Algo de Tango

(To most: “Some Tango”, to the others: “Tango Algorithms”)

Class: www.westchestertango.com

Contact: Laxmi Parida (tangoWNY@yahoo.com)

“Teachers open the door, but you must enter by yourself”, old Chinese wisdom.

0. Raison d’etre

A dance is always to music and a good dancer feels the music in himself/herself. This “feeling” is hard to define and describe: as they say it’s an art and not science. However, there is a structure and a science to a well-articulated dance such as tango. How does the intertwining of the limbs and the bodies of the dancers work and work with such ease and grace? And, so easy on the eyes! The passion and the sensuousness aside, there is a method to this art and I will take the liberty of labeling it an algorithm. I am tempted here to share what once my friend, philosopher and guide, Alberto said about engineering students who are not compelled to study art or Latin: they are like efficient blenders brrrring away monotonously.

As a lot of followers will agree, there are some dancers that are a delight to dance with and others not. And, so say the leaders. I wondered why. It is not some inexplicable feeling, but with time and with thought, I have learnt that every “why” has an answer and surprisingly simple ones. I hope in the class, I am able to communicate these insights and the following notes will help to reinforce them.

Roadmap: When I announced the milonga in upper Westchester, a performing artist from the Zydeco group, called me, and among other penetrating questions asked how is Argentine tango, a rather difficult dance, taught to otherwise busy and much less committed suburbanites. The answer was and is: persistent drill of (1) technique exercises and (2) elementary dance figures. So, shall the notes in this presentation be organized. Usually, depending on the gathering, a lagniappe is thrown in, which is documented in the last section of this presentation.

0.1 What is the origin of the word “tango”?

Tango historians and scholars are not in complete agreement about the origin of this word and a few possibilities are offered, amongst which are two of the following:

• A type of music of African origin played on a kind of drum to which couples danced in close embrace
• A place where people gathered to dance

0.2 Who can tango? The good, the bad and the ugly

The only one who really can’t, is the one without a pulse. Anyone who can walk, can tango. Also, my good friend Rob told me that he often dances with an excellent dancer who is deaf. Some of the impeccable dancers that I have encountered have been Argentinean grandmothers and grandfathers, not necessarily in the prime of their shapes. Need I say more?

However, observed hard facts differ from the utopic conclusion of the last paragraph: Less than 5% of the social-dancing community can and will do the Argentine tango in their lifetime. And, we are not even talking about the population at large but a very specific subset that indulges in social dancing. The lateral hip undulations, the flaying of the arms, the total abandon and ecstasy- this self-absorption that fetches cheers in a regular social dance, actually is a hindrance to tango. The person who said it takes two to tango wasn’t mincing her words. The connect between a tango couple is at the micro level- it is the maestro and the danseuse in perfect harmony!

So who can tango? Are you a sportsfan or a sportsman? Are you a patron or a poet? It is one thing to admire poetry and quite another to write your own. Tango is a beautiful, sensuous dance that will stir your soul; alas it takes persistence, effort, commitment and most importantly the will power. Need I say more?

0.3 The Asymmetric Roles of the man & the woman

Tango is very follower-centric: it is a dance to flaunt the female of the species. While the follower adds to the dance, the leader can only take away from the dance. So, all you ladies out there who are fuming and fretting about the unfair “following” role on the dance floor, rejoice in the bigger picture! It’s all about the follower: the leader is the background and the follower the focal point! Figures are designed around the follower, the leader merely enables it. However, it is vital that the enabler and the enablee are in perfect coordination, no wonder it takes two to tango.

In my experience, the average learning curves of the leader (in blue) and the follower (in red) are as shown below. It appears that the follower learns much faster in the beginning and then as the level of the two increases, it takes more time for the follower.

Yet another asymmetry is that most women optimistically estimate their skill level and the men pessimistically. Perhaps a result of this is that the women prefer to dance with more advanced dancers whereas the men prefer the opposite. My suggestion to every dancer is to attempt to reach the tango-nirvana: a state where everyone is an equally acceptable partner.

1. Technique Exercises

There are two components to the skills one must acquire to be a good tango dancer:

• Individual form: Like any other dance, a good form is about 50% of the whole! The exercises that we do at the start of every class should help and they are described below.
• Partnering skills: This is the most important skill to acquire in tango. The leader must be subtle and the follower sensitive. It is a difficult skill and beginning leaders tend to be loud in their lead but with time and practice, they mellow. Beginning followers tend to anticipate and “back-lead”. Again, following is also a difficult skill but it helps to focus and not let the mind wander. Also, it is not a good idea to work both on your leading and following skills: move on to the other only after you have mastered one.

The Stretch-Step Exercise:

Points to remember

1. Weight on right foot and maintaining the axis of balance
2. Stretch left foot to front and then feet together
3. Stretch left foot to side and then feet together
4. Stretch left foot to back and then feet together
5. Repeat with weight on left foot

The Lapize Exercise:

Points to remember

1. Weight on right foot and maintaining the axis of balance
2. Draw an outward circle on the floor, then feet together
3. Repeat with weight on left foot
4. Repeat steps 1-3 with weight on left foot
5. Repeat steps 1-4 by reversing the direction of the circle
6. Repeat steps 1-5 by hooking one foot behind the other while feet together

The Lapize exercises are done in-place. If you feel you are moving back (while hooking in the front in Step 6) or moving forward (while hooking behind in Step 6), then rotate your hips slightly to aid in the hooking, keeping shoulders absolutely square to minimize any forward or back movements.

The Tango Walk Exercise:

The ABC’s of posture:

• Axis (be aware of your axis, along your spine; always pivot around your axis to change direction)
• Balance (keep upper body quiet, like you are balancing a stack of books on your head as you move)
• Core (initiate movement, walking or pivoting, from your core, breathing comfortably)

The 123’s of walking (move like a cougar, yes the big cat..):

1. Stay GROUNDED (… more like a cougar and less like a gazelle…)
2. Always pass through vertical neutral (knees & ankles together)
3. Always step straight perpendicular to your hips or at zero degree for a side step (never at an angle, exceptions only in certain figures)

Move to the music in the line of dance, counterclockwise on the dance floor, looking straight ahead, not at your feet, even when with a partner J

Walking with a partner:

1. Leaders: Express your intent through upper body

2. Followers: Follow that “sternum”

Contact-walking with a partner:

Leaders: When she steps back with her left, make contact with the inside of her right foot with the inside of your right foot. Similarly, you can work on the left side. This will enforce a good balance in your walk as well as get you to lead her to take the back step with your upper body. Followers: Follow that “sternum” and do not anticipate the contact.

Corrida with a partner:

Corrida is a little run: for example the rhythm could be walk-walk-quick-quick-quick. This exercise helps you listen to the music and also helps in breaking the monotony of the walk.

The Sacada-Walk Exercise:

This is a “displacement” walk exercise. It is a slightly advanced exercise, that emphasizes the lead and follow of the dancers. This is done in a crossed system (see the next section on terms). The steps 1-2 below are repeated till the music stops.

	Leader	Follower	Comments
	Left, side	Right, side
	Left, forward	Left, back	In crossed system
	Right, forward	Right back
	Left forward	Left back
1	Right, forward positioning his right outer upper leg to make contact with her	Right, back in an embellishment
2	Right, forward	Left, back

The Push-to-cruzada Walking Exercise:

Again, this is a slightly advanced exercise, that emphasizes the lead and follow of the dancers. This is done in a crossed system (see the next section on terms). The last steps 1-2-3 (right front cross) 1-2-3 (left front cross) below are repeated till the music stops.

	Leader	Follower	Comments
1	Left, side	Right, side
2	Left, forward	Left, back	In crossed system
3	Right, side, gliding her right foot in front to a cross	Right front cross, shift wt to right
1	Left forward	Left back
2	Right forward	Right, back
3	Left, side, gliding her left foot in front to a cross	Left front cross, shift wt to left
1	Right forward	Right, back
2	Left, forward	Left, back
3	Right, side, gliding her right foot in front to a cross	Right front cross, shift wt to right

The Forward Ocho Exercise:

1. Weight on right foot

2. Pivot, initiating from the hips, to the right by about 20 degrees

3. Step forward with your left

4. Bring right foot together (vertical neutral)

5. Weight on left foot, pivot to your left

6. Continue the step-pivot routine until tired, very tired Remember to keep your shoulders facing the front squarely (the so-called disconnect between your hip and the upper body)

The Back Ocho Exercise:

1. Weight on right foot

2. Pivot, initiating from the hips, to the left by about 20 degrees

3. Step back with your left

4. Bring right foot together (vertical neutral)

5. Weight on left foot, pivot to your right

6. Continue the step-pivot routine until tired, very tired

7. Remember to keep your shoulders facing the front squarely

The Boleo Exercise:

First, practice balancing on one leg, and then practice the boleo by hooking the free leg around

The Molinete Exercise:

This is the “windmill” move, which is a little difficult, done in a circle. So, the first exercise is the grapevine on a straight line. Once, you have understood and mastered it, you can do the grapevine on a circle in four steps and then circle in three steps. It is important to master this, since a lot of figures are built on this move. If the molinete is not executed correctly, these figures don’t work.

Sub-exercise 1 (along a straight line)

Keep shoulder and upper body square to the facing direction and in this exercise you move from left to right on a straight line

1. Forward- Pivot around right leg and forward step to the right with the left
2. Side- Step with right
3. Back- Pivot around right and back step to the right with the left
4. Side- Step with right

Continue this till you reach the right end of the line. Then repeat the steps by switching legs and direction to move from right to left

Sub-exercise 2 (along a circle – four points)

Keep shoulder and upper body square to the center of circle, move in counterclockwise direction and then repeat in clockwise direction

To facilitate equal-sized steps, mark four points on a square on the floor and step only on these points during the exercise

Sub-exercise 3 (along a circle – three points)

This is the hardest and do this only after mastering sub-exercise 2

Keep shoulder and upper body square to the center of circle, move in counterclockwise direction and then repeat in clockwise direction

Mark three points on an equilateral triangle on the floor and step only on these points during the exercise

2. Elementary Dance Figures:

The Central Dogma:

It takes two to tango & the follower is never wrong

Terms: (w.r.t. = with respect to)

1. General position: follower in front of leader
2. Right outside position: follower in front and right of leader. Also called the outside position.
3. Left outside position: follower in front and left of leader. Also called the inside position.
4. Crossed (or cross) system: Leader’s left foot synchronized with follower’s left a & leader’s right with follower’s right

5. Parallel system: Leader’s left foot synchronized with follower’s right & leader’s right with follower’s left

6. Cross/open position: The is the configuration w.r.t. the partner. In a stepping forward position, if your hips are open w.r.t. your partner, you are in open position. If your hips are crossed (if you know what I mean), you are in cross position w.r.t. your partner. Note that this definition depends only on the location of your partner, irrespective of his state.
7. Outside/inside direction in a turn (giro): Instead of a left or a right turn (which is usually used w.r.t the leader), I will use the gender-neutral term of outside turn and inside turn. The outside turn refers to the direction towards the open part of the embrace (left of leader and right of follower). The inside turn refers to the direction towards the close part of the embrace (right of leader and left of follower). In this terminology, the direction is the same for the leader and the follower and we don’t have to switch terms such as right-for-leader and left-for-follower.

Note that Cross is an overloaded term: (a) the cruzada or cross which is the special feet-together position, (b) the cross system of stepping, as (2) above, and, (c) cross position, which is the configuration w.r.t your partner.

Basic Guidelines:

The leader and the follower should practice each figure in phases, moving to the next phase only after some confidence is achieved at the current phase.

Leader:

• Phase 1: Repeat and understand the feet positions

• Phase 2: Focus on upper body to make sure you are expressing your intent to the follower correctly
• Phase 3: Practice with a follower

Follower:

• Phase 1: Repeat and understand the feet positions

• Phase 2: With the leader, work on your “following-sensitivity” by focusing on the leader’s upper body
• Phase 3: Erase the steps from your conscious mind and follow the leader

Figure: Six-count Box (Baldosa)

This is a figure one can resort to, to make simple forward, back and steps.

Count	Leader	Follower	Comments
1	Left, side	Right, side
2	Right, forward	Left, back
3	Left, forward	Right, back
4	Right, side	Left, side
5	Left, side	Right, side	Feet together
6	Right, back	Left, forward

Figure: Eight-count cruzada (left cruzada)

This is a foundational figure. Most later figures will be put in the context of this one, hence it is good to understand and internalize this one.

Count	Leader	Follower	Comments
1	Left, side	Right, side
2	Right, forward	Left, back	Right outside position
3	Left, forward	Right, back
4	Right meeting left	Cruzada ,(left front)	General position
5	Left, forward	Right, back
6	Right, side	Left, side
7	Left meeting right	Right meeting left
8	Right, back	Left, forward

Steps 5-7 called La resolucion or the salida or the exit

Cruzada troubleshooting:

1. Leader: Why didn’t the follower cross? Oracle: The upper body didn’t convey and/or you were not in the right outside position.
2. Follower: It was difficult to cross in spite of a clear lead. Oracle: Take looong back steps.

Figure: Eight-count with forward ocho

When the follower is in cruzada (at step 4) the leader takes a back step, leading the follower to a forward ocho (to the follower’s left & forward direction) and back in 2 counts. After this the leader can use the exit steps (counts 5-8 in the basic 8-count cruzada figure).

Figure: Cruzada with an embellishment

The follower executes a boleo at the cross. So can the leader while bring feet together at step 4 in the basic 8-count cruzada figure

Figure: Double Cross - 1

In this figure the follower executes two crosses, one with right front and the other with left front. The second cross is the same as in the basic 8-count cruzada figure. The first cross (step 3) is lead by the leader’s leg and the second (step 6) by the leader’s upper body.

Count	Leader	Follower	Comments
1	Left, side	Right, side
2	Right, forward	Left, back	Right outside position. Between steps 2 & 3, the leader nudges the follower’s right upper leg to cross
3	Left meeting right	Cross (right front) Shift wt to right	The leader “settles” indicating to the follower to shift weight to right foot
4	Right, forward	Left, back	Right outside position
5	Left, forward	Right, back
6	Right meeting left	Cross (left front) Shift wt to left	General position

Exit using steps 5-7 salida of the basic 8-count cruzada.

Note that if the leader does not nudge but gets feet together in Step 3, so will the follower, without crossing and will shift wt to right foot when the leader “settles”. The is also called a “check”.

Figure: Double Cross – 2 (left front OR left back Cross)

In this figure the follower executes two crosses, both with left front. Both the crosses are lead by the leader’s upper body.

1. Steps 1-4 are the same as that of the 8-count cruzada, ending in a cross.

2. Then the leader steps back with his left leading the follower to his right-outside position; the follower steps forward with her right (by gently uncrossing first). Next the leader brings his right foot together with the left (thus executing a check) and the follower does a left front cross to stay in front of the leader. The other alternative for the follower is to do a left back cross (instead of front cross) and for the following salida the follower must gently uncross before stepping back.

Exit using steps 5-7 salida of the basic 8-count cruzada.

Figure: Ocho Cortada 1 (cut eight)

Count	Leader	Follower	Comments
1	Left, side	Right, side
2	Right, forward	Left, back	Right outside position
3	Left, forward	Right, back
4	Left, back	Right, forward
5	Right, side	Left, side
6	Left meeting right	Cross with left front	Leader may cross behind

Follow this with the La resolucion or the salida or the exit (Steps 5-7) of the basic 8-count figure

Figure: Ocho Cortada 2

The ocho cortada can be lead by the leader when the follower has executed a side step, following a forward step by getting the follower to retrace her last step ending in a forward cross. So, a simple variation is to take the follower to a cross in the basic 8-count figure, get her to do a forward and then a side while the leader does a back and a side and then get her to do the forward cross and exit as in the basic figure. The leader could cross behind everytime he leads the follower to cross in front.

Figure: Ocho Cortada –giro-Ocho Cortada

This is a variation say from Ocho Cortada 1. After Step 5, the leader spins to his right, so she does a molinete around him and she is in the side step of the molinete (after completing her 360 turn), he can do the ocho cortada as in Ocho Cortada 2 and continue

Figure: Titurn (a tight 360 degree turn OR left giro)

In this figure the leader and the follower execute a 360 degree rotation. Steps 1-4 are the same as that of the 8-count cruzada, ending in a cross.

The left turn of the leader is broken up into two 180 degree turns and a step back, as follows:

1. Then keeping the follower in position by closely embracing her upper body while she has her weight on her left (crossed) foot, the leader takes a small forward step with his left foot planting it close to the crossed foot of the follower, then he ratates by 180 degrees about this left foot, to his left, while moving his right foot behind and rotating the follower about her axis.

2. Then he shifts his weight to his backfoot (right foot) and rotates the next 180 degrees around his right foot, forcing the follower to take a side step (she steps to her right and stays on her right foot).

3. Now the leader takes a step back with his left getting the follower to lean forward since he is holding her in close embrace, pauses dramatically for a moment.

Exit using steps 5-7 salida of the basic 8-count cruzada.

Figure: Barrida-cruzada 1 (inside position)

This is a cruzada that is thrown inside a drag or barrida (also called arrastra). The first figure begins by el retroceso ie the reverse start.

Count	Leader	Follower	Comments
1	Right, back	Left, forward	By the time the follower gets her feet together, the leader catches the inside of the follower’s left foot with the inside of his left foot
2	Shift wt to left foot, forward with right	Right back	Left outside position
3	Left, forward dragging follower’s left foot	Left back (arrastra)	Move the left foot past the the right foot into a stepping forward position
4	Shift wt to left foot and right forward	Right back	Left outside position
5	Shift wt to right, move the dragging leg to the outside of follower’s left foot And side step with left gently pushing follower’s upper leg to a cross	Cross in front with left and shift wt to the left foot	While the leader does his side step, his weight is completely on his right foot and he must immobilize the follower by holding her in place. The follower shifts wt to the left foot since the leader solidly steps to his right in the side step

Follow this with the La resolucion or the salida or the exit (Steps 5-7) of the basic 8-count figure. This figure works well if the steps taken by the leader as well as the follower are long steps. Also the leader must stay in the left outside position until Step 5, when he moves squarely in front of the follower (general position). Steps 2-3 can be repeated a few times i.e. walking in the barrida mode

Figure: Barrida-cruzada 2 (outside position)

Mirror-image of the previous, this is easier as it is in the outside position which is more comfortable for the leader.

Count	Leader	Follower	Comments
1	Left, side	Right, side	By the time the follower gets her feet together, the leader catches the inside of the follower’s right foot with the inside of his right foot
2	Shift wt to right foot, forward with left	Left back	Right outside position
3	Right, forward dragging follower’s right foot	Right back (arrastra)	Move the right foot past the the left foot into a stepping forward position
4	Shift wt to right foot and left forward	Left back	Right outside position
5	Shift wt to left, move the dragging leg to the outside of follower’s right foot And side step with right gently pushing follower’s upper leg to a cross	Cross in front with right and shift wt to the right foot	While the leader does his side step, his weight is completely on his left foot and he must immobilize the follower by holding her in place. The follower shifts wt to the right foot since the leader solidly steps to his left in the side step

Follow this with a left turn or simply walk to the cross (Walk to the cross is steps 2-4 of the basic 8-count cruzada) This figure works well if the steps taken by the leader as well as the follower are long steps. Also the leader must stay in the right outside position until Step 5, when he moves to general position. Steps 2-3 can be repeated a few times i.e. walking in the barrida mode.

Figure: Zig-zag to left giro

This a left giro followed by the cross and then the exit as in the 8-step cruzada. The left turn of the leader is broken up into two 180 degree turns- (1) a “pencil turn” about the leaders right leg and (2) a turn in the straddle position.

Leader	Follower	Comments
Left, side	Right, side
Rotate by 20-35 degree about left leg to the leader’s left	Rotate about right leg, mirroring the leader	Zig
Left, front	Left, back
Rotate by 20-35 degree about right leg to the leader’s rightt	Rotate about left leg, mirroring the leader	Zag
Right, front	Right, back
180 “pencil” rotation or giro (to left) around right leg with planeo and hooking left behind the right leg	Molinete (forward, side)
Step forward right leg and turn around by another 180	Pivot preparing for a back step	Sacada; the leader brushes the leg on the floor and could also invoke a leg wrap by staying towards the back leg
Right forward	Left back
Feet together	Right back, cross

Exit using steps 5-7 salida of the basic 8-count cruzada. In this figure you end facing the same direction that you started with.

Figure: Double-cross to left giro

This a left molinete followed by the two right-front cross and then the exit as in the 8-step cruzada.

Leader	Follower	Comments
Left, side	Right, side	Count = 1
Rotate by 5-10 degree about left leg to the leader’s left	Rotate about right leg, mirroring the leader	This helps in the cross that follows
Right front gently contacting follower’s upper right leg	Left, back	Count = 2
& left cross behind	Right front cross	Count = &
Right front gently contacting follower’s upper right leg	Left back	Count = 3
& left cross behind	Right front cross	Count = &
Rotate in place getting the follower around, starting with her back step	Molinete (left back, right side, left front), and pivot around left to squarely face the leader

Exit using steps 5-7 salida of the basic 8-count cruzada. In this figure you end facing the same direction that you started with. During the two right front cruzada, the leader can rotate around by a good 90 degrees or more to his left shortening the span of the molinete.

Figure: back ochos-giro-back ochos

He leads her to back ocho. Call the first ocho as position 1 (she is pivoting on her right foot) and the second as position 2 (she is pivoting on her left foot). He can exit from pos 2 by taking her to a cruzada and then salida. He can exit from pos 2 by going to the salida.

His left (outside) giro:

Leader	Follower	Comments
	Weight on right foot	At pos 1 of back ocho
Cross left foot behind right and spin by 180 (to his left) and stop	Left back, right side, left forward	Slow-quick-quick rhythm
Side with right while continuing the turn	Right side	Back to pos 1

Now they are back in pos 1 and he can lead the back ochos again from here and exit.

His right (inside) giro: This is done at pos 2 by hooking his right leg behind him and doing the exact mirror image of ”his left giro” (see last paragraph), ending in pos 2 and continuing the back ochos again.

Figure: Drag and contra-drag

This is a series of rapid drags (barrida) that take the follower by surprise, ending in a 360 degree turn for her.

To describe the steps, I give relative directions, so the reader has a reference point at the tricky steps.

(1) The leader leads a couple of back ochos. He begins facing South and she is facing North.(2) When she is stepping back with her left, he freezes her in position while her weight is on her back (left) foot. (3) One option is to “nudge” her upper right thigh to get a “right front” cross. A more porteno option (contra-drag) is to counter-drag to the front cross as follows: He places is right foot next to her right foot. The insides of both the right feet alongside each other, but his foot is on the opposite side of the direction of the drag, so he locks his right knee with her right knee, but to the left of her knee and then gently “pushes” her knee back to a front cross. This is a great move but needs a lot of practice and attitude to execute it well. (4) As he does the contra-drag cross, he shifts weight to his right leg, getting her to shift weight to her right (crossed foot). She is facing West at the cross. (5) He makes an inside turn of 180 while she pivots on her right foot. He is now facing West and she is facing South ready for a forward step. (6) She steps forward with her left (moving Southwards), he drags her right trailing foot for a “right behind” cross and gets her to shift weight to her right and turn around by 180 degrees so that she is facing North now and he has turned around to face South. Then execute the usual exit or salida. This looks more complicated than it actually is. A textual description just makes it tedious and difficult-looking.

Leader’s Forward Sacada Nomenclature

(This is not a figure, it is the explanation of the numbering system)

There is a sacada numbering system that is passed on by word mouth like the ancient Vedas. They go 1-2-3-4-5-6 where configurations 3 and 6 are fake or mere placeholders (for barrida, leg-wraps etc).

The numbering is based on the relative configuration of the two dancers: a dancer can be in cross position or open position with respect to the other. This numbering can be studied naturally when the follower (referred to as “she” in the table) is doing the molinete, either left or right while the leader (referred to as “he” ) does the sacada while shifting the axis of the molinete.

#	(he, she)	sacada	Right molinete	sacada	Left molinete	System
		He	She	He	She
1	(open,cross)	L	R forward	R	L forward	Parallel system
2	(cross,open)	R	L side	L	R side
3	Place-holder	L	R back	R	L back
-	-	&	L side	&	R side
4	(cross,cross)	R	R forward	L	L forward	Cross system
5	(open,open)	L	L side	R	R side
6	Place-holder	R	R back	L	L back
-	-	&	L side	&	R side

Herringbone CADENA: (in parallel system)

In this cadena, the leader and the follower always face the same direction w.r.t. the line of dance. Each unit has only three steps (since the dancers are not crossing each others paths)

(outside direction)

B->F S B->F S B->F S B->F S B…… OR

qk qk tog qk qk tog qk qk tog qk qk tog … OR

qk pl tog qk pl tog qk pl tog qk pl tog …

pl = pull: The leader “pulls” (gently, of course) the follower with him at the second qk step.

Can you elaborate this (class of) cadena from its encoding above ? A little exercise for the brain, feet and your mutual bearings.

CADENAs

(This material is for advanced dancers who are fluent in the vocabulary of the dance, both in theory and practice.)

Cambio de frente (CDF) elements in a CADENA:

Cadena is a chain. This is the repeated execution of a (usually) small figure. For simplicity of exposition, we discuss few elementary versions of a cadena: in each the repeating figure has just four step units. This utter simplicity in the description of the cadena is possible only in terms of the different flavors of cambio de frente (CDF). CDF is interpreted as “change of direction in a turn”.

I often say in my classes: the man is irrelevant. What I mean by this is that most figures are follower-centric or best understood (and encoded) by studying the steps of the follower. In the following exposition, B is a back step; F is a forward step and S is a side step. B->B is to be interpreted as back step (B) of the woman followed by another back step (B) brought about by a CDF (->). Similarly, B->F, F->B and F->F. A CDF entails a change of direction (for the follower w.r.t. the leader), hence there must be two CDFs in the basic unit of a cadena.

There are two flavors of CDF. I will adopt terms from statistics for ease of exposition. I encodeType I in blue and Type II in red+bold (for non-color displays).

· Type I CDF (B->B or F->F): This can be done in various ways. (a) Follower pivots in an ocho. (b) Leader steps in front of follower to convert her cross to an open position. [(c) Or, a event soltada turn for leader or follower]

· Type II CDF (B->F or F->B): This is the nuevo-rock step turn, where both the leader and the follower pivot and step for the CDF.

For the rhythmicist in you, you can also have the figure in a timing vocabulary of qk (quick), sl (slow). Note that the rock step (or Type II CDF) is sometimes executed in the qk-qk mode, so that the follower is not taken by surprise for the rock step.

Cadena 1 (a & b) (outside direction (a); inside direction (b))

F->B S->F F->B S->F F->B S->F F->B S->F F…..

(1a) Outside direction: Here the repeating unit is F->B S->F F where the very last F becomes the first F of the following unit. F->B is a Type II CDF in the outside direction i.e., she takes a forward step (F) towards her right (i.e., his left) while he takes a side step; he rocks and pivots to his right taking the follower with him so that her F step is now a B step. This is followed by a side step (S) for her. Then a forward (F) step. Notice that this is a conventional B S F of a molinete. S->F is a Type I CDF which in this case is a pivot for the follower.

What about the leader’s steps? I leave this as an exercise for the reader. Hint: the leader can do a forward sacada on her F step.

(1b) Inside direction: The very first F in the repeating unit is in the inside direction i.e., she takes a forward step (F) towards her left (i.e., his right) while he takes a side step; he rocks and pivots to his left taking the follower with him so that her F step is now a B step. This is followed by a side step (S) for her. Then a forward (F) step. F->F is a Type I CDF which is a pivot for the follower.

Cadena 2 (a & b) (outside direction (a); inside direction (b) OR clockwise/counterclockwise) [gancho embellishment]

B->F S->B B->F S->B B->F S->B B->F S->B B……

(2a) Outside direction: Here the repeating unit is B->F S->B B where the very last B becomes the first B of the following unit. B->F is a Type II CDF in the outside direction i.e., she takes a back step (B) towards her right (i.e., his left) while he takes a side step; he rocks and pivots to his right taking the follower with him so that her B step is now a F step. This is followed by a side step (S) for her. Then a back (B) step. Notice that this is a conventional F S B of a molinete. S->B is a Type I CDF which in this case is a stepping forward for the leader.

What about the leader’s steps? I again leave this as an exercise for the reader.

(2b) Inside direction: The very first F in the repeating unit is in the inside direction i.e., she takes a back step (B) towards her left (i.e., his right) while he takes a side step; he rocks and pivots to his left taking the follower with him so that her B step is now a F step. This is followed by a side step (S) for her. Then a back (B) step. B->B is a Type I CDF which in this case is a stepping forward for the leader.

Cadena 3 (a & b??) [sacada embellishment]

B->F F->S B->F F->S B->F F->S B->……

Here during the B->F CDF follower and the leader are at 90 to each other.

Cadena 4??? (a&b???)

F->B B->S F->B B->S F->B B->S F->……

Similar relative position as in the previous

Cadena 5??? (a&b???)

S->B.S->F S->B.S->F S->B.S->F ……

Start with her on left-outisde position (after the very first side step)

Some more cadenas, sil vous plait:

Can we have few more cadenas ? Yes we can.

I am now going to give my cadena-theorem, which is a completeness theorem. It is constructive in nature so you also use in your next choreography.

Of course, we must be precise with definitions:

1) A 4-step unit is the one where BOTH take 4 progressing steps in each unit.

2) A 4-count unit is the one where at at least one of the dancers takes 4 steps in each unit. Thus every 4-step is a 4-count but the converse does not hold.

Note that in the description we use only the followers steps—but it automatically encodes the leader’s as well. Whether a follower’s step is S or F or B is determined by the position of the leader w.r.t. her and thus this implicitly determines his moves.

In the following by “isomorphic” we mean “identical”. But I prefer to use “isomorphic” since the identity is not always obvious to the eye, even the experts’ eyes.

In the following, “C” is a cross step (i.e., either forward “F” or back “B” step, by the usual nomenclature) and “O” is an open step (i.e., a side steo “S”, by the usual nomenclature) of the follower. Then:

(C->C & O->O Lemma) .There are 5 distinct ways of executing a C-> C and 5 distinct ways of executing an O->O.

Proof: Consider C->C.:

(1) & (2) Nuevo-rocks: clockwise and counterclockwise respectively. (3) Step: Leader steps across the follower’s path. (4) Ocho: (either back or forward, depending on the C step) (5) Soltada: Leader stays stationary and under-arm turns the follower by 180.

Consider O->O.:

(1) & (2) Nuevo-rocks (3) Step (4) Rock in place- shift wt from one leg to another (5) Soltada: Follower stays stationary and leader turns 180 QED

(CDF Completeness Lemma) .Any CDF is isomorphic to one of the descriptions in the C->C & O->O Lemma (see above).

The cadena has the two following characteristics in each unit/motif:

· (petite) 4 step or 4 count

· (aesthetic) has at least one O and one C

(Cadena-Completeness Theorem) .Any 4-count cadena is isomorphic to one of the following mother cadena descriptors (follower’s steps):

1) C O C C | C O C C | ..... [= |O C C C| = |C C C O| = |C C O C|]

2) O C C O | O C C O | ..... [= |C C O O| = |C O O C| = |O O C C|]

3) O C O O | O C O O | .... [= |C O O O| = |O O O C| = |O O C O|]

Proof: Following the definition (4 steps and at least one O & one C), the complete enumeration is shown above. QED

Note that each C can be F or B. However, in the encoding, we don’t distinguish between the two.

(Corollary) (a) Sans-embellishments the number of distinct 4-count cadenas is 75. (b) Sans-embellishments the number of distinct 4-step cadenas is 48.

Proof: (a) Since there are 5 distinct ways to execute a CDF (via O-> C or C-> O). Since each descriptor has two CDFs, then there are 25 ways for each. (b) Same as (a) except that there are 4 distinct CDFs. QED

Remember that if a combination is feasible, it CAN BE EXECUTED. I will take up the challenge and execute each with a willing partner. Any volunteers?, You may not like ALL of them, but as they say C'est la Vie. The instantiations with CDFs of the descriptors corresponding to the cadenas described in detail above (and taught in the class on different occasions) are as follows:

F F->S B->

B->F S->B

F->B S->F

B B->S F->

S->B S->F

So, when you have to perform a keynote dance and you want to surprise the (seasoned and perhaps somewhat jaded) audience with something they have never seen before, feel free to dive into this sack of cadenas.

Also, this large number of distinct looking cadenas can keep many semesters alive! Since most students prefer spelt-out figure-recipes (and shun any theories), this theorem should keep the teachers in business for a long time to come. This will not only keep me employed but also my children’s children J

Cadena-completeness theorem in practice:

Most of the cadenas that one sees commonly are isomorphic to |C O C C| (and done ad nauseum in the classes). So, with Rob we tried few different renditions of |O C C O|. These turned out to be elegant and different. Here are the observations and the details of the spelt-out cadenas.

Observations:

· A nuevo-rock CDF or (1) or (2) of “C->C O->O” Lemma, is dramatic and is accompanied by a simultaneous pivot in the range 90-270 degrees for both partners. Thus in a cadena that includes this CDF, each dancer can face the line of dance at one point and can have his/her back to the line of dance at another point. So this does have a “twirl” effect on the cadena.

· A step CDF or (3) of “C->C O->O” Lemma, has the effect of a stylish caminada.

· A soltada turn CDF or (5) of “C->C O->O” Lemma is a “neuvo” underarm turn. So very nice in a vals rhythm. Also, note the this reduces the number of “steps” by one.

Cadenas (descriptor = |O C C O|):

1. S B->B S->| S B->B S->| ….(a stylish forward caminada-esque cadena)
In our rendition, the first side is follower’s side to her right. The first CDF is a step or (3) and the second is a (1) of the “C->C O->O” Lemma.

2. S F->F S->| S F->F S->| ….(a stylish backward caminada-esque cadena)
In our rendition, the first side is follower’s side to her right but facing the line dance while he has his back to the line of dance. The first CDF is a step or (3) and the second is a (1) of the “C->C O->O” Lemma.

3. S B->F S->| S B->F S->| ….
In our rendition, the first side is follower’s side to her right. The first CDF ->is a nuevo-rock or (2) and the second CDF -> is (1) of the “C->C O->O” Lemma.

4. S B->F S->| S B->F S->| ….(an unusual cadena --works very well to vals rhythm)
In our rendition, the first side is follower’s side to her right. The first CDF ->is a soltada turn or (5) and the second CDF -> is (1) of the “C->C O->O” Lemma. Since there is a soltada turn, it is a 4-count but not a 4-step (the soltada step does not involve a stepping), hence, the two soltada turns are in opposite direction as well as the two adjacent step (1) of the Lemma are in opposite directions.

3. Lagniappe of the evening: (for seasoned dancers)

Figure: Sacada-to-molinete

Leader	Follower	Comments
Left, side	Right, side
Shift weight		in crossed system
Left, front	Left, back
Right, front & sacada follower’s left leg	molinete, starting with back step
180 rotation (to left) using both “stepped feet”	molinete
180 “pencil” rotation or giro (to left) around right leg with planeo	molinete
Lead forward ocho to right & back	Forward ocho
Exit starting with left foot	Exit	La resolucion

In this figure you end facing the same direction that you started with.

Postscript: Rising above the competent fake

Most of us dance well-established figures. Though tango is an improvised dance, yet we tend to draw from known sequences. Like in mathematics, most teachers can teach established theorems, but how about stating and proving new theorems? How does one do it? It takes a thorough understanding of state-of-the-art and a curious mind, whether it is math or tango. Here are some valuable steps for inventing new figures: (1) First identify the focal element(s) [E.g., a legwrap or a series of gancho or…] (2) The dance is follower-centric, so focus on the follower’s role, the leader’s will most likely fall into place. (3) Finally, field-test your idea to some music that you love.

Cadena: This is a chain of more-or-less identical units. If you need to come up with your own cadena, work on a few steps that bring you back to some identifiable initial position and then the units can repeat themselves.

Of course, you could challenge yourself to discover/invent a new element, say a serpiente sinous.

Acknowledgments

Without Gustavo’s creative suggestions, the title of this presentation would not have been as interesting. I owe the technical correctness to the diligence of the students. Their feedback has also helped tighten the presentation.