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Spin ratios

A spin ratio counts one pattern twice: how many circles the hand travels, and how many rotations the prop makes over the same span. It is written hands first, so 1:3 is one hand circle to three prop rotations. The Kinetic Alphabet counts the same motion as turns, where one turn is 180 degrees of prop rotation on top of the base rotation the motion already carries.

Three ratios carry most of the vocabulary. Lorq Nichols, who publishes as Spin Science(opens in a new tab), built the 144 Shape Matrix from 1:1, 1:3, and 1:5. The same construction keeps working the rest of the way up the turn ladder, which is what the tables below lay out.

Reading a ratio

Hand cycles, H
Complete circles the hand travels.
Prop rotations, P
Complete rotations the prop makes over those circles.

For a moving hand the two systems convert directly. Prop rotations per hand cycle are P / H = 2 × turns + 1, and the same relation read backwards is turns = (P / H − 1) / 2.

The reduced ratio also fixes the petal count. A prospin flower draws |P − H| petals and an antispin flower draws P + H. Both counts follow one end of the prop. A staff draws with both of its ends, and what the second end adds depends on the ratio, as One end or two lays out below.

Float sits outside the arithmetic. The prop makes no rotation of its own while the hand circles, which is the ratio 1:0, and the Kinetic Alphabet names it Float instead of a number.

Common names

Cat-eye
1:1 antispin
Triquetra
1:2 antispin
4-petal antispin flower
1:3 antispin
3-petal inspin flower
1:4 prospin

Each name describes the shape one end of the prop draws. Inspin is another name for prospin; Prospin and Inspin compares the two.

1:3, one turn
 Prospin 2 petals
 Antispin 4 petals

P is 3 and H is 1, so prospin draws 2 petals and antispin draws 4.

Ratios and turns

Every turn value the Kinetic Alphabet carries, set out by the level that first allows it. Each card gives the ratio, the turns it names, and the two flowers one hand draws at that ratio, following one end of the prop. A level keeps everything the levels before it allow and adds the cards under it.

Through Level 3 each ratio shows four flowers: prospin and antispin, each from a start with the prop pointing in and a start pointing out. At Level 1 those are four different base motions. From Level 2 on, the second start draws the first flower turned half a petal, so each flower is named by how it sits: a petal pointing up or down, petals stacked vertical or lying horizontal, four petals in diamond or box. At Level 4's quarter turns both starts draw the very same flower, so those cards show one, and every one of them puts a petal straight down, prospin and antispin alike.

Tinted cards are the three ratios of the original matrix.

1 Level 1, Base Motions Base paths with zero turns

  1. 1:1 Starts in

     Prospin Isolation
     Antispin 2 petals, horizontal

  2. 1:1 Starts out

     Prospin Extension
     Antispin 2 petals, vertical
2 Level 2, Whole Turns Adds whole-turn possibilities

  1. 1:3 1 turn

    Prospin Antispin
    2 petals4 petals

  2. 1:5 2 turns

    Prospin Antispin
    4 petals6 petals

  3. 1:7 3 turns

    Prospin Antispin
    6 petals8 petals

Each whole turn adds two petals to both flowers, and a half turn adds one, so Level 3 fills the gaps between these counts.

3 Level 3, Half Turns + Float Adds half turns and Float

  1. 1:0 Float
    Holds one angle while the hand circles.

  2. 1:2 0.5 turns

    Prospin Antispin
    1 petal3 petals

  3. 1:4 1.5 turns

    Prospin Antispin
    3 petals5 petals

  4. 1:6 2.5 turns

    Prospin Antispin
    5 petals7 petals
4 Level 4, Quarter Turns Adds finer quarter-turn increments

  1. 2:1 −0.25 turns

    Prospin Antispin
    1 petal3 petals

  2. 2:3 0.25 turns

    Prospin Antispin
    1 petal5 petals

  3. 2:5 0.75 turns

    Prospin Antispin
    3 petals7 petals

  4. 2:7 1.25 turns

    Prospin Antispin
    5 petals9 petals

  5. 2:9 1.75 turns

    Prospin Antispin
    7 petals11 petals

  6. 2:11 2.25 turns

    Prospin Antispin
    9 petals13 petals

  7. 2:13 2.75 turns

    Prospin Antispin
    11 petals15 petals

Quarter turns need two hand circles to bring the prop back, so they are written over 2. At 2:1 the prop turns slower than the hand: a quarter turn backwards.

Same petals, different laps

1:2 and 2:1 draw the same number of petals, one prospin and three antispin, yet they move nothing alike. Watch the hand, the solid dot on the dashed circle, and the prop, the line from it out to the blue end that draws.

At 1:2 the hand goes around once while the prop spins twice, and the drawing meets its start after that one lap. At 2:1 the prop turns once while the hand goes around twice, so the drawing laps the center twice before it closes. The 1:2 side finishes first and waits.

The petal count uses the two numbers together, |P − H| for prospin and P + H for antispin, so swapping them leaves it alone. The laps tell them apart: here the hand circle is wider than the prop's reach, so the drawing goes around the center once for every hand circle.

Every quarter turn ratio laps twice. That second lap is also why a staff draws nothing new there, as One end or two shows.

  • 3 1:2 1 petal

    Hand cycles, H
    0.0
    Prop rotations, P
    0.0

    Still drawing

  • 4 2:1 1 petal

    Hand cycles, H
    0.0
    Prop rotations, P
    0.0

    Still drawing

The original twelve

Nichols took four even petaled driving styles from each family, which gives twelve shapes for one hand. Three ratios, two spin directions, and two starting orientations reach the same twelve: prospin or antispin, started in or started out. A start pointing in puts the prop toward the center of the hand path, a start pointing out puts it away, and that choice moves where the figure sits.

The 1:1 prospin pair shows what the start does most plainly. Starting in holds the tracked end of the prop in one place, so it draws a point. Starting out carries that end around the whole hand circle. On a staff the two starts are the two ends of one prop, so the twelve fold into six.

1:1 0 turns, level 1 Open the 1:1 band
  1.  Prospin no petals, starts in
  2.  Prospin no petals, starts out
  3.  Antispin 2 petals, starts in
  4.  Antispin 2 petals, starts out
1:3 1 turn, level 2 Open the 1:3 band
  1.  Prospin 2 petals, starts in
  2.  Prospin 2 petals, starts out
  3.  Antispin 4 petals, starts in
  4.  Antispin 4 petals, starts out
1:5 2 turns, level 2 Open the 1:5 band
  1.  Prospin 4 petals, starts in
  2.  Prospin 4 petals, starts out
  3.  Antispin 6 petals, starts in
  4.  Antispin 6 petals, starts out

One end or two

Every flower above follows one end of the prop. A poi or a club is held at one end and draws with the other, so that end is the whole drawing. A staff is held in the middle, spun alone or as double staff, and both of its ends draw.

The two ends of a staff point opposite ways, so when one starts in, the other starts out. A staff draws the in figure and the out figure at once: two one ended flowers become one staff flower that carries both.

Level 1 shows it most plainly. Prospin started in is an isolation, the end held in place as a point, and started out it is an extension around the big circle. On a staff they are one motion. The two antispin starts draw cat-eyes at right angles, and a staff draws both.

Through Level 3 every ratio takes one hand circle, and there the out figure is the in figure turned half a petal, so a staff doubles the petals. Level 4's quarter turns take two. After the first circle the prop is back where it began with its ends swapped, so the far end retraces the near end's path and nothing doubles. In and out draw the same figure there, which is why the Shape Engine fills its second quarter turn start with the prop pointing along the hand path instead.

1 Level 1, Base Motions

  • 1:1 Prospin

     Starts in Isolation
     Starts out Extension
     Both ends Point in a circle

  • 1:1 Antispin

     Starts in 2 petals
     Starts out 2 petals
     Both ends 4 petals

The isolation and the extension are one staff motion, and the two cat-eyes make a cross.

2 Level 2, Whole Turns

  • 1:3 Prospin

     Starts in 2 petals
     Starts out 2 petals
     Both ends 4 petals

  • 1:3 Antispin

     Starts in 4 petals
     Starts out 4 petals
     Both ends 8 petals

Out is in turned half a petal, so each flower doubles.

3 Level 3, Half Turns + Float

  • 1:2 Prospin

     Starts in 1 petal
     Starts out 1 petal
     Both ends 2 petals

  • 1:2 Antispin

     Starts in 3 petals
     Starts out 3 petals
     Both ends 6 petals

The same doubling at a half turn: 1 petal becomes 2, and 3 become 6.

4 Level 4, Quarter Turns

  • 2:3 Prospin

     Starts in 1 petal
     Starts out The same path
     Both ends 1 petal

  • 2:3 Antispin

     Starts in 5 petals
     Starts out The same path
     Both ends 5 petals

Two hand circles: the far end retraces the near end, so a staff draws what a poi draws.

The 144 pairings

One left hand shape over one right hand shape makes a cell. Twelve shapes on each axis is 144 cells, and that is the whole matrix at the three original ratios. Blue rows are the left hand and red columns are the right hand, so a cell shows both paths at once.

Choosing a cell opens that pairing in the Shape Engine, where it animates. With a keyboard, the arrow keys move between cells.

The grid is wider than this screen. Slide it sideways to reach every column.

 Row, left hand
 Column, right hand
 The cell
1:3 prospin in the left hand over 1:5 antispin in the right. Open this pairing

Building flowers

Past the original twelve

The pairing does not stop at three ratios. Levels 3 and 4 bring in the half turn, quarter turn, and Float cards from the ladder above, and each hand picks its ratio on its own, so the two do not have to sit in the same family. Past the levels entirely, any two whole number ratios up to 15 on each side pair the same way.

Sources

The Shape Engine was built independently by Austen Cloud. It does not reproduce Nichols' original diagram and is not an official Spin Science release.