Sen sen no sen - is an early timing, almost done the moment uke flinches to attack. Much of my personal study as of late has been at this timing. Tomiki Sensei in his writings considers it the highest level of timing.
Sen no sen - Is a fairly standard timing in the world of Aiki and especially Tomiki classical 17 kata. Charles Clark Sensei always called it middle of the road timing, and when I was part of the Jiyushinkai he wanted the junana hon kata to demonstrate this timing.
Go no Sen is a retaking the initiative timing. Tori was too slow, and the initial attack overwhelmed standard aiki distance and timing. Drawing backward to regain initiative is the name of this game. From what I have seen, it looks like the Kihara students use this timing extensively.
Here is a karate video that nicely demonstrates 3 kinds of Sen
In Tomiki Sensei's own words
from Fundamental Principles of Judo
by Kenji Tomiki
In all athletic sports one must, in order to gain the victory, surpass the opponent in mental power, technical skill, and physical strength. These three factors must be united in gaining the mastery over an opponent. The mastery is brought into play in the form of various techniques, and although there are a large number of them, they may be summed up and resolved into one word sen (initiative or lead).
In the old densho (books of secret principles) the way of taking the initiative is explained in three stages.
1. Sen-sen-no-sen (superior initiative). Superior initiative is given play in a delicate situation where one confronts an opponent who intends to attack, and gains mastery over him by subtly guessing his mentality and forestalling his actions. This is the highest reach of the mental cultivation in any military art and is regarded as not easily attainable. But if you consider it more deeply, you will find it too late to try to gain command over anything when it has taken a concrete form, and you must have the mental preparedness to hold it down beforehand. For this purpose it is necessary to learn to maintain the openness and serenity of mind as signified by the old expression, "Clear as a stainless mirror and calm as still water." Lao-tse teaches this almost divine state of mind in the following words: "It is the way of heaven to prevail without contention."
2. Sen (initiative). This is to forestall your opponent by starting an action before he begins attack on you.
3. Ato-no-sen (initiative in defense). This is not to guess the mentality of your opponent and check his action before it is done, but to start action in defense the moment you have an inkling of the offensive of your opponent. It is to avoid the opponent's attack the instant it is about to be launched upon you, and to make a counter-attack taking advantage of a pause in your opponent's movement and a disturbance in his posture. A man who takes the initiative in defense rises in opposition to his opponent's attack, and parries or averts it. Seemingly it is a defensive move. In order to stave off the opponent's attack at the last moment and restore one's position one must keep the moral attitude of initiative so as not to get worsted by the adversary.
The secrets of victory thus lie in taking the initiative, and in getting the start of one's adversary there are included the following factors:
* The first is the eyes. From old times it is said that the important things in a bout are "first the eyes, second the feet, third grit, and fourth strength." The eyes are said to be the window for the mind. They are an index to your mind. Where the eyes are fixed, there the mind is concentrated, and naturally the will is attracted.
* The second in importance is the posture. In a wider sense, it is the bodily attitude. It is a preparatory posture either for attack or for defense. Therefore, unless a proper posture is well maintained, not only is it impossible to take advantage of any opening for attack in the adversary, but you get your posture broken and are given a blow.
* The third is the movement. Even though you maintain the proper posture or bodily attitude, you cannot attain your object unless your movement and action conform to the rules.
* The fourth is the space condition. It consists of your distance, direction, and position as against your opponent. It is essential to study the principles of space condition, for from this study you will realize the secret principle of "fighting after getting the better of the opponent first."