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There is more to Tai Chi than T'ai Chi Ch'uan...
T'ai Chi Ch'uan or Taijiquan or "The Form" = a solo practice
The style we teach in TCF is the 37-posture Yang Short Form, as developed by Professor Cheng Man-Ch'ing - the first person to teach Tai Chi outside of China. There are other Yang style variants, and other styles whose lineage comes from other ancient families, eg Chen or Wu. China has also re-introduced a 24-posture form purely as a form of exercise.
Twey Shou or Tui Shou or "Sensing Hands" = a 2 person practice
This is a Tai Chi partner exercise that challenges students to continue to embody Tai Chi principles whilst interacting with another person - an additional distraction / pressure.
Contact with a partner gives immediate feedback about your balance and relaxation. They are trying to sense, and then use, any lack of balance or relaxation in you. You are trying to sense, and use, any lack of balance and relaxation in them. Both of you are learning.
We teach Sensing Hands to those who have done Fundamentals level form.
3 minutes on the concept of Qi (pronounced "Chi")
T'ai Chi Chien or Taiji Jian or "Sword" = both a solo practice ("Sword form") and a 2 person practice ("Fencing")
Sword form and fencing are taught only to experienced students - typically on our Summer School or at special weekend workshops.
Ch'i Kung or Qigong or "5 Element Qigong" or "Roots & Branches" = a well-being / healing practice
"All Tai Chi is Qigong, but not all Qigong is Tai Chi." Ours definitely is, as it works with the flow of energy inherent in our form movements and focuses us on how they develop our Qi (or Ch'i), the Chinese word for energy - what, in this context, we might call "life force". Qigong uses mental imagery and a focus on breathing, combined with either holding of an individual position, or continuously moving between left and right versions of the position - sometimes developing this into a flowing "walk".
When we run Qigong workshops, we typically focus on the one particular type of energy associated with the season, which is also represented by a particular "element". In the Chinese system there are 5 seasons and 5 associated elements: Winter/ Water; Spring/Wood; Summer/Fire; Later Summer/Earth; Autumn/Metal.
Although Qi is pronounced a bit like the Chi in Tai Chi, it is in fact a different Chinese word. The video from TCF's "Roots & Branches" DVD explains the concept of "Qi".