Magic

A mystery distinct from magecraft.
“Magic” is that which makes the impossible into the possible, for a given era.
In the past, when civilization was young, most magi were also magicians.
However, in the present era where almost anything has become possible (so long as you disregard the capital and time required to realize it, and focus only on whether or not a thing is “possible” in the purest sense), the number of things that can be called “magic” has been reduced to a mere five.
Consequently, there are only five existing magicians.
Because the ultimate goal of magi is to arrive at magic, there is a possibility that this number may increase, but probably it will just keep dropping even more from here on out.

Tsukihime Data Collection: Tsukihime Dictionary
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① A mystery distinct from magecraft.
② Magic is that which makes the impossible (something that can't be achieved regardless of the time and money one has), possible. So, in the present era, in which almost everything is possible, there are only 5 magic. Accordingly, there are only 5 existing magicians.
③ The ultimate goal of most magi is to achieve the power of magic. Roa also falls into this category.1
④ At this time only 2 magicians have been revealed. Aozaki Aoko and Zelretch.
⑤ The details of the 5 magic are unknown, however we do know that bringing the dead back to life is a magic, and that Aozaki Aoko's magic is known as “Magic - Blue.”
⑥ Also note is that magic doesn't follow the rules of magecraft, a big reason Crimson Moon lost to Zelretch is due to not fully grasping this.

Colorful MOON Tsukihime: Tsukihime Glossary
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A mystery distinct from magecraft. The final destination of magi.
“Magic” is that which makes the impossible into the possible, for a given era. A “result” which can be realized with the application of time and effort is not magic.
In the past, when civilization was young, most magi were also magicians, but currently only five remain.
…Well, that's what they say, but there are actually only four still alive.
The magician that handled the First magic already died a long, long time ago.
Of the remaining four, two have disappeared, and two are bothersome people that pop up all over the place leaving trouble in their wake.

Fate/side material: Fate Encyclopedia
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A mystery different from magecraft. The final destination of every magus.
“True Magic” achieves things that cannot be realized in a given era. An “outcome” which can be achieved through the investment of time and resources is not True Magic.
Currently, the Association has determined five Magics.
The so-called First and Second Magic are only known by a limited few in the Association.
Although it is said that no more new “Magics” will emerge, Kokuto Mikiya insightfully pointed out the unrealized Magic.

Garden of sinners Pamphlet: Kara no Kyoukai Settings Glossary
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A mystery distinct from magecraft. The final destination of magi. “Magic” is that which makes the impossible into the possible, for a given era. A “result” which can be realized with the application of time and effort is not magic. In the past, when civilization was young, most magi were also magicians, but currently only five remain.
…Well, that's what they say, but there are actually only four still alive.
The magician that handled the First magic already died a long, long time ago. Of the remaining four, two have disappeared, and two are bothersome people that pop up all over the place leaving trouble in their wake.
As for why they are still commonly referred to as the five magicians regardless, well, that comes down to a matter of perspective. It's the difference between counting a dead person as somebody that no longer exists, or counting them as still being “alive” in a way, so long as some trace of them still lives on.

Tsukihime Dokuhon Plus Period: Tsukihime Dictionary Revised
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A mystery distinct from magecraft. The final destination of magi.
“Magic” is that which makes the impossible into the possible, for a given era. A “result” which can be realized with the application of time and effort is not magic. In the past, when civilization was young, most magi were also magicians, but currently only five remain.
Each particular magic is named by its number: i.e., the First, the Second, and so on. Aozaki Aoko is the user of the Fifth magic.

MB Act Cadenza PS2 Manual: Tsukihime Dictionary
Translator's Notes
  1. ^ Magi are different than Magicians. Magi use magecraft. Magicians use magic.