appear before three-cells (Rule 9) if used.

Rule-Checked Kopanitsa (2+2+3+2+2)

Lane	Role	Steps	Hits	Rotation	Subdivision	Velocity	Ghost	Mutation	Swing	Humanize
1	Tupan low (cell heads)	11	5	7	1/8	115	0	0%	0	0ms
2	Tupan stick (fill)	11	7	1	1/8	70	45	8%	0	3ms
3	Quick pulse	11	11	0	1/8	50	20	0%	0	0ms
4	Melodic accents	11	4	2	1/8	85	25	8%	0	4ms

Lane 1’s five hits must land on pulses 0, 2, 4, 7, 9 — the cell heads of 2+2+3+2+2. E(5,11) at its default rotation gives 8, a different spacing — but the cell heads are the same gaps (four 2s and one 3) rearranged, so they are E(5,11) rotated: rotation 7 (rotate-right, the M068 convention) lands the five hits exactly on the cell heads. Set the rotation explicitly, or drive the lane from the additive-cells parameters (or timeline mode) — the cells, not the Euclidean default, are the authority.

What Breaks the Idiom

• Any lane on a foreign cycle length. An 8-step lane against an 11-pulse aksak is not fusion by default — it erases the dance (Rule 5). (Deliberate aksak-polymeter hybrids belong to Chapter 14’s cross-tradition territory, done knowingly.)
• Swing (Rule 6) and heavy humanize (Rule 7).
• Even accents. All cell heads equal, or accents drifting inside cells — the limp disappears (Rule 2).
• Missing quick pulse. Without the fast stratum, long cycles (11, 13) become uncountable to the listener (Rule 3).
• Euclidean-only thinking. Several aksak accent patterns are not the E(k,n) distribution for their cycle. (The kopanitsa cell heads happen to be a rotation of E(5,11) — see the note above — but longer additive cycles need not match any E(k,n) at all.) The cell sequence is the ground truth; Euclidean patterns are a frequent but not universal match.

Sources

Primary: Brăiloiu 1951 (the aksak system), Rice 1994 (Bulgarian practice and dance linkage), Goldberg 2015 (measured long-beat timing), London 2012 (non-isochronous meter theory), Holzapfel 2015 (the related Turkish usul system). See also Goldberg 2025 on notation, identity and the politics of Bulgarian metre, and refs 26, 27, 28, 29, 30, 31.

Attribution: the aksak cell theory (Rule 1) is Brăiloiu 1951; the dance linkage and ensemble tightness (Rules 1, 7) summarise Rice 1994; the long-beat timing claim (Rule 8) is Goldberg 2015’s measurement; the meter theory framing is London 2012. Rules 3, 4, and 9 are this guide’s distillations of performance practice described across those sources and standard tupan pedagogy rather than claims any one source states as rules. All patch values are ours.