The interest in the time, when the Relevations were written, in the number 22 was already existent. The Hebrew Alphabet had 22 letters. This interest was somehow manifested by a specific psalm, called the golden AbC, in which each passage started with a different letter according to the row of the alphabet.
The revelations were a book of great interest in 14th/15th century. The Visconti library around 1420
http://trionfi.com/0/l/0701/
had about 1000 books and was the second greatest library in Europe. It had about 20 "Revelations" - so it definitely was really a favoured topic at the relevant time, and really also at the right place, that's in Milan - where very old Trionfi decks were produced.
Nonetheless there are various possible reasons, why the number 22 finally was chosen as number of the Major Arcana.
22 - is a number in the dice-game, which has 21 possibilities in a throw with 2 dices. This is the reason, which most researchers seem to prefer
22 - letters has the Hebrew alphabet - this hypothesis was a time long very prefered, and it somehow also presents the Revelation-thesis ... now it looks a little bit deranged in its importance, that the earlier suggestions of Eliphas Levi and Golden Dawn were a little blue-eyed.
22 - years Galeazzo Maria Sforza was in the year 1466, when his father died and he became duke of Milano. 22 years old was Maria Bianca Sforza, Galeazzo's mother, when her father, Filippo Maria Visconti died, in the year 1447.
Filippo Visconti is a "great man" in the theories about the origin of Tarot, see:
http://trionfi.com/0/b/
Bianca Maria is a "great Tarot woman" in the early documents, in which the name "Trionfi" appeared or cards appeared(1425 as babe, 1.1.1441 in preparation of a marriage, Oktober 1441 as bride in a marriage, 1452 in a letter, which signifies her as "Trionfi-deck-commissioner".)
http://trionfi.com/0/d/
http://trionfi.com/0/e2/00b
http://trionfi.com/0/e2/08
22 years old was Galeazzo Maria's father, the famous condottieri Francesco Sforza, when his father Muzio Attendola, himself also a famous condottieri and a legend, drowned in a river near Aquila.
So in 1466, three accidently 22's in near context to each other (father-mother-sun) run together, and Galeazzo Maria on his step "out of youth" to become a mature "duke of Milano", could see them all - and was personally involved.
Later historians stated, that Galeazzo was very superstitious. Could he haven't seen this with all the astrologers around him, who thought about such details?
The Visconti-Sforza's became famous as Trionfi card producers. If the Tarot already had 22 cards in this moment of time, the familiary 22-accident would be really crazy. Then Francesco Sforza - a man who was known as not very superstitious - would have died on a sort of "playing card command". This seems not really realistical.
Much more likely it is, that this relation of four "22's" at one spot evolved, cause there is a hidden logic in it. Which means: The familiary Tarot got 22 cards, cause Galeazzo Maria had this crazy accident of three "22's" before in the year 1466.
Galeazzo Maria was rich enough and had influence enough to cause that.
Trionfi decks existed already, and we know from the document of 1457, that Galeazzo Maria played with them, but these decks are reported to have 70 cards, not 78.
In general Tarot history - just at this moment - some people don't stop to speculate, that the origin of the Tarot in a 22-trumps-version (or 21 trumps + fool) took place 1420 - 1440 and that it existed already, although we at trionfi.com had made it obvious that not a single document gives really evidence for this assumption, but in the contrary all points to decks with a 5x14-structure or 5x16 or other creative compositions, and between them a 4x14+22-version (standard Tarot) has the quality "not detectable".
In the contrary we offer the suggestion that Galeazzo Maria ordered a deck with the mentioned 4x14+22-structure in the year 1468 at he occasion of his marriage with Bona of Savoia. A provisional page to this:
http://trionfi.com/0/g/61/
This "reconstructed, speculated" deck in our opinion was in choice of the motifs and inner structure very near to that, what later evolved as Tarot, however, some details were different: it had no devil and also likely no tower. Instead of the devil it likely had a Visconti snake, that is a card with familiary heraldic.
Returning back to your question .. why got the Tarot 22 trumps.
Galeazzo's action ... in the case, that we've analysed the historical conditions correctly ... alone doesn't explain the "why" completely. Galeazzo Maria could make a creative impulse by inventing this form of deck, but others must have taken the proposal and imitated it, so that the "successful farspread Tarot" could get reality. And the collective player, who accepted and adapted the game, possibly modificating it by new productions, surely was not specifically interested in Galeazzo's story, why he choose 22 trumps or 21 trumps and a fool.
These persons were in their decision for acceptance probably much nearer to the other explanations, that is 21 possibilities of the roll the 2 dices, 22 chapters of the relevation, 22 letters of Hebre alphabet, probably each of the factor played a role in the "acceptance and imitation process".
So all suggestions to the "why" of the 22 finally run together in one process, each of the answers is "somehow right", as not only the inventor is of part of the process, but also the public, which agrees occasionally to an invention - and mostly disagrees .... another story, about which lots of game inventors could sing complex aries.
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Welcome!