This is a Karate stance frequently used in Kata. Its name comes from the Seishan Kata*. It is a strong, middle-width stance that lends itself well to both blocks and strikes, and easily converts or steps into both Kokutsu dachi (back stances) or Zenkutsu dachi (forward weighted stances).

It comes in two flavours: Yoko Seishan dachi and Tate Seishan dachi.

Yoko means 'horizontal' and this stance is most easily formed by first forming Naifanchi dachi and then imagining a line running behind the heels perpendicular to the direction faced and stepping one foot behind that line, whilst retaining the inward turn of the feet. The knees should be slightly bent to prevent too much stress on the joints.

Tate means 'vertical' and this stance can be formed by starting with the feet together, turning both feet to one (the same) side by about 15°, and then sliding the outer of the two straight back by a bit more than shoulder width. Turn the back foot back towards vertical very slightly so it isn't pointing off to the side as much as the front and bend the knees a bit to prevent army knee.

At first glance the two modes above seem almost totally unrelated but after throwing off a few combinations such as Sotouke (front arm, body half facing), Gyakuzuki (rear arm obviously, body full facing), you begin to see that they're similar in their close quarter strength and stability.
The main feature of these stances that I personally appreciate is their interchangeability. For example the quick rotation from a left Tate Seishan to a right Yoko Seishan rotated 90° to your right and then another quick right rotation to a right Tate Seishan effectively opens up a full 180° of strong footwork (footwork as in stances not kicks). If you were to find yourself backed up against a wall you could effectively execute strong close quarter strikes and blocks switching between the Seishan stances, Naifanchi dachi and as soon as you were to create an opening, the mid-range nature of the Seishans would also offer quick transition to a longer Zenkutsu dachi or Kokutsu dachi from which you could start flinging out kicks and general Karate mayhem. I approve of Seishan dachi.

*Or maybe the Seishan Kata is named after the frequent use of the stance. This is not how I understand it but if I'm wrong please let me know.

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