Actually it would take several training sessions to cover them, but, let me start by correcting an inaccuracy.  There are not seven principles of kata but rather seven aspects of kata taught to me by my teacher.  There is a great yet subtle difference between principles and aspects.  A principle is a fundamental tenet or axiom while an aspect is a feature or element of ones kata.  As often happens when things are conveyed between those speaking different languages something gets lost in the translation.  The seven aspects are: pattern; breathing; combination and timing; meaning; tight\not tight; eyes; and kiai.  (OSensei added an optional aspect a while back-hit without being hit, but that is sometimes only talked about with his senior students.)  To make sense of the kata as a progressive learning vehicle the aspects must sit on top of principles which are both tangible and intangible.  Some of the tangible principles are: height, distance, angle, stance, and timing (a different form of timing than the aspect of timing-stay with me).  Some of the intangible principles include: intent, ruthlessness, justice, and restraint. By the way, OSensei's way of ensuring we were developing as he wanted was tohave us perform in front of seven judges.  Each judge was responsible for evaluating on of the seven aspects-so everything had to be "there".  This was gernerally done for those 5th Dan and below (mayb twenty years or less of training).

Let me aslo point out that it might at first or second glance seem as though aspects and principles are interchangeable-on some levels of training that would be correct, on some levels not so.  (In the hope of preventing any unnecessary confusion let me mention that aspects are focused on during kata embu {performance of the form}, principles become more important during true application training.)  The distinctions (our mental constructs of the "differentness" between aspects and principles which must be made during our first two decades or so of training so that we can get out of the starting blocks) actually fade the "older" ones karate gets.  It is the same with the "separateness"of each kata.

Over time we come to understand that in the learning of kata there are no "lower" or "higher" kata.  There are only kata we learn sooner and kata we learn later.  They are drawn from one another and lead to one another.  All of our kata eventually become ONE KATA from which we intuitively select, incorporate, and execute techniques, aspects and (tangible and intangible) principles when called upon for life-protection..  I hope that doesn't burst anyone's bubble, it's simply the direction some of the Grandmasters wish us to journey in-as passed on to me by my teacher long ago.  I do not ask that you agree with me, the "path" is wide and accomodates many travelers with different views-this is just my answer to your important question.

If it helps, think about how we come to enjoy boods.  First of course we need basic spelling and comprehension skills.  We come to understand works, sentences, paragraphs, and chapters.  Plot, character development, and other aspects and principles of good writing all have their places.  But only when none of these things are separated one from the other ("separate" kata, "different" principle) can we truly enjoy a good piece of literature.  (Imagine trying to fully understand and enjoy the latest Tom Clancy novel by focusing on the third letter in the seventh work of the second paragraph on page 216 in chapter seven?)

We'll never understand a doughnut by gazing at the hole, but, it ain't a doughnut without the hole!

Remember, we live our arts prospectively, but we can only truly understand them retrospectively-looking back provides the "long view" vital to getting better "tomorrow".