In music, the rhythm might be 2/4, 3/4, 4/4, 2/2, or some other variation which denotes how many beats in a measure and how long to hold a whole note. Likewise the rhythm of a horse’s gaits might be 4 beats (walk), 2 beats (trot), or 3 beats (canter) (or in a gaited horse, some other variation!). However, rhythm says nothing about the speed, how quickly or slowly, the rhythm progresses in either music or horses. For that we need tempo. A horse may walk in a quick tempo or a slow tempo, but either way, there are four beats in the walk rhythm. Get it? Takt encompasses both rhythm and tempo.  

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Takt is generally translated as rhythm, but it also refers to the horse’s tempo.
How is takt achieved? Rhythm is generally a horse’s natural state. In most cases, this will happen on its own. Tension can disrupt it, so keeping your horse calm and relaxed is important. If your horse is used to being well cared for, fed and exercised just the right amounts on a regular schedule, protected from harm, and treated kindly, he will be accustomed to being calm and happy. This will carry over to his training. Similarly, each horse has his own natural tempo which they generally settle into readily as long as they are relaxed.  
Some horses do show impurities in their gaits, for example a horse that moves its front and hind feet on the same side nearly together in the walk is said to be “pacey.” Instead of a clear one – two – three – four, clip – clop – clip – clop, you might see/hear onetwo—threefour, clipclop—clipclop.  If you can't hear the footfalls, you can look at the shape made by the horse's legs.  In a good quality walk, the horse's front and hind legs on the same sidewill form a V at 2 separate times within each stride.  Check out the first and fifth frames of the picture below.  
One way that the canter may be impure is when the diagonal pair – the front and hind feet that land simultaneously to make up the second beat of canter – land separately. The horse is said to “four-beat” at the canter. Either the front or hind hoof may land first in the impure canter.
Takt
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Impure gaits can be caused be incorrect training which can be very difficult to correct. This is definitely a problem to avoid! It can also be a horse’s natural tendency, in which case the likelihood of the horse developing satisfactory gaits is not good. Most trainers are not interested in working with horses that have naturally impure gaits.  

Strategies for improving impure gaits depend on the specifics of the situation but frequently include riding or longeing over carefully spaced ground poles or cavaletti and using a rider with very good hands.  

Tempo is more easily adjusted. The horse’s natural tempo should be respected, however some horses may need some help finding the tempo most comfortable for them, or in maintaining a steady tempo. Strategies for doing that are found in the RIDER section of the website.

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