"If the ridden horse has the advantage, among many others, over the unridden horse that it is able to move easily and with regularity in a small space in the gaits nature gave it, this is because of the flexibility of its entire body that dressage training has given it."
Gustav Steinbrecht (Das Gymnasium des Pferdes, 1935, English translation: 1995, 79).
Lateral Bend (Biegung), Longitudinal Flexion (Beizäumung), Elevation (Aufrichtung), and Permeability (Durchlässigkeit) are closely linked and mutually interdependent. One interesting little cultural and historical footnote in this context is that the Old Masters used the term "Biegung" to refer to the flexion of any joint. They talk about the "Biegung", i.e. bend/flexion of the poll, the neck, the back, and the hind legs. The fully trained horse was sometimes referred to as "durchgebogen" - thoroughly bent/flexed/flexible, which goes right to the heart of the matter of training.
The truly trained horse was also referred to as "geritten" (ridden). In classical terms most horses today may qualify as "broken", but they are far from being "ridden". Another one of my favorite terms for a trained horse is "tätig", which you could translate literally as "active". All of these old terms are aimed at quintessential elements of the horse's training. The criterion for a trained horse was not so much how many advanced movements he could perform, but how obedient he was to the rider's aids, how supple he was, how well he would yield to the rider's legs and rein aids. In other words, the focus was more on quality than on quantity.
As I said before, bend, flexion, elevation, and permeability are interconnected. True permeability (Durchlässigkeit) to the rider's aids, nowadays commonly referred to with the neologism "throughness", is the result of thorough suppleness, which in turn is achieved by bending/flexing exercises, as Hans v.Heydebreck writes in his commentary to the third edition of Gustav Steinbrecht's "Gymnasium des Pferdes" (1935, English translation: 1995, 154, fn. 1):
"After all, lateral bending work is the only means for acquiring suppleness, that is, the relaxation of all joints and muscles, and thus setting the horse straight, giving it an impulsive way of going, a swinging back, balance, and self-carriage."
Muscles are suppled and strengthened by alternating between contracting them actively and then stretching them passively by contracting the antagonistic muscles. Bending and flexing exercises do just that. One set of muscles is contracted to flex certain joints, or to bend the horse's neck and ribcage. The opposite set of muscles has to stretch in order to allow the bend or flexion, and vice versa.
The easiest bending exercise is the 20 meter circle, which is where the young horse's education begins (at the longe line). The next steps are corners (rounded off at first), then serpentines, spirals, and voltes. When the horse has gained a certain amount of balance and flexibility, the lateral movements are added, which allow the rider to access deeper muscle groups and to stretch and strengthen the horse's muscles even more. Gustav Steinbrecht points out the importance of bending exercises for the development of the swinging back in his "Gymnasium des Pferdes" (1935, in: 1995, 112):
"The joints of the spine are moved by the dorsal muscles disposed above it
and on its sides and by the abdominal muscles. Working of the back must
initially be limited to loosening these muscles and thus making the spine
flexible. This, however, can be accomplished only by lateral bending work
since the rider is able to influence the horse effectively and reliably only
in this direction. If the horse has thus been relaxed and loosened, the
supple up and down movement of the back under the natural influence of the rider's weight will develop automatically and is expressed in elastic
swinging of the spine."
The same thing applies in essence also to the hind legs. Due to their design, the flexibility of the haunches is of a more longitudinal kind, whereas the back is suppled more laterally. In the course of the horse's training, the hind legs are worked separately, individually, by shifting the combined body weight of the horse and rider into one hind leg at a time. This can be done through weight aids, through bending exercises, or a combination of both. The intention of this part of the training is to flex the joints of the hind legs more deeply, which stretches and strengthens their musculature. During the extension phase and the airborne phase of the stride, the previously flexed hind leg will "rebound", not unlike a bouncing basketball. The more energetically the ball is pushed into the ground the higher it bounces back. Analogously, the more deeply the hind leg is flexed, the more energetically it should bounce off the ground again. In other words, increasing the collection (deeper flexion of the haunches) should also result in greater impulsion.
Any exercise that is done with a lateral bend sends the inside hind leg forward, closer to the center of gravity, which makes it possible to flex it more effectively. In the shoulder-in, e.g. the horse's entire front end is moved around in front of the inside hind leg. This increases the share of the body mass that it has to support. In the haunches-in, the outside hind leg is moved towards the inside shoulder, closer to the center of gravity,
while the inside hind leg is grounded more by the rider's weight. In turns on the haunches, passades and pirouettes the shoulders are moved around the inside hind leg (without letting the outside hind leg escape). Simultaneously, the back is suppled and strengthened by the same exercises. In other words, suppling the back and engaging the hind legs one at a time are inseparable. One cannot have one without the other.
When the hind legs have been sufficiently prepared and strengthened individually, the rider can start to practice exercises that flex both hind legs simultaneously. It is especially the airs above the ground that serve this purpose. You can therefore see that these two phases correspond roughly to Campagne School and High School equitation, respectively. Gustav Steinbrecht (Das Gymnasium des Pferdes, 1935, English translation: 1995,128f.) explains the very same thought in much greater clarity than any other author:
"Moreover, the hind legs must be made flexible individually until they have been prepared for simultaneous bending by alternating exercises. The rider will then have to overcome mainly the resistance of one hind leg, that is, only half the resistance, and the horse will be able to rest the leg that has been previously stressed more when changing from one hand to the other. This now involves lateral bending of the horse which is the only way to intensively work each hind leg individually as the inside hind leg. The more perfectly the entire spinal column is able to assume the necessary carriage and lateral flexion, the finer and more reliably will the rider be able to act on the individual leg. Work on the spine and the hind legs is so intimately related that it cannot be performed separately at all. The spine finds one of its main supports in the hind legs; the resistance which the horse poses against lateral flexion of its body is thus usually to be found in the hind legs. If the horse bends correctly in the spine on a circle it bends the inside hind leg. An increased bend in the individual hind leg is conceivable only on a curved track and with the horse bent accordingly. Bending the spine is therefore the only means for primarily working the individual hind leg. It must unconditionally precede the uniform bending of both legs. This work on the inside hind leg by letting the horse carry itself in a bent position begins on one track on a circle and on other bent lines. From this then develops the shoulder-in with its various gradations which must be so well established that the remaining exercises on two tracks evolve correctly from it."
So far we have only talked about the horse's back and hind legs. There is a tendency in modern classical dressage circles to ignore the relevance of the head and neck placement as well as the rein aids, just as there is an equally pronounced tendency among the "sports riders" to focus their attention exclusively on the head and neck position and the rein aids, while ignoring the horse's back and hindquarters and the rider's seat and leg aids. Neither camp will be able to truly train a horse. It may come as a surprise to many neo-classical dressage riders that the Old Masters often remarked that the rider cannot very well gymnasticize the hindquarters until he has given the head and neck a certain posture that allows the energy of the hind legs to travel through the spine all the way into the bit, and that enables the rein aids to travel into each front leg and each hind leg. Even Gustav Steinbrecht (Das Gymnasium des Pferdes, 1935, English translation: 1995, 79) agrees:
"Motion is the element of the horse and all motion starts in the hindquarters. If therefore the flexibility of the hindquarters must be the ultimate purpose of all dressage training, this in no way means that lateral bending of poll, neck, and spine are unnecessary. Rather, the flexibility of these parts must first be obtained so that it can then be used as a means for the main purpose, namely to work the hindquarters."
In order to be able to use the horse's neck effectively as a tool for gymnasticizing the back and haunches, all the resistances that are situated in the neck and poll have to be removed. You can observe that many horses' necks are most flexible at their base, and stiffest at the poll. In order to make them into good riding horses, we have to stabilize the neck at its base and supple its top, so that the flexibility of the neck increases from the base towards the poll. The greatest source of resistances can usually be found in the conformation of the poll, jaw, and throat latch. In fact, horses whose poll region is very resistant to flexion and bend and who seem to be difficult to ride on the bit are almost always horses whose lower jaw begins to touch the neck while the nose is still a good deal in front of the vertical. When the rider attempts to increase the longitudinal flexion, the saliva glands consequently tend to get caught between the jaw and the neck, which is painful and can lead to all kinds of negative reactions from head tossing to spinning around and even rearing. The horse's gymnastic training has to change the musculature of his neck and stretch the tissue surrounding the saliva glands so that the glands can move just enough to the outside of the jaw in order not to get pinched any more. This reshaping of the neck musculature is done in part by flexions that the Old Masters called "Abbiegen" (bending the entire neck) and "Abbrechen" (bending just the poll/throat latch area). These flexions can be done mounted or unmounted at the halt, or in motion under saddle.
E.F.Seidler provides the most insights into the correlation between the horse's neck/throat latch conformation, resistance, and gymnastic flexions (Leitfaden zur systematischen Bearbeitung des Campagne- und Gebrauchspferdes, 1837, 134f., translation: TR):
"While working the poll on a straight line, but even more during flexions, the greatest enemy we encounter is the saliva gland. As long as we have not obtained the immediate contact between the jowls and neck muscles, as long as the saliva gland does not yield to the pressure of the jowl, so that the jowl presses against the saliva gland from below, the horse will resist in increased collection. He will try to fend off the effect of the bit by bracing, resisting with the lower jaw, or an unsteady head position; or he coils up behind the reins, flexes the joints of the hind legs, but remains stiff in the poll. A poorly positioned saliva gland on only one side causes the horse to resist in narrower turns in this direction; and on a straight line it is often the reason why he short-strides with one leg as if he were lame. Sometimes it is the front leg of the stiff side, or the diagonal hind leg, depending on what is more comfortable for the horse. (Horses who are high in the croup transmit this behavior more to the hind leg). The horse does not dare to reach forward on the stiff side, because he feels pain in his poll when he approaches the bit boldly. As soon as the constriction is eradicated by appropriate flexions, the lameness is gone. The lameness was not caused by the uneven movement of the leg muscles, but by the constriction of the poll; this is supported by the fact that a regular movement is shown when these horses are ridden on a loose rein."
In bending exercises, you can isolate the exact spot where the horse is blocked. If the horse is supple, you can secure the base of the neck with one rein, while the other rein asks the horse to bend, first just at the top, so that the rim of the jowl touches
the neck and pushes the saliva gland out. Then you can give a little with the outside rein, and you will see that gradually a larger portion of the neck begins to participate in the bend. The bend at the very top of the neck is often the most difficult one. Some horses will brace against the request. This resistance can sometimes be eliminated by giving more with the outside rein until the top half of the neck is included in the bend. Then you slowly shorten the outside rein to reduce the bend again from the bottom towards the top. Sometimes you have to wait a few seconds until the horse yields and chews ("Abkauenlassen" in German). When you continue with riding forward afterwards, the poll is more supple and as a result the permeability has increased.
Sometimes subtle - or not so subtle - resistances can creep in, especially on the outside during corners and turns. Resistances are more difficult to feel on the outside than on the inside. That's why it is a good idea to test the horse from time to time by feeling with the rein, positioning the horse carefully to the outside after a corner. If the horse does not yield immediately to the rein pressure, the rider can stop the horse and flex the neck and poll towards the outside until the blockage disappears. Then he resumes the previous gait. In the middle of a turn, or in lateral movements, the rider can try to bend and position the horse more towards the inside. If the horse braces against the rein pressure, the rider stops and flexes to the inside.
It is of the utmost importance that the rider's legs keep the horse thinking forward. The calf brings the horse to the rein, so to speak. The seat and legs also keep the hips and shoulders aligned properly, so that the horse cannot become crooked. This way, the horse is still going forward, even during flexions at the halt.