Isn't the Triforce itself loosely based on a Japanese myth? If i remember hearing correctly, the crest of a famous family in Japan was three golden triangles, stacked like the Triforce. The story behind it, if i remember correctly, is that the three triangles represent three scales given to someone in the family by a great dragon. three dragon scales, thus three pieces to the Triforce.
In the original Zelda, there were two pieces to the Triforce: Wisdom, and Power. the Triforce of Courage wsa supposedly lost long ago. Ganon had stolen the Triforce of Power, while Zelda split the Triforce of Wisdom into 8 pieces. These pieces are the ones that Link has to find in The Legend of Zelda. the Triforce of Courage is finally revealed in Zelda II: The Adventure of Link. it is the Triforce of Courage that is used to awaken Zelda in the end.
Thus makes three pieces. Courage, Widom, Power.
The so-called "Fourth piece" to the Triforce can't exist. the space in the middle of the Triforce is just that: a space. not meant to be filled by anything. the golden triangle at the bottom of the Hylian Shield in Ocarina of Time is just there for decoration. it's merely coincidence that it happens to fit inside the empty space in the middle of the Triforce.
The "Goddess of Time" mentioned in Majora's Mask has no connection to the Triforce. in fact, Majora's Mask has NO real connection to the Triforce at all. The appearance of the Triforce on the Hero's Shield in the game is there most likely because it's simply a mirror of the Hylian Shield. Remember, Termina is a "mirror", if you will, of Hyrule.
The Goddess of Time was never mentioned in the creation of Hyrule in
OoT. If she had anything to do with the creation at ALL, she would have been mentioned. If every god and goddess had something to do with creation, there'd be at LEAST five pieces: Power, Wisdom, Courage, Time, and Wind.
[and now for a little humor]Oh, while we're at it, let's make pieces for the sages! Forest, Fire, Water, Spirit, Shadow, Light! and then add the sages from Wind Waker, Earth and Wind, but since Wind is already covered, we get the addition of Earth! let's see, that makes Courage, Wisdom, Power, Time, Wind, Earth, Forest, Fire, Water, Spirit, Shadow, and Light! that makes Twelve Triforce parts!
And don't forget the Oracles! add in Ages, Seasons, and Secrets and we've got fifteen pieces to the Triforce!
[that was my humor]
And the most obvious evidence against the Fourth Triforce theory, is that Tri is a root word, meaning Three. not four. go back to elementary English class.
I saved this one for last because it's the most obvious (and most common), and is thus not as significant as the other facts.