Flow Arts Glossary

A Level 8 concept where two props operate on different spinning planes simultaneously. One prop might be on the wall plane while the other is on the wheel plane. Analogous to how Level 5 expanded from single-grid (diamond or box) to mixed-grid (skewed), Level 8 expands from single-plane to mixed-plane. By this level, the full 2D system (including interradial orientations from Level 6 and conjoined grids from Level 7) is complete, so all 2D knowledge carries into 3D. Not yet implemented.

• Left hand doing a wall-plane pattern while right hand does a wheel-plane pattern
• Intersecting two planes creates 3D motion even though each individual prop traces a 2D circle

A prop held at its center point, extending equally on both sides of the hand. The prop rotates around its center, which is where the hand grips.

• Staff
• Double-ended baton

The color assigned to one of the two hands/props in TKA notation. Blue is conventionally the left hand or lead hand. In pictographs, the blue prop and arrow are rendered in blue. The choice of blue vs red is a notational convention, not a physical requirement.

• Blue hand starts at N, shifts to E
• Blue prop shown in blue on the pictograph

A letter automatically inserted between two letters in a word when no direct transition exists between them. The sequence generator handles bridge insertion transparently.

• Σ inserted between B and O when no B→O transition exists
• Bridge letters appear in the generated sequence but not in the word spelling

A pair of letters that together complete a full cycle of motion, returning to the starting position type. In continuous spinning, you always perform compound units rather than individual letters.

• DJ (Disco Jam): D (β→α) + J (α→β) = pro/pro isolation cycle
• EK (Exploding Kitten): anti/anti compound
• FL (Fruity Loops): hybrid (anti/pro) compound
• MP (Magic Potion), NQ (Never Quit), OR (Open Road): γ→γ compounds
• ΦΨ (Phi-Psi): dash compound (β→α→β, one hand dashes while the other stays static)

A formal relationship between two letters that differ only in their rotation type (pro vs anti). Each letter has an inversion pair. These pairs are used in LOOP generation with the inverted transformation.

• A (pro/pro) ↔ B (anti/anti)
• D (pro/pro) ↔ E (anti/anti)
• W (pro) ↔ X (anti)
• Σ ↔ Δ, Θ ↔ Ω

The fundamental unit of TKA notation. Each letter encodes a specific combination of hand motions and prop rotations for one step. There are currently 47 letters organized into 6 types (22 + 8 + 8 + 3 + 3 + 3). Future levels will add more letters for centric positions (Tau, Terra, etc.).

• A is a Type 1 letter (both hands shift, both pro)
• Σ is a Type 2 letter (one shifts, one static)
• α is a Type 6 letter (both static)

A progressive difficulty tier that unlocks new positions, grid modes, turn counts, and orientations. Level 1: 0 turns only. Level 2: whole turns (0-3). Level 3: half turns and float. Level 4: centric grid with center point (tau, terra positions, not yet implemented). Level 5: skewed grid (zeta, eta positions). Level 6: interradial orientations (clockIn, clockOut, counterIn, counterOut: completes single-grid orientation freedom). Level 7: conjoined grids (dual grids sharing a junction point, new position combinations, bridges to 3D). Level 8: atomics (two props on different spinning planes simultaneously). Level 9: Rubik's cube tech (in-between points across intersecting planes, same expansion skewed brought to single-plane).

• Level 1: alpha, beta, gamma positions with 0 turns only
• Level 4: introduces center point with centric grid
• Level 5: introduces zeta, eta positions with skewed grid
• Level 6: interradial orientations double angular precision (completes single-grid 2D)
• Level 7: conjoined grids expand the spatial canvas with dual grids, bridging to 3D
• Level 8: one prop on wall plane, one on wheel plane (atomics)
• Level 9: skewed-equivalent access to in-between points across multiple planes

A visual representation of one step of motion in TKA. Shows two props, arrows indicating motion, and optional glyphs for letter name, timing, positions, and reversals.

• Each letter has multiple pictograph variations
• Pictographs can be sequenced into choreo cards

Where the two hands are relative to each other on the grid. Defined by the angle between them. Seven positions exist across the level system: alpha, beta, gamma, zeta, eta, tau, and terra.

• Alpha = hands opposite (180°)
• Beta = hands together (0°)
• Gamma = right angle (90°)

The physical object being manipulated (staff, fan, club, poi, etc.). The prop is what rotates. The hand is just the vehicle that carries it between grid points.

• Staff (bilateral): held at center, extends both sides
• Poi (unilateral): held at one end, extends outward

The color assigned to the other hand/prop in TKA notation. Red is conventionally the right hand or follow hand. In pictographs, the red prop and arrow are rendered in red.

• Red hand starts at S, shifts to W
• Red prop shown in red on the pictograph

Level 9 concept. Within the multi-plane context of Level 8 (atomics), the points between the relative cardinal points on each plane become individually accessible. The same expansion that Level 5 (skewed) brought to single-plane grid work, Level 9 brings to multi-plane work. Named for the Rubik's cube geometry that emerges when three intersecting planes each have their in-between points addressed. Completes 3D mastery the same way Level 6 (interradials) completes 2D orientation freedom. Not yet implemented.

• Level 5 mixed cardinal and intercardinal on one plane (skewed). Level 9 mixes equivalent points across two intersecting planes.
• The 3D grid formed by wall + wheel + overhead planes with in-between access resembles a Rubik's cube

An ordered series of pictographs representing choreography. A sequence includes a start position (step 0) followed by one pictograph per letter in the word. The visual output is called a choreo card.

• A 4-letter word produces a sequence with 5 pictographs (start + 4 steps)
• Sequences can be rendered as grid layouts or single-row strips

The plane in space on which a prop pattern is executed. Three planes exist: wall (vertical, facing the audience), wheel (vertical, perpendicular to audience), and overhead (horizontal, above the performer). All levels 1-7 work on a single plane at a time (any of the three). Level 8 (atomics) introduces patterns where two props are on different planes simultaneously.

• Wall plane: the prop traces a circle facing the audience
• Wheel plane: the prop traces a circle like a bicycle wheel (side view)
• Overhead plane: the prop traces a circle above the performer's head

The fundamental unit of a sequence: one step = one letter = one pictograph. A sequence of N letters has N steps of motion plus a start position (step 0). Each step shows what both hands and props do during that moment, regardless of its duration.

• A 4-letter word is 4 steps long
• Step 0 is the start position (no motion yet)
• Each step corresponds to one pictograph in the choreo card

The founding design principle that a pictograph represents the same letter under rotation, reflection, and color swap. This minimizes the alphabet by treating spatially equivalent arrangements as identical. The principle holds for symmetric positions (alpha, beta) and opposite-direction movement. It breaks for same-direction movement in asymmetric positions (gamma), which is why the quarter-same group has 4 letters (S,T,U,V) instead of the usual 3.

• Rotate a pictograph card: same letter
• Mirror a pictograph: same letter
• Swap red/blue: same letter (except STUV hybrids)
• U and V exist because color-swapping a quarter-same hybrid changes which motion type leads

The connection between two consecutive letters in a sequence. A valid transition requires the end position of one letter to match the start position of the next. When no valid transition exists, a bridge letter is inserted.

• A ends at alpha, next letter starts at alpha = valid transition
• B ends at alpha, O starts at gamma = needs bridge letter

A prop held at one end, extending outward from the hand in one direction. The prop rotates around the grip point, which is at the edge of the prop.

• Poi
• Fan
• Club

A specific instance of a letter with particular starting/ending positions and locations. Each letter can have many variations that all produce the same letter classification but differ in where on the grid they happen.

• Letter A has variations starting from alpha1, alpha3, etc.
• Variations differ by rotation direction and grid locations

A sequence of TKA letters that spells out a choreographic phrase. Each letter in the word is one step of motion. Words can be any length and may require bridge letters between certain transitions.

• STORM is a 5-letter bridge-free word (5 steps)
• MONSTROUS is a 9-letter bridge-free word
• TRUST is a 5-letter word
• DJ is a 2-letter compound word

A position where the two hands are at opposite grid points (180 degrees apart). Note: the Type 6 letter α (lowercase) shares this name because a static letter is essentially a held position: the same concept. When someone asks 'what is alpha?', context determines whether they mean the position (hands opposite) or the letter (both hands static at opposite points).

• alpha1: hands at N and S
• alpha3: hands at E and W
• The Type 6 letter α represents holding an alpha position with no motion

A position where both hands are at the same grid point (0 degrees apart). The Type 6 letter β (lowercase) shares this name. It represents holding a beta position with no motion, which is also a natural start position for 'together' patterns.

• beta1: both hands at N
• beta5: both hands at NE

A position where the hands form an acute angle (less than 90 degrees). Introduced in Level 5 with skewed grid mode.

• One hand cardinal, one intercardinal, forming ~45 degree angle

The hand that trails the leading hand in a Quarter-Same gamma motion (S, T, U, V). For S and T, the glyph's low slot belongs to the following hand. For U and V, slot assignment follows pro/anti PADS rules regardless of leading/following. Counterpart to leading. Not currently represented in the TKA software pipeline (code distinguishes hands only by color). See also: leader-follower.

• S-Low-One: following hand has 1 turn
• T-High-One: leading hand has 1 turn, following has 0

A position where the hands form a right angle (90 degrees apart on adjacent grid points). The Type 6 letter γ (lowercase) shares this name. It represents holding a gamma position with no motion.

• gamma1: hands at N and E
• gamma5: hands at NE and NW (box mode)

A distinction that arises in asymmetric positions (gamma, zeta, eta) when both hands shift the same direction. One hand is directionally 'ahead' of the other, creating a leader and a follower. This matters for letter assignment because the leader and follower can have different turn values. In the TKA glyph, the leader's turn number appears on top, the follower's on bottom. Leader/follower does NOT apply to opposite-direction movement (hands diverge/converge symmetrically) or to symmetric positions (alpha, beta). Leader/follower is combinatorially equivalent to mixed motion types: it doubles the variation space the same way that having one pro and one anti does.

• In gamma, same-direction shifts create leader/follower. Requires S, T, U, V letters
• In alpha (symmetric), no leader/follower. Uses A through L
• Opposite-direction shifts in any position have no leader/follower
• S,T,U,V each have the same variation count as hybrids (C, F, I, L, O) because leader/follower doubles the space

The hand that drives or initiates a Quarter-Same gamma motion. Applies to the Type 1 gamma-to-gamma letters S, T, U, and V, which have an inherent leader/follower asymmetry. For S and T (matching motion types pro|pro or anti|anti), the glyph's high slot belongs to the leading hand and the low slot to the following hand. This is how their base forms are disambiguated. For U and V (pro|anti hybrid), the leading/following asymmetry physically exists but the glyph slots follow the pro/anti PADS rule instead (pro-high / anti-low). Counterpart to following. Note: as of 2026-04-19, leading/following is a pedagogical concept from the Level 2 Guide that is not represented in the TKA software pipeline. The code distinguishes hands only by color (blue/red). See also: leader-follower.

• S-High-One: leading hand has 1 turn (leading occupies the high slot for S and T)
• T-Low-One: following hand has 1 turn, leading has 0
• U-High-One: leading hand has 1 turn, but here the high slot is pro, not leader, because U is pro|anti hybrid

A position where one hand is at the center grid point and the other is at a non-center point. Introduced in Level 4 with centric grid mode.

• One hand at center, one hand at N
• One hand at center, one hand at NE

A position where both hands are at the center grid point. Introduced in Level 4 with centric grid mode.

• Both hands stacked at the center of the grid

A position where the hands form an obtuse angle (greater than 90 degrees). Introduced in Level 5 with skewed grid mode.

• One hand cardinal, one intercardinal, forming ~135 degree angle

A letter type (Type 3) where one hand shifts and one hand dashes simultaneously. Named with a '-' suffix (e.g. W-, Σ-). When someone says 'Sigma dash', they mean the Type 3 letter Σ-, not a letter with dash motion.

• W-, X-, Y-, Z-
• Σ- (Sigma dash) is a Type 3 letter

A letter type (Type 5) where both hands dash simultaneously. Named with a '-' suffix like Type 3.

• Φ-, Ψ-, Λ-
• Only 3 letters in this type

A letter type (Type 1) where both hands shift simultaneously to adjacent points. The largest type with 22 letters (A through V). Organized by VTG timing and direction into pro+anti+hybrid triads: split-same (A,B,C), together-opposite (D,E,F), together-same (G,H,I), split-opposite (J,K,L), and quarter-opposite (M,N,O and P,Q,R). The exception is quarter-same (S,T,U,V), which has 4: same-direction shifts at a right angle (gamma) have a leader and follower, which splits the hybrid into U and V (breaking color-swap invariance). See domain topic 'stuv-anomaly' for the full explanation.

• Letters A through V
• A: both hands shift, both pro
• C: both hands shift, hybrid (one pro, one anti)
• S,T,U,V: quarter-same group has 4 letters due to leader/follower

The Type 4 letter τ- (tau-dash). One hand dashes while the other is static, with the static hand at center. Distinct from other Type 4 letters (Φ, Ψ, Λ) because the static hand position is center, not perimeter. τ- has NO Type 5 (dual-dash) variant because a hand at center cannot perform a standard dash: there is no 'opposite' of center on the grid.

• τ-: one hand dashes, static hand at center
• No τ-- exists (can't dual-dash from center)
• Type 4 = one dashes, one static

A hand motion type where the hand moves in a straight line to the diametrically opposite grid point (180 degrees across the grid). At 0 turns, the prop does not rotate: it translates along the straight path without spinning. Unlike shifts (curved arcs), dashes follow straight lines, so pro/anti/float distinctions do not apply. At 1+ turns, the prop rotates CW or CCW during the traverse.

• N to S is a dash
• NE to SW is a dash
• Type 4 and Type 5 letters use dashes

A reversal where both the hand and prop retrace their paths, like pressing rewind. The hand returns to its previous point AND the prop reverses direction. Unlike hand and prop reversals, this maintains the rotation type: prospin stays prospin, antispin stays antispin. Indicated by a colored dot on the left edge of the pictograph.

• Hand goes back to previous point AND prop reverses. Everything rewinds. Pro stays pro.

The trajectory a hand traces when moving between grid points. Four types: static (stay), shift (curved arc along perimeter to adjacent point), dash (straight line to opposite point), hash (straight line to/from center). The geometric shape of the path matters: shifts follow curved arcs (enabling pro/anti/float distinctions), while dashes and hashes follow straight lines (no pro/anti/float). The hand path determines the base rotation behavior.

• W to N clockwise is a curved shift arc
• N to S is a straight-line dash
• N to center is a hash (half-dash)

The +/- system that extends or shortens standard hand paths. Applies to both shifts and dashes. For shifts: skew+ (longer arc), skew- (shorter arc). For dashes: dash- (to/from center, called 'hash'), dash+ (cross-grid, L7), dash++ (cross-grid to opposite perimeter, L7). The modifier is displayed per-hand in the turns column of the TKA glyph. Modifiers do NOT change the letter type classification. Dash and dash- are both in the 'dash' family.

• Skew+ (shift+): S to NE, extended arc spanning 3 segments
• Dash- (hash): N to center, shortened straight line
• Dash+ (L7): perimeter to center of other grid

A reversal where the hand returns to the grid point it came from, but the prop continues rotating in the same direction. This switches prospin to antispin (or vice versa) because the hand's path direction reverses while the prop doesn't. The least disruptive reversal type. No special notation required.

• Hand was at N, shifted to E, now shifts back to N. Prop keeps spinning the same way.

A hand motion type where the hand moves in a straight line to or from the center grid point. Hash is **dash-** (dash with a minus modifier): the same straight-line traverse as a dash, but covering half the distance (center to perimeter or perimeter to center). 'Hash' is the official name for dash-, just as 'skew' is the official name for shift+/-. Introduced in Level 4 with centric grid mode. Same rotation physics as dash: at 0 turns, no rotation (1 state); at 1+ turns, CW or CCW (2 states per turn count). Pro/anti/float distinctions do not apply (straight line, not curved arc).

• N to center is a hash (dash-)
• Center to E is a hash
• Hash = dash- = half-dash, same physics as dash

A repeated-dash choreo pattern where the hand travels in a straight line through the center to the opposite grid point with one turn added per step (a 1-turn dash executed on repeat). Named 'linear extension' because the pattern extends along a linear hand path rather than a curved one. Iconic because with double staves, the prop's two ends exhibit opposite rotation relationships relative to the linear hand path: one end behaves like a prospin, the other like an antispin. The Level 2 Guide recommends focusing on the antispin half to ensure the hand passes directly through the center point.

• Repeated 1-turn dashes: N→S→N→S with one turn per step
• The prop's two ends: one end prospins, the other antispins. Focus on the antispin end for timing

A reversal where the hand continues to the next grid point but the prop reverses its rotation direction. Switches prospin to antispin (or vice versa). Indicated by a colored dot on the left edge of the pictograph in the corresponding hand's color.

• Hand continues N to E, but prop switches from clockwise to counter-clockwise.

A directional change in a TKA sequence. There are three distinct types: hand reversal (hand returns to previous point, prop continues, switches pro/anti), prop reversal (hand continues, prop reverses direction, switches pro/anti), and full reversal (both hand and prop retrace, maintains pro/anti). Reversals are indicated by colored dots on the left edge of the pictograph.

• Hand reversal: hand goes back, prop keeps spinning same way. Switches prospin to antispin.
• Prop reversal: hand continues forward, prop switches direction.
• Full reversal: everything rewinds. Pro stays pro, anti stays anti.
• Colored dots appear on the left edge of the pictograph when a reversal occurs

A hand motion type where the hand arcs along the perimeter to an adjacent grid point. The curved arc is what distinguishes shifts from dashes and hashes (straight lines). The prop behavior during a shift depends on the rotation type: pro rotates with the arc, anti rotates against it, float holds absolute spatial angle. On a 4-point grid, adjacent points are 90° apart; on an 8-point grid, 45° apart.

• N to E is a shift (4-point grid, 90° arc)
• NE to SE is a shift (8-point grid, 45° arc)
• Type 1 and Type 2 letters use shifts

A shift with a +/- path length modifier (Level 5+, 8-point grid). Skew+ extends the arc beyond a single segment (e.g., S to NE spanning 3 segments). Skew- shortens the arc to less than one segment. Skews support all three shift motion types (pro, anti, float) and are theoretically unbounded in arc length. For enumeration, the standard single-segment shift is counted; skews are extensions.

• Skew+ (shift+): extended arc, e.g. S to NE
• Skew- (shift-): shortened arc
• Skew++ (shift++): double-extended arc

A hand motion type where the hand stays at its current grid point. The prop may still rotate (with turns), but the hand does not move.

• Type 6 letters (α, β, γ) have both hands static
• Type 2 letters have one static hand and one shifting hand

A prop rotation type where the prop rotates opposite to the hand's arc. Also called 'antispin'. Creates petal-like patterns in continuous motion. At 0 turns, orientation reverses (e.g. in becomes out). At higher turn counts, the parity rules apply: even turns (0, 2) reverse orientation, odd turns (1, 3) preserve it, the opposite of pro.

• Hand shifts W to N clockwise, prop rotates counter-clockwise against the arc
• 0-turn anti: orientation reverses (in becomes out)
• 1-turn anti: orientation preserved
• 2-turn anti: orientation reverses again

Full name for anti. A prop rotation type where the prop rotates opposite to the hand's arc. Creates petal-like patterns.

• Hand shifts W to N clockwise, prop rotates counter-clockwise against the arc

The inherent prop rotation that occurs at 0 additional turns during any motion. Turn counts in TKA measure ADDITIONAL rotation on top of this base. For shifts (curved arcs), the arc causes center-relative angular change even at 0 turns. 0-turn pro and 0-turn anti are two different states because the prop either rotates with or against the arc. For dashes, hashes, and statics (straight lines or no movement), there is no arc, so base rotation at 0 turns means truly no rotation, producing exactly 1 state, not 2.

• 0-turn pro shift: prop rotates with the arc (base rotation preserves orientation)
• 0-turn anti shift: prop rotates against the arc (base rotation reverses orientation)
• 0-turn dash: no rotation, no direction (just one state)

Counter-clockwise rotation direction, as viewed from above the performer.

• Hand path moving N -> W -> S -> E is counter-clockwise

Clockwise rotation direction, as viewed from above the performer. Abbreviated as 'cw'.

• Hand path moving N -> E -> S -> W is clockwise

Counter-clockwise rotation direction, as viewed from above the performer. Abbreviated as 'ccw'.

• Hand path moving N -> W -> S -> E is counter-clockwise

Clockwise rotation direction, as viewed from above the performer.

• Hand path moving N -> E -> S -> W is clockwise

A prop rotation type where the prop does not rotate at all during a shift: it holds its absolute spatial angle. Float only applies to shifts because it requires a curved hand path; without a curve, there is no distinction between float and 0-turn static. Because the hand traces an arc while the prop holds still, the center-relative orientation changes even though there is no prop rotation. Mathematically equivalent to -0.5 turns from base rotation, which also makes float the symmetry boundary between pro and anti. Going past float means you've crossed into the opposite motion type.

• Hand moves from W to N, prop maintains its exact facing in space
• Center-relative orientation changes as the hand arcs (e.g., 'in' may become 'clock')
• Only meaningful during shifts: a non-moving or straight-line hand path has no float distinction

A prop rotation state at -0.25 turns from the base rotation: halfway between float (no rotation, -0.5 turns) and the base form (0 turns). The prop rotates in the motion's direction (pro or anti) but less than the base amount, producing an interradial orientation change (45 degrees) instead of the full cardinal change (90 degrees). Only meaningful at Level 6, where quarter-turn subdivision and interradial orientations exist. The name is mathematically literal: half the turn offset of a float. Like float, half-float applies only to shifts (curved hand paths).

• Pro shift E to N with half-float: orientation ends at counterIn instead of in (0 turns) or counter (float)
• Half-float is -0.25 turns; float is -0.5 turns; the name reflects the halved offset
• Completing the L6 turn continuum: ... float (-0.5) → half-float (-0.25) → base (0) → +0.25 → +0.5 ...

The four orientations at 45 degrees between the base cardinal orientations, introduced at Level 6. These double the angular precision of the orientation system from 4 values to 8. The four interradial orientations are: clockIn (between clock and in), clockOut (between clock and out), counterIn (between counter and in), counterOut (between counter and out). Quarter turns (0.25, 0.75, etc.) produce interradial orientations using the 8-point radial cycle: in → clockIn → clock → clockOut → out → counterOut → counter → counterIn.

• clockIn: prop faces 45° between clock and in
• Level 6 doubles orientation vocabulary from 4 to 8
• Quarter turns step through the 8-point radial cycle

Pro motion at 0 turns. The prop's center-relative orientation remains constant as the hand moves: the prop rotates with the arc, creating the visual effect of a fixed point while the hand orbits around it. Distinct from float, where the prop literally holds its absolute spatial angle. With additional turns, the motion is still pro but no longer an isolation since the prop visibly rotates beyond the base rate.

• Pro at 0 turns during a shift: center-relative orientation preserved, prop appears fixed
• DJ compound uses isolation (pro/pro at 0 turns)

The facing direction of a prop relative to the performer's center point. Eight possible values across the level system. Cardinal orientations (all levels): in (toward center), out (away from center), clock (clockwise-facing), counter (counter-clockwise-facing). Interradial orientations (Level 6+): clockIn, clockOut, counterIn, counterOut, the four orientations at 45 degrees between cardinal orientations.

• Pro at 0 turns preserves orientation (in stays in)
• Anti at 0 turns switches orientation (in becomes out)
• Level 6 adds clockIn, clockOut, counterIn, counterOut between base orientations

A prop rotation type where the prop rotates in the same direction as the hand's arc. Also called 'prospin'. At 0 turns, center-relative orientation is preserved (e.g. in stays in). This specific case is called an 'isolation', where the prop rotates with the arc creating the visual effect of a fixed point (distinct from float, which holds absolute spatial angle). At higher turn counts, the parity rules apply: even turns (0, 2) preserve orientation, odd turns (1, 3) reverse it.

• Hand shifts W to N clockwise, prop rotates clockwise with the arc
• 0-turn pro: center-relative orientation preserved (isolation)
• 1-turn pro: orientation reverses
• 2-turn pro: orientation preserved again

Full name for pro. A prop rotation type where the prop rotates in the same direction as the hand's arc.

• Hand shifts W to N clockwise, prop rotates clockwise with the arc

The geometric relationship between the rotation directions of two simultaneously-rotating props in a single step. When both hands rotate, their directions form either a 'Same' relationship (same direction relative to each other) or an 'Opp' relationship (opposite directions). Notated with a same-dot (above the letter) or opp-dot (below). Only meaningful when both props are actively rotating. Pictographs with only one rotating prop have no rotational relationship to describe. Lambda (Λ, Λ-) and Gamma (Γ) pictographs do NOT use rotational-relationship. They use opening/closing instead, which supersedes (rather than coexists with) same/opp because gamma's right-angle asymmetry requires a different disambiguation. In the codebase, this is derived at render time by comparing blueMotion.rotationDirection to redMotion.rotationDirection; it is not a stored field.

• W(s,0,1): shift and static both rotate in the same direction → same-dot above the W
• X(o,1,1): shift and static rotate in opposite directions → opp-dot below the X
• Φ(1,0): only the dash rotates → no rotational relationship, no dot
• Λ(0,1,op): rotating hand is opening. Opening/closing replaces same/opp for Lambda

One flip of the thumb-end's reference orientation during a motion (e.g., thumb in → thumb out). The Level 2 Guide's primary pedagogical counting framework for teaching turns: every motion has a base thumb-switch count, and each additional turn adds exactly one more thumb switch. Provides a discrete, physically-verifiable check during practice rather than requiring students to track abstract angular rotation.

• Isolation (0-turn pro shift): 0 switches (thumb stays in throughout)
• Antispin (0-turn anti shift): 1 switch (in → out)
• 1-turn antispin: 2 switches (in → out → in)
• 2-turn antispin: 3 switches (in → out → in → out)
• Base dash: 1 switch (in → out)
• 1-turn dash: 2 switches (in → out → in, back to start orientation)
• 2-turn static: 2 switches (in → out → in)

Additional prop rotation beyond the base rotation inherent to the motion type. 1 turn = 180 degrees of additional rotation. This unit is a deliberate pedagogical choice: at 180°, whole turns 0-3 stay as clean small integers (Level 2), half turns (90°) produce cardinal orientation shifts (Level 3), and quarter turns (45°) produce interradial orientations (Level 6). If 1 turn were 360°, interradials would require 1/8 turns; if 90°, Level 2 would need 6 turn values. At 0 turns, pro and anti still produce base rotation from the hand path. The turn count measures rotation on top of that base behavior. The turn axis extends into negative values for shifts: -0.25 (half-float) and -0.5 (float). Values beyond -0.5 are equivalent to the opposite motion type (e.g., pro at -0.75 = anti at -0.25), making float the symmetry boundary.

• 0 turns with pro shift: prop rotates 90 degrees (base only, no additional)
• 1 turn with pro shift: prop rotates 90 degrees base + 180 degrees additional
• 0 turns with dash: no rotation (pure translation)
• Full L6 continuum for shifts: float (-0.5) → half-float (-0.25) → 0 → 0.25 → 0.5 → 0.75 → 1.0 → ...

A grid mode where hands are placed only on intercardinal points (NE, SE, SW, NW).

• Position beta5 (both hands at NE) uses box mode

The four main compass points on the grid: North (N), East (E), South (S), West (W).

• Diamond mode uses cardinal points
• N is at the top of the pictograph

The 9th grid point, located at the center of the grid. Introduced in Level 4 with centric grid mode. Not yet implemented in Flow Arts Composer.

• Tau position: one hand at center
• Terra position: both hands at center

A grid mode introduced in Level 4 where at least one hand is at the center grid point. Creates tau and terra positions. Not yet implemented in Flow Arts Composer.

• One hand at center, one at N (tau position)
• Both hands at center (terra position)

A Level 7 concept where two grids share a junction point, expanding the spatial canvas and bridging to 3D. Each grid shows one hand's motion. The junction point creates new position combinations that can't exist on a single grid, including patterns with two center points. Uses existing terminology (alpha, beta, gamma, etc.) to express new spatial relationships across the paired grids. Placed after interradials (L6) so all orientation freedom is complete before expanding beyond one grid.

• Two grids sharing a north/south junction, blue hand on grid A, red hand on grid B
• Layouts: left-right, top-bottom, diagonal arrangements
• Patterns where hands are spatially further apart than a single grid allows

A grid mode where hands are placed only on cardinal points (N, E, S, W). The default grid mode.

• Standard positions like alpha1 (N/S) use diamond mode

The four diagonal compass points on the grid: Northeast (NE), Southeast (SE), Southwest (SW), Northwest (NW).

• Box mode uses intercardinal points
• NE is at the top-right of the pictograph

A grid mode introduced in Level 5 where one hand is on a cardinal point and one is on an intercardinal point. Creates zeta and eta positions.

• Hand at N and hand at NE
• Creates zeta and eta positions

The visual output of sequence generation: a composite image showing all pictographs in a sequence arranged in a grid or strip layout. Includes optional header (word, difficulty), step numbers, reversal indicators, and footer (username, notes, date).

• A 4-letter word produces a choreo card with 5 pictographs (start + 4 steps)
• Grid layout arranges pictographs in rows, strip layout puts them in a single row

A per-hand designation for a rotating prop in a Lambda (Λ), Lambda-Dash (Λ-), or Gamma (Γ) pictograph. 'Closing' means that if the hand's rotational trajectory were extrapolated into a subsequent pro-shift, the motion would resolve toward a beta position (hands at the same grid point, spatially 'closed'). Each rotating hand is independently opening or closing. Encoded in code as a 'cl' flag in the turn tuple. Complement of opening. See opening for the full rationale (alpha-vs-beta trajectory, codebase implementation in PropRotationStateTracker.ts).

• Λ(0,1,cl): Lambda with 1-turn static hand whose trajectory would resolve to beta
• Λ-(1,1,cl,cl): Lambda-Dash with both hands closing (both trajectories resolve to beta)
• Γ(cl,op): Gamma with blue closing (toward beta), red opening (toward alpha)

The reference point for VTG timing, located at the south (bottom) of the circle. VTG classifies patterns based on when and how props pass through the downbeat. TKA uses center-referenced positions instead, but maps to VTG for compatibility.

• Both props at south simultaneously = together timing
• Props 180° out of phase relative to south = split timing

A mnemonic framework mapping VTG's timing/direction categories to classical elements plus two additions. The original four elements (Earth, Water, Air, Fire) come from the poi community's VTG teaching tradition. TKA expands the model with Sun and Moon to cover gamma patterns. Same-direction elements (Earth, Water, Sun) are grid-mode invariant. Opposite-direction elements (Air, Fire, Moon) permute when switching between diamond and box mode.

• Earth = tog-same (G,H,I), Water = split-same (A,B,C), Air = tog-opp, Fire = split-opp
• Sun = quarter-same (S,T,U,V), Moon = quarter-opp (MP,NQ,OR compounds)
• Diamond DJ = Air/Fire, but Box DJ = Moon

A visual notation element displayed on a pictograph. Glyphs annotate the pictograph with additional information beyond the prop and arrow positions. The TKA glyph's turns column (high/low slots) is laid out per PADS.

• TKA glyph: shows the letter name and turn numbers
• TnD glyph: shows timing & direction relationship between hands
• Position glyph: shows start and end positions

The upper of the two turn-number slots positioned to the right of a letter in a TKA glyph. Which hand occupies the high slot is determined by PADS priority (Pro > Anti > Dash > Static) when motion types differ, by left-hand convention when motion types match, or by the leading hand for S and T. The corresponding low-slot sits below. TKA software handles slot placement automatically; the concept is defined in the Level 2 Guide (Glyphs / PADS section).

• In C(1,0), the '1' sits in the high slot and belongs to the pro motion (pro beats anti per PADS)
• In W(s,1,0), the '1' in the high slot belongs to the shift (shift beats static)
• In A(1,0), the '1' in the high slot belongs to the left hand (motion types match, so left goes high)

The lower of the two turn-number slots in a TKA glyph, sitting beneath the high-slot. Which hand occupies the low slot is determined by PADS priority (takes whichever motion type is lower: anti, dash, or static depending on the pair), by right-hand convention when motion types match, or by the following hand for S and T. Complement of high-slot.

• In C(1,0), the '0' in the low slot belongs to the anti motion
• In Φ(1,0), the '0' in the low slot belongs to the static hand (dash beats static)
• In A(1,0), the '0' in the low slot belongs to the right hand

A per-hand designation for a rotating prop in a Lambda (Λ), Lambda-Dash (Λ-), or Gamma (Γ) pictograph. 'Opening' means that if the hand's rotational trajectory were extrapolated into a subsequent pro-shift, the motion would resolve toward an alpha position (hands at opposite grid points, spatially 'open'). Each rotating hand is independently opening or closing; a pictograph can have mixed states (e.g., blue opening + red closing). Required because these pictographs' opening/closing variants cannot be produced from each other by rotation, reflection, or mirroring (a core TKA invariant), and same/opp rotational relationship cannot capture the distinction. Gamma's right-angle geometry creates asymmetric outcomes. Encoded in code as an 'op' flag in the turn tuple (e.g., Λ(0,1,op) for single-rotating-hand, Λ-(1,1,op,cl) for both rotating). In the codebase, derived at render time from (endLocation, otherHandEndLocation, rotationDirection) lookups in PropRotationStateTracker.ts, not stored on MotionData. Complement of closing.

• Λ(0,1,op): Lambda with 1-turn static hand whose trajectory would resolve to alpha
• Λ-(1,1,op,cl): Lambda-Dash with blue hand opening (toward alpha), red hand closing (toward beta)
• Γ(op,op): Gamma with both hands rotating such that both trajectories resolve to alpha

A dot placed below a letter in a TKA glyph to mark the rotational relationship as 'Opp': the two rotating props are spinning in opposite directions relative to each other. Encoded in code as an (o) parameter (e.g., X(o,1,1)). Read aloud as '[Letter]-Opp'. For example, X with an opp-dot is spoken 'X-Opp'. Same application scope as same-dot. Does NOT apply to Lambda or Gamma. Complement of same-dot.

• X(o,1,1): X with opp-dot below, 1 turn on each hand ('X-Opp-One-One')
• Θ-(o,1,1): Theta-Dash with opp-dot, 1 turn each ('Theta-Dash-Opp-One-One')
• Φ(o,1,1): Phi with opp-dot. Both dash and static rotating in opposite directions

The priority order (Pro, Anti, Dash, Static) that determines which motion occupies the high (top) slot and which occupies the low (bottom) slot of a pictograph's turns column. When the two hands have different motion types, the higher-priority type goes in the high slot: pro beats anti beats dash beats static. For pro/anti hybrids (C, F, I, L, O, R, U, V) this means pro-high / anti-low. For Type 2 (W, X, Y, Z, Σ, Δ, θ, Ω): shift-high / static-low. For Type 3 (W-, X-, Y-, Z-, Σ-, Δ-, θ-, Ω-): shift-high / dash-low. For Type 4 (Φ, Ψ, Λ): dash-high / static-low. When motion types match, A, B, D, E, G, H, J, K, M, N, P, Q, dual-dashes (Φ-, Ψ-, Λ-), statics (α, β, Γ), left goes high and right goes low. S and T are the exception among matching-type hybrids: leading hand goes high, following hand goes low. The TKA software handles placement automatically. Defined in the Level 2 Guide (Glyphs / PADS section). Implemented implicitly in the codebase via per-letter-type branches in TurnColorInterpreter and TurnsTupleGenerator. No explicit PADS constant array exists.

• C-High-One: pro hand has 1 turn, anti hand has 0 (high = pro per PADS)
• R(fl, 0): float marker in high slot means the float was applied to the pro hand (pro-high / anti-low for hybrids)
• W(1, 0): shift has 1 turn, static has 0 (high = shift since shift beats static)
• Φ(1, 0): dash has 1 turn, static has 0 (high = dash since dash beats static)
• S-High-One: leading hand has 1 turn (leading goes high for S and T)

A misnomer for gamma patterns (M through V) in VTG vocabulary. It describes a 90-degree phase offset between hands, NOT a timing or duration change. VTG's split and tog have formal phase designations, but quarter time never received equivalent formal naming. It was strapped onto VTG's framework by later practitioners without integration into the original four-category system. In TKA, these patterns are simply the gamma letters. No special 'quarter time' designation needed.

• 'Quarter time' = 90-degree phase offset, not a timing change
• In TKA, these are just gamma letters (M through V)
• VTG never formally integrated QT into its core four categories

A dot placed above a letter in a TKA glyph to mark the rotational relationship as 'Same': both rotating props are spinning in the same direction relative to each other. Encoded in code as an (s) parameter (e.g., W(s,0,1)). Read aloud as '[Letter]-Same'. For example, W with a same-dot is spoken 'W-Same'. Applied to Type 2, Type 3, Type 4, Type 5, and Type 6 pictographs when both hands rotate. Does NOT apply to Lambda (Λ, Λ-) or Gamma (Γ), which use opening/closing instead. Complement of opp-dot.

• W(s,0,1): W with same-dot above, 0 turns on shift, 1 on static ('W-Same-Low-One')
• Ψ-(s,1,1): Psi-Dash with same-dot, 1 turn on each hand ('Psi-Dash-Same-One-One')
• α(s,1,1): alpha with same-dot, 1 turn each ('Alpha-Same-One-One')

A VTG timing classification where the two props are 180 degrees out of phase: one is at the downbeat (south) when the other is at the top. In TKA terms, split timing corresponds to alpha positions (hands at opposite points).

• Letters A, B, C (alpha to alpha) are always split-same
• DJ compound can be split-opp depending on variation

A VTG category where props are 180° out of phase (split) and hands arc in opposite directions. Abbreviated SO or split-opp.

• DJ east-start variation is split-opposite

A VTG category where props are 180° out of phase (split) and both hands arc the same direction. Abbreviated SS.

• Letters A, B, C (alpha to alpha) are always split-same

Short for 'together'. A VTG timing classification where both props pass through the downbeat (south) at the same moment. In TKA terms, together timing corresponds to beta positions (hands at the same point).

• Letters G, H, I (beta to beta) are always tog-same
• DJ compound can be tog-opp depending on variation

A VTG timing classification where both props pass through the downbeat (south) at the same moment. Abbreviated as 'tog'. In TKA terms, together timing corresponds to beta positions (hands at the same point).

• Letters G, H, I (beta to beta) are always together-same

A VTG category where props are in sync (together) and hands arc in opposite directions. Abbreviated TO or tog-opp.

• DJ south-start variation is together-opposite

A VTG category where props are in sync (together) and both hands arc the same direction. Abbreviated TS or tog-same.

• Letters G, H, I (beta to beta) are always together-same

Vulcan Tech Gospel: an older, widely-adopted notation framework for flow arts that emerged from the poi community at the Vulcan Lofts in Oakland, CA. TKA uses VTG as a secondary notation layer. VTG is ground-referenced: the 'downbeat' (south/bottom of the circle) is the anchor point for all timing and direction classifications. 'Same/opposite' in VTG refers to hand path direction (both hands arc the same way vs opposite ways), not prop rotation direction.

• Split-Same (SS): props 180° out of phase, hands arc same way
• Together-Same (TS): props in sync, hands arc same way
• Split-Opposite (SO): props out of phase, hands arc opposite ways
• Together-Opposite (TO): props in sync, hands arc opposite ways

Continuous Assembly Patterns (CAPs): coined by Damien of Angers, France (posting as French_Saltimbanque and Zaltymbunk) in the Yuta move analysis thread on the Home of Poi forums, from ideas germinated with the OMCC crew (Alien Jon, Noel, Greg, Jordan, Zan) at Burning Man 2007. Canonical definition: a cyclic pattern assembled from 2+ elementary patterns (trochoid building blocks notated θ1 θ2 ; ρ1 ρ2 ; d) iterated 1+ times — the SERIAL composition process, contrasted with hybrids (PARALLEL superposition, one pattern per hand). The community later narrowed everyday 'cap' to mean the C-CAP (extension + antispin petal alternation). CAPs and LOOPs are parallel concepts, not parent/child. Neither is a subset of the other.

• C-CAP: the extension-arc + antispin-petal pattern most spinners call 'a cap'
• The Yuta CAP: 1 0 ; 1 3/4 ; 1/2 assembled with -1 4 ; 1 3/4 ; 1/2
• CAPs compose per-hand trajectories serially; hybrids compose across hands in parallel
• LOOPs compose per-step snapshots (one letter = both hands)

A rule applied during sequence generation that controls the style of the output. Constraints can be hard (must be satisfied) or soft (best-effort). Specified via preset names or natural language. Without constraints, the legacy random-walk builder is used. With any constraint, the reliable beam-search builder is activated.

• constraintPreset: 'smooth' minimizes reversals
• constraintPreset: 'isolation' forces all pro motions
• Natural language: 'maximize flow with blue clockwise'

A predefined set of constraints with a short name. Available presets: smooth (maximize flow), smooth-hands (hand path continuity), smooth-props (prop spin continuity), reversal (maximize direction changes), isolation (all pro), antispin (all anti), pro-cw (pro + clockwise), anti-ccw (anti + counter-clockwise), no-dash (shifts only), maximize-dash (prefer Type 4/5), maximum-chaos (maximize all reversals).

• 'smooth' preset minimizes both hand path and prop reversals
• 'isolation' forces all pro motions like the DJ compound
• 'maximum-chaos' maximizes every possible reversal

A LOOP transformation where positions mirror across the horizontal axis (top-bottom swap) to return home.

• Hand at N flips to S
• Top-bottom positions swap across the horizontal midline

A LOOP slice size where the sequence is divided into two halves of 180 degrees each. The transformation is applied once to create the second half, completing a 360-degree cycle. Used with the rotated LOOP type.

• A 4-letter word halved: first 4 steps + transformed 4 steps = 8-step LOOP
• Each half covers 180 degrees of the full rotation

A LOOP transformation where motion types flip between pro and anti. Prospin becomes antispin and vice versa.

• Pro motion in first half becomes anti in second half
• Changes the visual pattern significantly while keeping hand paths the same

A circular sequence that returns to its starting position through transformations. Six base transformations (rotated, mirrored, flipped, swapped, inverted, rewound) can be combined into compound types like mirrored-swapped or rotated-inverted. The word repeats with transformations applied until it arrives back home.

• DJII (8-count rewound loop)
• AABB with mirrored-swapped transformation
• 16-count loops use 4-letter words repeated 4 times
• Compound LOOP types combine multiple base transformations

A LOOP transformation where positions mirror across the vertical axis (left-right swap) to return home.

• Hand at E mirrors to W
• Left-right positions swap across the vertical midline

A LOOP slice size where the sequence is divided into four quarters of 90 degrees each. The transformation is applied three times to create quarters 2-4, completing a 360-degree cycle. Used with the rotated LOOP type.

• A 4-letter word quartered: 4 steps repeated 4 times = 16-step LOOP
• Each quarter covers 90 degrees of the full rotation

A LOOP transformation where the second half plays in reverse: hands trace their path backwards to return home. Like pressing rewind on a video. Not to be confused with rotated, where hands continue forward in the same direction.

• First half: A→B→C→D. Second half: D→C→B→A (rewound back home)

A LOOP transformation where positions rotate around the grid to return home. The second half continues rotating in the same direction as the first half to complete a full 360 degrees. Not to be confused with rewound, where hands reverse direction.

• Halved: two halves, each rotates 180° (total 360°)
• Quartered: four quarters, each rotates 90° (total 360°)

A LOOP transformation where the blue and red hands swap roles. What the blue hand did, the red hand now does (and vice versa). Changes body motion significantly.

• Blue was at N doing pro, now red is at N doing pro
• Body has to reorganize to execute the swapped version

Turning the torso to execute patterns, especially for longer staves.

Benefit: Add movement quality, handle longer staves, create dynamic contrast

• Rotating shoulders to reach behind
• Full body rotation during complex sequences

Passing the prop through space around the body without turning the torso.

Benefit: Face audience, reduce body movement

• Reaching behind to execute a pattern
• Using arm extension instead of body rotation

Tracking whether thumbs point inward or outward on each step to verify prop rotation.

Why it matters: Track rotations and check position on every step

• thumbs-in: starting position with thumbs toward center
• thumbs-out: thumbs away from center