Saturday, February 15, 2020


 This blog is dedicated to Alain Bougereal's "The Arithmological Tarot", originally written in French.

The first post below this one is my February-March 2020 revision of an essay I wrote in November of 1016 in appreciation of Alain's essay. The main changes are that I have provided more background material, in the form of an introduction, a conclusion, and six more illustrations, with discussion. There are also small changes throughout, plus a Bibliography at the end..I have also prefaced the whole thing with a Preamble that Alain asked if I would write.

Below that is my translation of Alain's essay, as revised Oct. 18, 2016, into English. In earlier form it is at

Below that comes the first draft of my own essay, which I leave on temporarily. It appears in that form at

Below that, I have put Alain's essay in his original French, as revised Oct. 18, 2016. It appears in an earlier form at

Below that, Alain has translated some of my essay, as it was in 2016, into French.

Finally, at the bottom is the original essay by Gosselin, as much as is relevant, in the original French and in English translation, for which I thank Steve Mangan on Tarot History Forum.

This post last modified March 31, 2020.


Wednesday, November 9, 2016

In Appreciation of Alain Bougearel's "! + 4 + 7 + 10"

Author's note: This is my March 31, 2020, revision of my previous version of 2016. This one takes precedence. 


Pythagoras was a legendary Greek thinker of the 6th and th century b.c., identified historically with the principle that all of nature, as well the archetypal realm beyond it, is governed according to number. People had only sketchy ideas of how that worked, but it was a conviction that greatly influenced ancient Platonism and early Christianity. and in a much different way continues to dominate the physical sciences. The accumulated tradition is called arithmology, that is, loosely defined, the philosophy of the powers and virtues of particular integers, i.e. whole numbers (Hopper 1938, p. 104). 

In various Pythagorean and Neopythagorean (i.e. Hellenistic and Roman era) texts, prominence was given to the first ten whole numbers, from 1 to 10. Under such circumstances, when playing cards reached Europe in the 14th century, ten number cards were tailor-made for Pythagorean allegories. In fact one deck, the Sola-Busca, has pictures on its number cards eminently suitable for such interpretation (for which see Howard, 2012). But this is all speculation.

We hear nothing explicit about number playing a dominant role in the meaning of the cards until Etteilla, in 1770-1790 Paris. So I will start there and work both forward and back in time. (I will end up at the very early Tarot, so bear with me.) So strongly did Etteilla hold to the role of number, he even insisted that divination with cards be called "cartonomancy," adding the first part of "nombre" in the middle of the word. He also insisted that the cards special to the Tarot deck were out of order, compared with the original sequence as he imagined it to have been; so any prior arithmology in the deck, except in the four regular suits, would have been difficult to find.

His number symbolism is what might be termed Hermetic, i.e. a mixture of Pythagorean, Christian, Christianized Jewish, alchemical, and magical ideas, plus the Corpus Hermeticum and not a few of each writer's own ideas. Etteilla's identification of his first trump, a scene of light shining through dark clouds, with the Creator, does correspond to the Pythagorean Monad, as the number most associated with God - (Hopper 1938, p. 38, quoted below in my "Essay in Appreciation"). His association of 4 with the Universe (Etteilla 1785a, p. 17) is recognizably Pythagorean (Theology of Arithmetic,1988, p. 57), although 5 also had this association. His association of 7 with Wisdom (Etteilla 1783, p. 33) may have had to do originally with a Pythagorean association of that number with Athena (Theology 1988, p. 99; Macrobius 1990, Ch. 6, p. 102). His association of 11 with sin (1783, p. 57)  is from St. Augustine (Hopper 1938,. p. 87). His interpretations of these numbers, with a few exceptions, had little to do with what is depicted on the individual cards bearing those numbers, or with his interpretations of them.

Ettailla did divide the cards of his special deck into groups. In the Second Cahier (Etteilla 1785b, pp. 130-146) he had seven ways of dividing them, into one, two, three, four, five, six and seven "books." As part of their explanations, he sometimes added up the numbers of the cards involved, or most of them, and then added up the digits in the result, attaching symbolic meaning to the end product. For example in the division into five groups, the sum of the numbers, excluding the first, of 1, 8, 9, 10, 11, and 12 is 50, which adds up to 5, the "great and divine name of the Eternal in Hebrew" (pp. 137-148). I am not sure what he meant by this last; it might be the letter Heh, meaning "breath" and "spirit." Those six cards are for God, before and after creation, plus the four cardinal virtues. So these six constitute one group, leaving cards 2-7 for the second group, the six days of creation. And so on. 

Regarding the number cards, Decker, Depaulis and Dummett, in their survey of the French tradition, said that "in Etteilla’s number cards, there is nothing peculiar to Hermetism," adding that its cartomancy" is largely fed from older French cartomancy" (1996, p. 94). If so, however, what inspired that tradition? I think that a close examination will indeed show parallels to Pythagoreanism, perhaps going back as far as the Sola-Busca (Howard 2012). However this is not the place to examine these parallels, as Alain's focus, which concerns us here, is on the whole and on the trumps.

For the whole, which is the subject of Alain's first Pythagorean essay (Bougearel, n.d.), a page from an article by one of Etteilla's followers is more intelligible to the uninitiated (Hugand 1789, p. 38). It ends with precisely the same triangle with base 12 and 78 points there (represented by numbers) that Alain bases his first essay on, albeit in inverted form. 78 is of course the sum of the first 12 numbers. Like Alain, Hugand has smaller triangles for particular themes, e.g., in his case, four general classes of profession (commerce, military, ecclesiastics, agriculture). But there the similarity ends.

In 1856 Eliphas Lévi, while continuing the Hermetic approach to the Tarot, reclaimed the Tarot of Marseille, with very few modifications, for divination (Lévi 2001, pp. 386-394). To the extent that Levi was interested n Pythagoras it was more for his "symbolae" (symbolic sayings) and sacred images (e.g. the "pentacle") than for his arithmology.

It was his follower Paul Christian who theorized about the cards in terms of number  For him the four letters of "INRI" (the abbreviation for "Jesus the Nazarene King of the Jews" in Latin, commonly used on crucifixes) each suggested a principle of creation, which he then converted into numerical terms (Christian 1863, pp. 83-84):
La même idée est représentée par les nombres des quatre termes de la création de toute chose: 1, esprit créateur; 2, matière; 3, union de l'esprit avec la matière, et 4, la forme créée. L'enchaînement de ces nombres produit la décade symbolique: 1 + 2 + 3 + 4 = 10, figurée par l'image de la Rose-Croix.

(The same idea is represented by the numbers of the four terms of the creation of all things: 1, the creative spirit; 2, matter; 3, union of spirit with matter, and 4, the created form. The sequence of these numbers produces the symbolic decade, 1+2+3+4=10, represented by the image of the Rose-Cross.)
Christian's Rose-Cross (above, Ibid p. 82) is a figure produced by inscribing eight circles within one big circle and adding one other circle inside the big one with the same center. Each circle is bisected by the arm of a cross, while the intersections of the eight circles form a series of petal-like segments emanating out from the center.

Papus, in Chapter Two of Tarot des Bohémiens (English translation 1896, original 1889), changed the letters INRI to Yod-He-Vau-He. The Yod, he said, corresponds to "the active principle preeminent." The first He is then  "the passive principle preeminent." The Vau is "the median letter, the link which unites the active to the passive," while the second He is "the passage from one world to another, the transition" (1896, p. 22). The first three are the "Trinitary law of the absolute" (loi Trinitaire du Absolu); the fourth generalizes from Christian"s "created form" (as opposed to form in the mind of God) and also serves as a new active principle (Ibid, p. 30), Papus’s means for repeating the original three on another level. He says that it was Pythagoras who "replaced this word [Yod-He-Vau-He] in his esoteric teachings by the sequence of the 4 first numbers or tetractys" (English translation, p. 33).

Papus deliberately called his three principles a "Trinity" with a capital "T," because in discussing the first three cards later, he explicitly associates them with the Father, the Son, and the Holy Spirit. It might be wondered how a feminine high priestess could be identified with the Son, i.e. Jesus and declared the passive principle. However he also identified the first principle with Osiris, the second with Isis, and the third with Horus, their son. If the Tarot is at base Egyptian, the riddle is solved.

In Chapter 3, Papus derived from the integers from 1 to 22 a whole series of repeating threes and fours. First he applied "theosophic addition" - adding to a number all those preceding it. Then to that result he applied  "theosophic reduction" - adding up the digits in a number until it reduced to one digit (Ibid, pp. 27-29). This is standard Hermetic practice, seen also in Etteilla. What results is a repeating series 1, 2, 3, 1, 2, 3, 1m etc. Every third number is reducible to unity, counting from the last with that property: he gives as examples: 1 (=1=1), 4 (=1+2+3+4 =10 =1), 7 (=1+2+3+4+5+6+7=28 =10=1), 10 (=1+2+3+4+5+6+7+8+9+10 =55=10 =1) and so on. Papus declared that the Tarot was a series of "ternaries," the first initiated by card 1, then card 4, then 7, then 10, etc.. He did not notice that those four numbers add up to 22, which is also a pentagonal number whose series of nesting pentagons defined, starting from unity, four groups within the 22, of precisely 1, 4, 7, and 10. So he did not try to divide the 22 into those four groups. Instead he divided the 22 into three "septenaries" (of 6 cards each, plus the transition card), and a "general transition" of 3 cards plus a transition (see his Table of Contents pp. xi-xii).

In the second edition of Tarot des Bohémiens, 1911, he applied "theosophic addition" to the number 12, yielding the 78 cards of the Tarot (p. 39). For him this was simply one instance of how the Tarot conformed to numerological principles; he did not take Alain’s step (and Hugand’s) of seeing 12 as the base of a triangular figure made up of 78 points. Likewise, for Papus the numbers 1, 4, 7, and 10 yielded only a series of triangles, corresponding to groups of three cards, and not a series of nesting pentagons adding up to 22. Alain in both cases has developed the further Pythagorean implications for the Tarot of these numbers put in geometric form.

It seems to me that Christian's and Papus's initial "Trinitary" threesome, apart from any "reduction" or "addition", is Pythagorean in a way that relates directly to the imagery of the tarot and its interpretation. A derivation of the Holy Trinity from Pythagorean principles had been articulated by Nicholas of Cusa in his book On Learned Ignorance, published in Rome of 1440 but written in preparation for the Council of Florence in 1438-1439. First, in Chapter 7 he argued (1997, p. 96):
But because unity is eternal, equality is eternal, and connection also eternal, therefore unity, equality, connection are one. This is the threefold unity that Pythagoras, the first of all philosophers and the glory of Italy and Greece, taught ought to be worshiped.
Iin chapter 8 he went to argue that the One "generates" Equality. Then in chapter 9 he concluded that Union "proceeds" from Unity and Equality, and that Unity corresponds to the Father, Equality to the Son and Union to Love or the Holy Spirit.

This argument, according to note 32 of the modern translator, in turn derives from John of Salisbury (d. 1180), a teacher at the great cathedral school at Chartres, in his De Septem Septenis 7. Here is the passage, with a translation by Marco Ponzi at
Deus est unitas: ab unitate gignitur unitatis aequalite procedit. Hinc igitur Augustinus: Omne recte intuenti perspicuum est; quare a sanctae scripturae docturibus patri assignatur unitas, Filius aequalitas, Spiritui Sancto connexio; et licet ab unitate gignatur aequalitas, ab utroque connexio procedat: unum tamen et idem sunt. Haec est illa trium unitas: quam solam adorandam esse docuit Pythagoras. ....

(God is unity: generated by unity he proceeds from the equality of unity. Therefore Augustine: everything is clear to he who examines in the right way; for this reason those who have studied the holy scripture attribute unity [unitas] to the Father, equality [aequalitas] to the Son, union [connexio] to the Holy Spirit; it follows that equality is generated from unity, and that union proceeds from both [unity and equality]: yet they are one and the same. This is the unity of the three [trium unitas] which Pythagoras taught to be the only thing [deserving] to be adored.)
The Pythagorean roots of this language can be seen in various Pythagorean works, for example Martianus Capella's Marriage of Mercury and Philology, an early 5th century work on the seven liberal arts that was used extensively as a text in the Middle Ages. "The Monad is unity," it says, and "Father of all" (Capella 1992, p. 277). The Dyad is "the first expression of equality" (p. 278). It attributes Union to the Dyad rather than the Triad; so for connexio, another source will be needed. Capella, however, at least described the Triad as a mean between extremes. Besides Pythagoras, John mentions Augustine. The modern notes mention his On Christian Doctrine, Book I, Chapter 5, which ends::
In Patre unitas, in Filio aequalitas, in Spiritu Sancto unitatis aequalitatisque concordia. Et tria haec unum omnia propter Patrem, aequalia omnia propter Filium, connexa omnia propter Spiritum Sanctum.

(In the Father is unity, in the Son equality, in the Holy Spirit the harmony of unity and equality; and these three attributes are all one because of the Father, all equal because of the Son, and all united [English translations wrongly say "harmonious"] because of the Holy Spirit.)
In the century before John, connexio had become preferred over concordia, even though Augustine used both. Stephen of Liège had put it in the liturgy; the reason is unclear (Albertson 2014, p. 327, n. 101; he mentions Alcuin as an influence, but I cannot find the formulation in accounts of his works). From then on, "connexio" was the preferred word  - even by Thomas Aquinas, who like Augustine used both (Summa Theologiae I.I.39.8). His English translators have "union" as the translation for "connexio." That medieval writers knew this formulation as Pythagorean is clear enough, since some say so; probably they recognized the terms from overtly Pythagorean texts, such as Capella.

All of this is not far from Christian and Papus. John's "unity" has become Christian’s "creative spirit" and Papus’s "active principle." John's third principle, union or connection, has become Christian’s "union of spirit with matter" and Papus's "median letter, which links the active and the passive." But their second principles are different. For John's "equality," Christian has "matter" and Papus, "the passive principle." Matter, which very much has to do with the Son"s role in salvation, is another manifestation of the Dyad. Capella had said (Book VII, p. 278 of translation):
nam monadem fabricatori deo, dyadem materiae procreanti, triadem idealibus formis consequenter aptam.

The Monad refers to the Divine Creator, the Dyad to generating matter, and the Triad to ideal forms.
Only the third term is different; I suspect a copyist's error, or even a translator's. The original meaning might have been "formed ideal," i.e. something material formed according to an ideal, similar in effect to Christian's "created forms.". In any event what matters here is the second term.

Papus, identifying trump one with the Father, trump two with the Son, and trump three with the Holy Spirit, was not bothered that the second trump was feminine (a Popess or High Priestess, sometimes Juno).  But assuming that the Tarot did not in fact derive from ancient Egypt (a safe assumption, in my opinion), and considering that even numbers were considered female and odd numbers male (Macrobius 1990, Ch. 6, p. 99), how could trump 2 represent the Son? I don't think it did, to the extent that Pythagorean symbolism can be applied to the Marseille cards. Capella, for example said of the Dyad, "It is called Juno or wife or sister of the Dyad" (1992, p. 277).

The Marseille order comes from the Lombard order (Depaulis 2013, chart p..23). Now let us go back as the Bembo workshop in Cremona, painters of what is probably the oldest extant tarot deck, from the 1440s, followed by a second deck, the oldest one with a Bateleur (Magician) and a Popess, in the 1450s. Both were probably done for the court of Milan. Art historian Marco Tanzi (2011, p. 26) observes of this workshop that all three of their Coronation of the Virgin paintings showed her being crowned by the Father together with Christ (at left, one now in the Musée du Petit Palace in Avignon), as opposed to the usual way, where Christ crowns the Virgin. The significance, Tanzi theorizes, is that this scene is therefore not after her Assumption, when Christ would already have been crowned, but rather at the beginning of the world. This is suggested by the doctrine of the immaculate conception. Mary alone among mortals does not fall under St. Paul's dictum that all the descendants of Adam are tainted by original sin. If so, She as well as Christ are from the time before the fall of Adam. 

Tanzi says that Mary's immaculate conception had been part of the turbolenze at the Council of Basel, which closed in 1439 Florence, and that a resolution supporting it was part of its proceedings. Edith Kirsch (1994, p. 49) adds, "The Sforza rulers of Milan, like their Visconti predecessors, vigorously promoted the cult of the Virgin Immaculate," She says that it was also dear to the Augustinians who commissioned the Coronations. In such a scenario, the Virgin could be crowned with Christ, as in the unusual Bembo altarpieces, at the beginning of time. Then before Christ's birth, first the sinless Mary descends into the womb of St. Anne, and next, proceeding from her and the Father, Christ incarnates in her womb.
All of this is in consonance with John's and Nicholas's Pythagorean arguments, except that the Dyad, formerly "equality" but now "resembling matter,"  is assigned to the feminine Virgin, who provides the material part of Christ, and the Triad as "union" is assigned to the Christ-child, both God and man. The Crowned Virgin was in fact sometimes portrayed wearing a crown similar to the pope's, as in two examples above, at left (from a 1446 manuscript at King's College, Cambridge) and center (by Martino di Bartolomeo. c. 1400, Los Angeles County Museum of Art). As for the Son, there is the position of the shield on the third card, the Empress, where the eagle can be seen as a symbol of Christ as well as of the Holy Roman Empire and its heir (above right, detail of the Bembo Empress, 1450s, in the Morgan Library in New York, is above right).

Another odd thing about the Bembo Coronations is that unlike most, there is no dove representing the Holy Spirit. Perhaps their patrons thought that Mary herself might be an embodiment of the Holy Spirit, or a manifestation of the same archetype. Tanzi says only, "l’assenza dello Spirito Santo è legata a una precisa questione dottrinale": "the absence of the Holy Spirit is linked to a precise doctrinal question" (2011, p. 27). I am not sure precisely what he is referring to.

A relevant detail in the card, from the earliest depiction onward, is the book the lady is holding; it is by her side in the earliest, and open in the "Marseille" version. The book associates her with the Old Testament's Wisdom, typically with a book as her attribute in medieval illuminations and writings (Katzenellenbogen 1964, index). In Proverbs  8:23 she says, "I was set up from everlasting, from the beginning", like the hypothesized immaculate Mary. The open book also associates her, even if she looks too old, with Mary at the Annunciation, where she is reading the prophetic words of Isaiah. One card maker, Jean Dodal (1701, on Gallica, at left below) even called the card "Pances", a dialect word for "belly".

In these assimilations I do not mean to include Papus's distinction between active cards and passive cards. That is a bit of Aristotelian misogynism picked up from Scholasticism.(Aristotle held that the mother's role in reproduction was passive, providing the material basis for a child, while the father's seed and activity provided its essentially human characteristics, like a potter on his wheel. That was a point on which he and Plato differed.)  Isis, for example, was hardly passive.

Then what of the first card, the street magician? As usually depicted, he does not much look God the Father. But in Plato's Timaeus the business of fashioning the cosmos was assigned to a figure called the "Demiurge," (Stanford, 1917), the Greek word corresponding to "artificer" in the English translation of the Theology. The Stoics assigned this role to what they called the Logos, or Word, the same term used in John 1:1-3: "In the beginning was the Word, and the Word was with God, and was God ... All things were made through him..." So this sleight of hand artist could correspond (with no slight intended) to Jesus as the "active principle" before his descent into matter.

As further support, the three types of objects on his table (knife, cup, balls or shells) plus the stick in his hand, seen not only in the esoteric Tarot but also in the first known version of the card (Bembo 1450s, in the Morgan Library, New York) could well represent not only the four suits but also the four elements from which traditionally our world was fashioned, including the little world created by the players of the game.The straw hat on his table then might allude to the hidden nature of his activity. I would note that the Magician's face is quite similar to that of Jesus in the Bembo Coronation altarpiece. By the same token, there is a noticeable resemblance between the Mary of the Coronation and the Popess (but not the Empress) of the 1450s Bembo Tarot (below).

Given the attention then given to Cusa's book, as well as to Pythagorean principles in architecture and other endeavors in the 15th and 16th centuries, it is not hard to imagine not only the Sola-Busca number cards but the trump sequence being put, over time, in conformity with the same principles. In Italy several different orders existed simultaneously, making it difficult for any one application of Pythagoreanism to be convincing. But in France a particular variation of the Lombard order took hold, that known as the "Marseille," an order that first is evident in the Catelin Geoffroy cards of 1557 Lyon (Depaulis 2013, p. 21).

Since no documents have been found confirming Pythagorean influence on this order, any application is invariably speculative. The most that can be shown is a certain reasonableness given the knowledge of the time. Since by then the numbers had accumulated a large number of meanings, there are various ways they can reasonably be correlated with the tarot sequence. Here I will reference in particular those in the Theologumena srithmeticae, translated as Theology of Arithmetic (Waterfield, 1988), which was available to some in Italy from the 1460s, and was published in 1543 Paris. There was also Macrobius’s In Somnium Scipionis (On the Dream of Scipio); for its application to the sequence see especially Ron Decker, 1999 and 2013. There are also Capella and others, as well as their Christian continuer.

From the perspective of the Theology, the first is the Monad, whose direct influence in our world as as its divine "artificer" (Theology 1988, p. 38), a unitary figure compared to God (Ibid. pp. 36-37), who creates our world of multiform appearances. Then comes the Dyad, the Monad’s feminine-imaged opposite number, "a fount of flowing and liquidity," an impulse to action, also a mean between unity and multiplicity (Ibid. pp. 42-43), thus the number governing the Popess. Together they produce the Triad, the actuality of action, abstract form manifesting in matter, against which the first two are mere potentiality (Ibid pp. 50-51), the Empress's progeny indicated by the eagle on her shield. To the Tetrad is assigned full realization, totality in a material sense, with its four directions, elements, seasons, etc, a totality of which, as its Emperor, the Tetrad is its "custodian" (Ibid, p. 62). It is indeed a repetition of the One, now not in the sense of "artificer" but as ruler. It is also the secular world which is the earthly Emperor's domain.

By the Five, the number of the vegetative soul (Ibid. pp. 72-73), death comes into the world, and so the need for religion, with its Pope as head. From Christian arithmology there are also the 5 wounds of Christ and the 5 loaves that fed 5000. It is also the male number of marriage 3+2, Christ and his Church (in another interpretation of the Popess) Six is the number of the animal, i.e. instinctual soul (Ibid), also the product of 3 and 2, the multiplying force of the joining of male (3) and female (2) (Macrobius 1990, originally Roman era, Vol. 1 Ch. 6; see also Hopper 1938, p. 38, quoted below). In another interpretation, Six is the ‘Pythagorean Y’, the choice between good and evil. Seven corresponds to the rational soul (Theology 1988, p. 73), Plato’s Charioteer in the Phaedrus. Eight for Macrobius (1990, Ch. 5, p. 98) was the number of Justice, nine is near the decad’s end, so appropriately an old man or Hermit; ten is the end of one phase and the beginning of another, on the Wheel of Life as in the numbers. In the Tarot, the Wheel is 1 as well as 10. After that the way is less clear: one method is to add the digits: Strength as 2 (11 = 1+1) and so on, applied to the next nine triumphs in ways other than to the first 10. The remaining three are then perhaps beyond number. Another way is simply drop the additional digit, as Decker has done (11=1), comparing the new card with the previous occurrence of that number.

That is for the individual trumps. Papus had groups of cards, and those, too, can be organized on Pythagorean principles.On the basis of the Pythagorean "trium unitas" and the four numbers of the Tektraktys, he divided the "minor arcana" of 14 cards of each suit into four groups, a court card and three numbers for three of them, and a court card and one number for the fourth. Then for the "majors" he had three groups of six and seven plus one of three and four on the same basis. But this is not the only Pythagorean way to divide the cards and perhaps not the most meaningful. Following an initial essay using geometric configurations within a pyramid of 78 points,, Alain has now given us another, in an original and quite rigorous essay based on the pentagonal number 22 and the pentagons that nest within its geometrical representation. It is that essay on which I would now like to focus.

In Appreciation of Alain Bougearel's "1+4+7+10=22"

Here I would like to make some comments in appreciation, defense, and further development of Alain's presentation of the Tarot sequence in terms of the pentagonal number 22's 1 + 4 +7 + 10 as governing its division into four groups of trump cards that make up the whole, from 1 to 22.

1. Introduction: Dummett's three groups

In his classic Game of Tarot, 1980, Tarot historian and philosopher Michael Dummett examined the differences and similarities in the Tarot’s order of trumps among the various centers in northern Italy where the game was first played. The variations in the order shows certain patterns which permitted him to say that after the game started in one region, it spread to two others in which, for the most part, players had little contact with players outside that region. Since there were no numbers on the cards, variations crept in that even while different from one another, their orders shared commonalities within their region which were not shared by the other regions. The main differences were in the placement of the virtues. In region A, i.e. Bologna, Florence, and points south, the three virtue cards invariably were all between Love and Death. In Region B, i.e. Ferrara, Venice, and points east, the virtue Justice was second highest, so far above the others. And in region C, i.e. Lombardy and France, Temperance was after Death. Within each region there were many variations, but none in the features just described.

Besides the differences that characterized the regions, there were also, perhaps surprisingly, commonalities among all the orders in all the regions (Dummett 1980, p. 398). Excluding the Fool and the three virtue cards, the orders divided into three groups, with much variation within groups but none outside them. Somehow people understood and respected the group each card belonged to, but not the precise order within the group. The groups were first the five trumps, from I to V (Bagatto, Empress, Emperor, Popess, Pope, in no specific order), then the five from VI to XII (Love, Chariot, Wheel, Hermit, Hanged Man, same conditions) and finally the eight from XIII to XXI (Devil, Tower, Star, Moon, Sun, Angel of Judgment, World, again not necessarily in that order) (Ibid, pp. 398-399).

But by what criteria would players have known what could be moved where? Dummett said, "The first segment consists of the Bagatto and the four Imperial and Papal cards." But why should people have perceived that as one group, as opposed to three? What ties them together?

The late Michael J. Hurst offered an answer: Including the Fool, they represent "ranks of society," high and low, a truncated version of a hierarchy, of which an example is the first ten figures, out of fifty, of the so-called Tarot of Mantegna, c. 1465 Ferrara or Venice. Above are cards 1 Misero, 3 Artixan, 9 Imperator, and 10 Papa; Misero is of course visually like the Fool, the next like the Bagatto, then the  Emperor and Pope (these particular cards are in the Cleveland Museum of Art). The other ranks were 2 Servant, 4 Merchant, 5 Gentleman; 6 Knight, 7 Doge, 8 King.

A similar depiction of these ranks is found in a  c.1400 illumination that is at the top left of each post in Hurst"s blog (; on its fringes are an entertainer with a monkey on his back (as in the Bateleur card of so-called Cary Sheet, c. 1500) and a poor man with a stick, as well as a king, a Pope, and six others in between.

Yes, that works, more or less. Many early lists actually did have the Fool first. On the other hand, Dummett had excluded it on the grounds that it wasn’t really a trump, since it could not win a trick. Also, it seems to me, Madmen or Fools exist in all ranks of society; they are not all impoverished. And why would a Madman be on the low end and not the much more reviled Traitor, which is what the "Hanged Man" image meant in Italy at that time? There is a problem on the other end as well: in what sense is a female Pope a high member of society, when there really is no such position? We have to add ‘imagined counterpart to the Empress’ for her, or else have recourse to some abstraction, such as "The Faith" or "The Church," neither of which is a high member of society in the same sense as the other three.

For the second group Dummett in Game of Tarot simply listed the cards, with no attempt to explain how they formed a group that belonged together. Later, in a 1985 article in the journal FMR, he called his second group "conditions of human life" (p. 47). This time he included Death as well as all three of the virtue cards in the second group. Then he went back to putting Death in the final group, and the virtues in no group (Il Mondo e L'Angelo, 1993). Why "conditions of human life" should exclude the Bagatto (as someone trying to make a living), the Fool (Folly as a condition of life) and the virtues, is not said. The classification is a step in the right direction but not enough. Moreover, the boundaries are not well defined, if Death can be in either of two groups.

Hurst called this group, including Death, "Good and Bad Fortune." But Love and War (the Chariot) are not univocally good, the subject of the Hanged Man is not a victim of fortune, and Death is simply a fact of life, with good and bad aspects.

The final group is again hard to unify conceptually. What do Death (perhaps), the Devil, the Star, the Moon, the Sun, the Angel of Judgment, and a strange card called the World have in common, so as to make them one group? In Game of Tarot Dummett just listed the cards. In the FMR article he said they were the "spiritual and celestial powers." That is two groups! And is Death a ‘spiritual power’? It was personified as as a skeleton with a weapon. But if so, why isn’t the Wheel of Fortune also a "spiritual power," since it was controled by a personification turning a Wheel? And what makes the Sun, Moon, and Stars a "power." as opposed to, through its effects, a "condition of life"?

Hurst identified this group (excluding Death) as "Apocalypse and New World." This is possible; but none of the scenes depicted except that of the Angel of Judgment is unique to the Apocalypse, even if it was used there as well. 

There is also the question, why exclude the virtues from these groups? Dummett dealt with this question in a 2004 article called ‘Where do the virtues go?’, making the hypothesis that originally there were no virtue cards in the sequence, and that when two of the regions heard that in another region the three virtues temperance, fortitude, and justice had been added, the players in the other regions "made up their own minds on the matter, with divergent results" (Dummett 2004, p. 165). To me it seems dubious to suppose a time of some duration in which inter-regional communication was so bad that two regions close to each other could add the same three virtues, and only those, and yet not be able check with a third region to see where the virtues went, in a deck that previously had varied at most only slightly in all three.

Hurst’s proposal was that the virtues relate specifically to our responses to good and bad fortune. But in two whole regions Justice or Temperance is outside Hurst’s preferred region.The point of the groups was to explain why the cards didn't go outside their group. Ad hoc explanations would have to be advanced for why those two are exceptions. Whatever they may be, the virtues are no longer simply our responses to good and bad fortune, assuming Hurst's characterization of that group is valid.

2. The Pythagorean meanings of 1, 4, 7, and 10 as defining the content of the corresponding groups of Tarot cards.

From this perspective, it seems to me that Alain's division 1 + 4 + 7 + 10 gives a certain rationale--not the only one possible, to be sure—to the order, resulting in something very similar to Dummett’s groups but now four of them and including the virtues. Separating off the Bataleur (Magician) leaves just four high dignitaries, easy to see as a group. Adding seven more takes us to Death, more or less, depending on whether the 7 include 2 or 3 virtues. Then there are 10 left, if the Fool is number 21 or 22.

In that case what the players would be respecting above all else, when confining each card to a particular group, would be that of maintaining the groups defined by the properties of pentagonal numbers, i.e. the nesting pentangles that make them up, and in particular those of the number 22.

I see two problems. First, it seems rather too much to ask of a game played by members of all ranks of society, to keep the cards in groups defined by a rather obscure property of the number 22. What is so important about pentagonal numbers? Also, any order whatever of 22 items will fit Alain’s groups, unless otherwise defined as well. And once a card thus grouped, what is so bad about its moving to another group over time, if another card can take its place?

One answer might be that it isn’t just the properties of pentagonal numbers that is at work here. In Pythagorean arithmology the numbers 1, 4, 7 and 10 also had meaning in themselves. The ordinal "First," with the cardinal "One," is the number, in monotheism, Pythagorean or otherwise, of God the Father, the Prima Causa and Creator. Also called the Monad, it is the beginning of everything. The Pythagorean basis of this idea is expressed by Vincent Foster Hopper in his Medieval Number Theory (2000, originally 1938, p. 39:
Hence it is very natural that the Pythagoreans should have considered the monad as the first principle from which the other numbers flow (20). Itself not a number, it is an essence rather than a being (21) and is sometimes, like the duad, designated as a potential number, since the point, though not a plane figure, can originate plane figures (22) As first originator, the monad is good and God (24). It is both even and odd, male and female (24), for when added to odd it produces even, and when added to even it produces odd (25). It is the basis and creator of number, but, although it is actually the great Even-Odd, its nature is considered to be more akin to masculine oddness than to feminine evenness. In short, it is always taken to represent all that is good and desirable and essential, indivisible and uncreated. (26)

If 1, the point, is the Father of number, it follows that the duad, the line, is the Mother of number... (27)
20. Nichomachus, Introduction [to Arithmetic], II, vi, 3; Plotinus, Enneads, V, I, y; Photius, Biography of Pythagoras, 7; Proclus, Elements of Theology, A; C, 21.
21. Plotinus, Enneads, VI, 9, 3.
22. Nichomachus, op. cit., II, vi, 3.
23. Eennads, VI, I; 9, 6; V, I, 7.
24. Macrobius, In Somn. Scip. I, 6.
25. De E apud Delphos, 8.
26. Capella, De nuptiis, VII.
27. Capella, ibid.; Plutarch, De animae procreatione in Timaeo, II.
I include the footnotes because it is important to know if this account would have been known during the Renaissance. Nichomachus, Macrobius and Capella were well known throughout the Middle Ages. These plus some Christian writers would have been enough to convey the basic principles to an educated designer.

There was also, for some, the Theologumena Arithemticae (translated as Theology of Arithmetic, 1988), a Roman-era Greek text brought to Italy by the Greek church official Bessarion; it was available in Rome in the 1460s and Venice thereafter, with a copy in Florence, according to Vittorio de Falco in the 1922 Leipzig edition of the Greek text. These copies were accessible to fortunate scholars and nobles. In 1543 Paris (per WorldCat) came a printed edition, still in Greek. Authorship was assigned to the Neoplatonist Iamblichus but in fact is unknown. Its chapter on the Monad (Theology 1988, pp. 35-40) confirms Hopper's summary, as far as the first ten numbers; for example (Ibid, p. 37)
Nichomachus says that God coincides with the monad, since he is seminally everything that exists, just as the monad is in the case of number...
Since in Christianity God the Father is also God the Son, the Christian God is also one of the physically weakest and lowest of his own creation, at least among humanity. So besides the Bagatto's association with the One, there is also his position in the hierarchy, as the least powerful of the triumphs. Yet this very figure can be seen allegorically as the Creator, who in the Gospel of John (1:3) is the logos by whom “all things were made” (the Vulgate’s omnia per ipsum facta sunt). The four types of object on his table and in his hands then can symbolized the four elements out of which the Universe classically was thought to be made, as well as the regular four suits which even he, in the game, triumphs over. This is to be sure a different interpretation than Alain gives to the card, but it is one suggested by Pythagorean philosophy.

So already we have the Monad begetting the Tetrad, the next number in Alain’s series.. The number 4 is in Pythagoreanism the number of the three-dimensional universe, the Creator’s creation. It takes a minimum of 4 points to define a solid, as opposed to 1 for a point, 2 for a line, and 3 for a plane figure). And the first four numbers added together make the sacred "tetraktys." Here is Hopper, pp. 42-43:
The tetrad completes the list of the "archetypal" numbers, representing the point, line, surface, and solid (55). But the particular glory of the archetypal numbers is that they produce the decad, either as a sum (1+2+3+4=10) or in the figured presentation of 10 as a triangular number. This figure was known as the tetraktys (56), the legendary oath of the Pythagoreans (57). ... Four is also the number of the square (60), and is represented in the elements, the seasons, the 4 elements of man, the 4 principles of a reasonable animal, the lunar phases, and the 4 virtues (61).
55. Philo, On the Ten Commandments, 7.
56. Photius, Biography, 4; Iamblichus, Biography, 28; Capella, op. cit., VII.
57. Iamblichus, Biography, 28.
60. Plutarch, De animae procreatique, 1.
61. Diogenes Laertius, Biography of Pythagoras, 19, 7; Theolog. Arith., 22.Ennead s, VI, 6, 16. Capella, op. cit. VII.
For specific quotations from Diogenes Laertius and Capella, see my post at Here the information comes from pagan Greek sources brought into Italy during the fall of Constantinople. Christianity extended the list of tetrads to include Adam, hence humanity, and even the four gospels, which Irenaeus had argued arithmologically could not be more or less, as pertaining to God's existence in the three-dimensional world. Here again is Hopper (pp. 83-84):
The principal Christian innovation in number science was the identification of this spiritual-temporal duality with the archetypal numbers, 3 and 4. Four, by the known analogues of the 4 winds, the 4 elements, the 4 seasons, and the 4 rivers, is specifically the number of the mundane sphere; and, as the first 3 days of creation foreshadow the Trinity, so the fourth is the"'type of ma" (56). Mystically, the fact that man is a tetrad is evidenced in the name, Adam, whose letters are the 4 winds (57). For this reason, knowledge of divine things is disseminated throughout the world by the 4 gospels, evangelists or beasts, emblemized by the 4 extremities of the cross (58), the 4-fold division of Christ's clothing, and the 4 virtues, or forms of love, as Augustine names them (59). "It is not possible," says Irenaeus, "that the gospels can be either more or fewer than they are." (60)
56. Theophilus of Antioch, To Autolycus; AN III, 82; also Ambrose, De fide II, Introduction; Augustine, On John, IX, 14.
57. Augustine, On John, IX, 14; see above, p. 31.
58. The cross was conceived to have 4 or 5 points--5 if the intersection was included. As the image of 4, it is encompassed man in the universe. As an emblem of 5, it coincided with the 4 wounds in providing the salvation of man, with his 5 senses, or of those living under the Old Dispensation of the Pentateuch.
59. Of the Morals of the Catholic Church, XV, 25.
60. Against Heresies, III, 11, 8.
So also in the Tarot, there are the two pairs, spiritual and temporal, who hold sway over the human world: Emperor and Empress in the temporal, Pope and the Church, represented as the Pope’s female counterpart, in the spiritual. And there are also the four suits. One of only two Renaissance texts discussing the meaning and basis of the Tarot finds the choice of this number of philosophical significance. Francesco Piscina, in 1565 Piedmont, writes (Piscina 2010, pp. 26-27):
...ora perchè più presto, in numero quadernario che in altro potremo dire come in più perfetto anzi perfettissimo de gl’altri si come fra tutti & ispetialmente moderni il dottissimo Ficino ha scritto nel argomento fatto sopra il Timeo di Platone dal XX. Fino al 24 Cap

( why in the number of four and not another we can say because it is more perfect than all the others. Among all, and especially modern writers, this has been explained by the learned Ficino in his discussion on Plato’s Timaeus from chapter XX to 24.)
"More perfect" applied to numbers is a Pythagorean way of speaking. Strictly speaking, it applies to numbers whose divisors add up to the number itself, e.g. 6 is perfect because it is the sum of 1 + 2 + 3. But Piscina is probably thinking of the Tetraktys, the most divine figure in Pythagorean mathematics, derived from the number 4 and those below it, as my initial quotation from Hopper explained. It is also one of the first Pythagorean notions that Ficino discusses in his chapter 20 (Ficino 2010, p. 32). He also speaks of the"‘fullness" of the Tetrad and explicitly attributes these doctrines to the "followers of Pythagoras" (Ibid). Fullness in the sense of all-encompassing, especially in the material realm, is a Pythagorean property of the Tetrad, explaining why we have four winds, elements, seasons, etc.

The number 7, in Christian Pythagoreanism, is that of the virtues, the vices, and many other things pertaining to the world of humans and their choices for good or evil. Hopper writes (pp. 84-85):
From the triune principle of God and the quadruple principle of man are produced the universal symbols, 7 and 12. The addition of 3 and 4, spiritual and temporal, produces 7, which is therefore the first number which implies totality (61). It is the number of the universe and of man, signifying the creature as opposed to the Creator (62). Seven gifts of the Holy Spirit were derived from Isaiah XI: 1-3 (63) The Lord's Prayer was found to contain 7 petitions (64). Similarly, the Beatitudes were found to be 7, and by the principle of contraries these septenaries were balanced by the 7 deadly sins (66). Later, the addition of the 3 theological virtues (Faith, Hope, Charity) to the 4 cardinal virtues produced one of the best known heptads of Catholicism. The habit of presenting these spiritual entities in precise numerical groupings indicates that a relationship was felt between them, but it remained for Augustine to show the precise connection of the 7 petitions of the Lord's Prayer to the 7 beatitudes, which in turn relate to the 7 gifts of the spirit or to the 7 steps to wisdom (67). Seven is the number of the Sabbath and Salvation, but it is also the number of sin (68). Necessarily the churches on earth are 7, forming a likeness of the universe (69).
61. Augustine, Civ. Dei, XX, 5.
62. Augustine, On the Sermon on the Mount, II, 10, 36; Letter LV, 15, 28.
63. Tertullian, Against Marcion, V, 8; Victorinus, On Creation.
64. Cyprian, On the Lord's Prayer; Tertullian, On Prayer, II. 8.
65. Augustine, On the Sermon on the Mount, II, 10-11.
66. Tertullian, Against Marcion, IV, 9; Augustine, Harmony of the Gospels, VI, 13.
67. On the Sermon on the Mount, II, 10-11. Contra Faustum, XII, 15; On Christian Doctrine, II, y, 9-11.
68. Augustine, Harmony of the Gospels, VI, 13.
69. Augustine, Letter LV, 5, 9.
Seven, it seems to me, is the number of humanity's trials in the here and now of life, which are to be conducted according to the dictates of the Eternal. This group of Tarot subjects, including at least two of the virtues, are about situations which people universally face: loves, triumphs, the vagaries of time, fortune, and shame. The Bagatto is excluded as allegorically above the world as its creator, while the Fool is excluded by his lack of reasoning capacity. Death is then a suitable upper boundary not to be crossed by allegories below it, once the placement of the virtues has been fixed, and the dignitaries form a lower boundary not to be crossed, and seven the number of trumps in between.

How the virtues are placed, however, is then not determined solely by Pythagorean considerations. Their natural home is indeed with the middle group. Yet the theory works best when there are only two in that group. The resolution of that paradox is beyond the scope of this essay. I can only refer the reader to my Tarot origins blog "From Marziano to the Ludus Triumphorum" at

The number 10 is that of the cycle of the basic numbers, after which one can go on forever. Hopper observes (p. 34) that for the Pythagoreans: 
all things are contained within the decad, since after 10 the numbers merely repeat themselves.
 Also (p. 44):
Ten and 1 are mystically the same, as are also the 100 and 1,000, the 'boundaries' of number. In the decad, multiplicity again returns to unity.
Some in the Renaissance and after (see my comments on the number 1) would have known the Theolgumena Arithmeticae, which says of the Decad (Theology 1988, pp. 109-110):
Hence the Pythagoreans in their theology called it sometimes 'universe,' sometimes 'heaven,' sometimes 'all,' sometimes 'Fate' and 'eternity,' 'power' and 'trust' and 'Necessity,' 'Atlas' and 'unwearying,' and simply 'God' and 'Phanes' and 'sun.'
It is called "Atlas," the text explains, "because he carries heaven on his shoulders" (p. 111). Also, "The spheres of the universe are ten and fall under the decad."

With Ten, we return to the realm of the One, but now in a multiple manner: one cosmos with multiple spheres. After Death, we are beyond this life. In Alain's way of dividing the Tarot, the group of ten begins in the sphere of earth, when one is buried at death, and ends in heaven, following the road of the "mystical staircase" (Vitali, 2018). For the order of these ten, Alain follows the B order of the late 15th century Sermo on games, with its earliest known list of Tarot trumps (Ibid). There the next allegorical figure after Death is the Devil, found, according to medieval tradition, at the center of the earth.

For an ascent to heaven, of course, that is the wrong way, fit only for doomed souls. But Devils were also associated with the sphere of Air that surrounds the earth. They were shown in frescoes grabbing, or trying to grab, souls on their way upward, e.g. in the so-called "Triumph of Death" in Pisa of the 1330s. Like angels, they used their wings, even if they also prowled the earth's surface. Here is Francesco Piscina, writing in 1565 Piedmont (Piscina 2010, pp. 22-23) of the card that some apparently called I Demoni.
Posia che etiamdio è stato opinione di molti, & ispitialmente de Platonici, che stano i Demoni Spiriti fra l'Aria & che stanno come certo mezo fra i Dii e gl'huomnii.

(It has been the opinion of many, in particular the Platonists, that the Demons are spirits that are in the Air & that they are somehow in the middle between gods and men.)
After air comes the sphere of fire, the realm whence lightning comes. The earliest names for the Tower card were Saeta or Sagitta, Arrow, i.e. lightning, and Fuoco, fire. In Dante’s Paradiso, the Mount of Purgatory had a ring of fire on top, after which the poet passed into the spheres of the planets. (See for example the painting by Dominico di Michelino, 1456, in the Duomo of Florence, online at of which the relevant detail is below (from 
 For Piscina, however, fire is also part of the medieval cosmograph of successive rings around the earth:
Dietro i Demoni viene il Fuoco, per debito mezo fra le stelle cose celesti, & le mondane..

(After the Demons comes Fire, as the due mean between the stars, which are celestial, and mundane things...) 
That language of a "due mean" echoes Plato at Timaeus 31d-32a, who sought by arithmetical reasoning to establish why there should be two means between earth and heaven, represented by air and fire. The speaker is the then-famous Pythagorean philosopher Timaeus (
Wherefore also God in the beginning of creation made the body of the universe to consist of fire and earth. But to things cannot be rightly put together without a third; there must be some bond of union between them. ... If the universal frame had been created a surface only and having no depth, a single mean would have sufficed to bind together itself and the other terms; but now, as the world must be solid, and solid bodies are always compacted not by one mean but by two, God placed water and air in the mean between fire and earth,and made them to have the same proportion so far as was possible (as fire is to air so air is to water, and as air is to water so is water to earth); ...
Plato’s speaker is articulating a characteristically Pythagorean mode of reasoning. Piscina has simplified Plato, leaving out water. After all, dry land, where people live and have their remains buried, is higher than the water around it. He has also demoted fire, following medieval tradition, from the heavens to just below them.

The next cards, with Star before Moon, if we follow medieval cosmology and Dante, are out of sequence: the Moon is first above the earth. But Piscina has an explanation which, although directed at why the Sun is higher than the Moon, can also be applied to the Star. Speaking of the game's designer, he says (Piscina 2010, pp. 22-23):
...volendo significare, di quanto maggior utilee dignità sia il giorno nel qual il Sol luce, della Notte, nelle qual la Luna risplende...

(.. he represents that the Day, when the Sun gives light, is of greater utility and dignity than the Night, when the Moon shines...)
That which gives more light has more dignity and utility, and thus belongs higher in the sequence, than that which gives less That elevates the Moon in comparison to mere points of light. It is again a quantitative approach to the Tarot sequence.

It seems to me that there may also be a Christian message here, because the A and B order Star cards suggest "the Magi guided by the star," as a 1613 commentary on Minchiate put it (in Vitali, n.d. [no date] 1). That star is the first glimmer of humanity's coming redemption, while the Sun might be meant to reflect the Second Coming, and the Moon perhaps the Virgin Mary and the Paraclete, comforters in this time of trial. It is the Pythagorean progression of odd-even-odd, repetition but also increase. Below are two Bolognese Star cards (a tarocchi, left, now at the Louvre, c. 1500, and Minchiate, of the Endebrock collection,, mid-18th century) and one Ferrarese (d'Este, c. 1473, at Yale University) Star cards, together with an "Adoration of the Magi" by the Bembo workshop of Cremona (now at the Denver Art Museum), 1440s but with additions in the 1460s, where the Magi are represented similarly, in the upper right corner. This workshop is known to have made Tarot cards for the Sforza ruling family of Milan, but no Star card in the style associated with them has survived..

After the Star, Moon, and Sun, the Angel of the Last Judgment blows his trumpet to summon the dead to Judgment, after which, in the B order, follows the Justice card, God's judgment on individual human. Then, number 21, comes the card known as the World. In the B-region cards, an angelic figure either sits on a cloud dividing him from a scene within a circle of towers on hills (far left, the d'Este card, held by Yale University) or embraces it with its arms (second from left, from the Metropolitan Museum in New York). Considering the Metropolitan card's manner of a protective angel, we might think of Divine Providence, or of the Hebrew Bible's Sophia, God's Wisdom, of whom it was said, "She reaches mightily from one end of the earth to the other, and she orders all things well" (Wis. 8:1). The other might be the same, or else the Eros of the Orphics (
Keeper of the keys of heav'n and earth, the air, and spreading seas   ...
For thee, all Nature's various realms obey, who rul'st alone, with universal sway;
These pagan hymns were well known to the humanists. A manuscript was brought to Venice in 1423 and others soon followed; from those some 36 extant codices derive (Athanassakis and Wolkow 2013, p. ix). Eros would have been particularly appropriate given that this deck probably commemorated a d'Este wedding: it displays d'Este arms with those of Aragon, which could mark marriages in either 1444 or 1473.

As Alain divides the cards, this World card is the ninth card of the fourth group. If so, the angel on the B order card might be emblematic of the ninth sphere, that of the Primo Mobile or First Moved, the sphere just beyond the fixed stars inhabited by God's first creations, the angels. In the "Tarot of Mantegna," the ninth sphere, 49th card, has an angel holding a sphere while standing on another, no doubt representing that of the Fixed Stars (second from right above, from the Cleveland Art Museum).

That would leave the Fool for the highest position, that of the Prima Causa, First Cause (far right above). It would then represent a mystical oneness with the divine mind, a state beyond conceptual understanding. Thus there is the mystery of the Trinity, three persons who are also one. We are left at the top of the sequence in the state that Nicholas of Cusa gave to the title to his book in 1440  "Learned Ignorance."

The preacher of the Sermo said of the 21st card: "El Mondo, cioe Dio el Padre," "The World, that is, God the Father," according to the transcription (Steele 1900, p. 187). God the Father is the Prima Causa, in the tenth sphere of the medieval cosmos. However the female figures on various early Word cards do not correspond to the aged figure that typically represented God the Father, so they are probably a particular attribute of the Father, such as his Wisdom or Providence.

Yet tthere is room for something more, namely that which encompasses Father, Son, and Holy Spirit in a unity beyond our ability to understand rationally. At the end of the preacher's list is "El Matto," i.e. the Madman or Fool (the Italian word corresponds to both terms, which in modern English are slightly different in meaning), someone who is mentally deranged. We might recall St. Paul’s characterization of Christians as "fools for Christ's sake" (I Cor. 4:10), and Christ's message as "the foolishness of God" (I Cor 1:25). In connection with the former, Vitali (2018) has observed that St. Francis was called '"Lo Sancto Jullare e il Sancto Folle di Di'", the Holy Jester and Holy Fool of God. Reminiscent of the latter, a tarocchi poem in 16th century Ferrara characterized the Fool as “divine brain,” cervel divino (Vitali 2005).

In the tarot depictions of the Fool I would call attention especially to the facial expression on the earliest extant example, that of the Bembo workshop of the 1450s. While his disheveled appearance and vacant stare suggest despair, the look at is similar to how they painted martyrs and saints (details of two panels at the Brera Gallery, Milan). Gertrude Moakley (1966, p. 114) suggested, based on Italian custom, that the seven feathers in his hair represented the seven weeks of Lent, the time of purifying repentance. They also form a kind of halo, it seems to me. In the "Marseille" version, e.g. the Chosson above right, the figure seems equally oblivious to this world. Unique to the Chosson is the stream that flows between his feet; like the crossing from one world to to another. 

As the active principle, the Monad corresponds to the sleight of hand artist, the Bateleur. As the goal, it corresponds to the Fool. These are the Alpha and the Omega of which Alain speaks, of which Jesus is both the one and the other, the first as the formative principle of John 1:3 ("all things were made by him" [the Logos]"), the second as first the judge of the "quick and the dead" and then as that which transcends the three separate members of the Trinity altogether.
Alain’s diagram (above) provides a convenient visual summary of the sequence just gone through. The 1 is in the center, with the 4, 7, and 10 as concentric enclosures, U-shaped, around it. In the center is the Creator, a kind of "big bang" point. The authorities in this medieval world get their legitimacy from that center, divinely appointed earthly representatives of that Creator. Beyond that are humans in general, all confronted with the life-concerns of the middle section. Beyond that is the cosmograph, now represented as dots on a U that forms three sides of a square, starting with representatives of the four elements and ending with the Fool.

3. The position of the Fool at the end of the sequence.

For Alain’s interpretation to work, the Fool has to be at the end of the sequence. In the transcription of the Sermo, that is where we see it, after the World. Yet the preacher also gave it the number 0 and said of it, rather cryptically, "Matto sie nulla (nisi velint)": Madman or nothing (unless they want)."  The "nothing" suggests how the preacher thinks the Madman/Fool should be regarded, a typical attitude at that time to the insane or mentally challenged. Yet it is also last, in a list where lower indicates greater power.

In the game the Fool was in all indications a wild card, which could be played at any time but could never take a trick. Since it belonged to no suit, not even that of trumps, by rights it shouldn’t be in the list at all. Yet some mystics would have seen an analogy with the object of their worship: if God could be numbered both as 1 and as 3, that was in the Cosmos; but in essence He was beyond number, like the Hebrew En Sof, meaning "No limit": it is in the nature of concepts to set limits, to say "this, but not that" and reason accordingly. Appropriately beyond the tenth circle in the Prima Causa card shown earlier there is a diffuse light.

In France some three centuries after the Sermo, Court De Gébelin (1781, p. 368) commented on the card in a manner to that of the Sermo (1781, p. 368):
Quant à cet Atout, nous l'appellons Zero, quoiqu'on le place dans le jeu après le XXI, parce qu'il ne compte point quand il est seul, & qu'il n'a de valeur que celle qu'il donne aux autres, précisément comme notre zero: montrant ainsi que rien n'existe sans sa folie.

(As for this Triumph, we call it Zero, which one places in the game after the XXI, because it counts for nothing when it is alone, and has no value other than what it gives to others, precisely like our zero: showing thus that nothing exists without folly.)
I think he meant that it only has value in relation to other cards, just as the value of zero is as a place-holder, for example, in 1000, in which case it is of unending value. This is something to be borne in mind: “0” is ambiguous. Besides denoting "nothing" it is a place-holder in the decimal system, an Arabic innovation (although with Greco-Egyptian precedents) that the Renaissance seems to have been quite impressed with. So a card numbered "0" can be either before the beginning or--standing for the idea of the place-holder--after any given end whatever, "without limit," En Sof.

So de Gébelin said we put it after XXI. While saying this, however, he nonetheless listed this card first, before the Bateleur. Putting it first in a list does not exclude its also being last! This double meaning of “zero” is something the Renaissance would have been well aware of, since it was an innovation not present in classical Greek and Roman literature and was an elegant solution to the problem of how to write and do arithmetical operations large numbers unambiguously and easily. Yet by itself zero is nothing.

In the game, the Fool had a role that de Gebelin was perhaps alluding to, of filling in the blank spaces in sequennces that counted for extra points in the scoring. That is another way it is like “zero”:  adding 0 between two others number increases its value by a power of ten. The Fool’s value is “what it gives to others,” as de Gébelin put it. Piscina referred to the same practice, although concluding that it only shows the closeness that Kings, Queens, Knights and Pages enjoy with Fools (2010, pp. 14-15 and note 7, p. 31).

In the game of Minchiate, the Fool’s important role in giving points to other cards is perhaps one reason it was often put last in the list, even though being "without number." Thus we have, in a treatise on Minchiate of 1716 (Vitali n.d.3), after the author lists the World and "infine le Trombe" (finally the Trumpets, meaning the Angel of Judgment):
A questi 40 Tarocchi veniva aggiunto il Matto, senza numero, posto per il quarantunesimo Tarocco.

(To these 40 Tarots was added the Fool, without number, set as the forty-first Tarot.)
And later in the same treatise, after recounting the same cards:
 ... Aggiungendosi alli detti Tarocchi anche il Matto che non ha numero et è cosi detto perché è vario e si mista con tutte le carte e da esse tassativamente si scioglie come si dirà in apresso, che si pone per il 41. Taroccho.

(...Adding to said Tarots also the Fool which doesn’t have number and is so called because it is various and mixes with all the cards and from them detaches absolutely as will be said later, which is set for 41. Taroccho.)
It appears everywhere with the cards and yet is detached from them as well, outside their world, just as we would expect from this contradictory card.

There is also another point, made by Alain in his note 5: the Fool’s role in the “slam.” in French "chelem," giving the Fool the power to take the last trick, provided that player has taken all the tricks before then. The "chelem" seems not to have been alluded to in print before around 1765, as "vole" and in relation to the game of Whist, 1765 (Hoyle 1765, p. 118), and then others played with the regular pack (see Teikemeier, 2016). But if the rules in 1585 and earlier (in Ferrara and Mantua) were similar to those of 1637, then the situation would have surely occurred sometime with experienced players, when one player, or pair of players, could win all the points except in the trick playing the Fool card. In such a case, as an added incentive to achieve such a goal, it would have been just as natural then as later to grant the Fool the last trick and so attain the supreme triumph, even if such a rule was not written in stone, so to speak.

There is also the fact, described on p. 6 of Dummett and McLeod's Games Played with the Tarot Pack, that in the 18th century some versions of the game in German-speaking regions did make the Fool the 22nd triumph, dispensing with its former role of substituting for any card in a trick.

We have seen that in both the B order's Sermo and in the A order's customary listing of the trumps in Minchiate, the Fool is put last, even though it is also "nulla" and of no trick-taking power. It is true that there is no early C listing that has the Fool on the 22nd line. As Alain observes, the 1637 Regles [Rules] indicate 22 triumphs (p. 3). If so, the Fool must be one of them, but it is not said where in the order it would go. There are only hints, which Alain highlights, from the way in which the order "Monde, Math, Bagat" keeps repeating, as though to say that the Fool was both after the World and before the Bagat, as though in a kind of circular movement.

There is also La Maison Academique, contenant les jeux, in its editions from 1659 to 1702 (all online, for which see my Bibliography under the title just given). The 1702 says on p. 168 that there are 22 triumphs; but on p. 172, there are 21. When listing the 21 by name and number, it lists the Fool as well, but on its own line, unnumbered, after the others (p. 173). The editions of 1659 (page number not given in trnscription) and 1697 (p. 176), both have "21" in the place where the 1702 edition has "22," and no other changes. These people seem to have been as confused about 21 vs. 22 as we are! The 1659 and 1697 editions still list the Fool after the others. If it is thought of as after the others, that is the main point.

The person who inspired the printing of the Regles is said to have been Louise-Marie de Gonzague-Nevers. Her history is suggestive: she was not only the daughter of a Duke of Mantua but also the great-great-granddaughter of Isabella d'Este (I owe this point to Lothar Teikemeier on Tarot History Forum); so she probably played something like the same Tarot as that condemned by the c. 1500 Sermo. These games passed down through the families devoted to them.

That the 1659 account occurs close in time to the 1637 Regles, inspired by a descendant of the ruling family of Ferrara suggests to me that the French placement of the Fool at the end probably derives from the B region of Italy, going back to the Sermo. Whether it goes back further, and in other regions, cannot be said.

4. Application of Alain’s division to the order of the triumphs in the three regions.

Alain concludes that his schema of four groups applies well to the B region, is possible for the C order and to the A region not at all. This proposition needs to be examined in relation to the Pythagorean meanings of the four groups explicated in section Two of this essay.

The B order has Justice in the fourth group. If so, on my account of what the fourth group is about, it is Justice not as a human virtue to be practiced in this world, but as something beyond this world, comng from the spiritual realm of the angels. Given that Justice is placed between "Angel"--i.e. the Angel of Judgment--and the World, i.e. Heaven, what seems to be implied is God's Justice. Dummett, for example, observed (1980, p. 400):
In orders of type B, ... the World is the highest trump, and Justice is promoted to the second highest position in the sequence, coming immediately below the World and above the Angel, the third highest card. There is clearly here an association of ideas: the Angel proclaims the last Judgment, at which justice will be dispensed.
This does not mean that the card loses its value as a human virtue; it is still one of the four cardinal virtues of the Church. It is just that the primary meaning in the sequence is now divine justice.

The C order instead puts Temperance immediately after Death. If we see Death as the sphere of earth Temperance, with its lady pouring water from one vessel to another, could be that of water, thus fitting a cosmographic interpretation of the last 10 trumps perfectly. The card could also be seen as part of the ritual of Holy Communion, a necessary prelude to the soul's rising to heaven. Or it could have been taken as illustrating the soul's move from a physical body to a lighter in the air, as Dante had described (Dante 2000, Purgatorio XXV, 97-102):
...e simigliante poi a la fiammella
che segue il foco là ‘vunque si muta,
segue lo spirto sua forma novella.                                 99

Però che quindi ha poscia sua paruta,
è chiamata ombra; e quindi organa poi
ciascun sentire infino a la veduta...   

(And then, in the same way a flame will follow
After the fire whichever way it moves,
So the new form is following the spirit.
Since it has its visibility from air,
It’s called a shade, and out of air it forms
Organs for all the senses, even sight...)
This meaning of the two jugs, with the soul in between, does not exclude Temperance as a cardinal virtue; it is just that the position in the order brings other meanings to the fore. All of the last ten cards bear interpretations that fit the theme of ascent to heaven after death. In that case, the Judgment card represents the level before the Empyrean, that of the primum mobile, the “first moved,” which is where angels were historically put.

Such a placement of Temperance in the spheres of ascent to God gives particular relevance to a remark by Ficino in the chapters of his Compendium in Timaeum to which Piscina referred in his discussion of the four suits. Ficino says at the beginning of chapter 21 (Ficino 2010, p. 33):
Again, if I did not fear prolixity on the one hand and novelty on the other, I would list some remarkable statements by Iamblichus, Syranus, and Proclus, who designate four levels higher than the celestial world: One, Limit, Limitlessness, Combination.
We have here a summary of the entire trump sequence in four groups, now conceived as four levels above the physical world as represented by the four suits, i.e. the four elements. In terms of Alain’s 1 + 4 + 7 + 10, the 1 is the One, of which the Bateleur is an image, the 4 is the archetype of those who set limits; and the 7 is the boundlessness of human feeling, action, and thought.

That much applies to the Tarot order in all three regions. But in C the 10 can be seen as the tetraktys itself, through combination of the first four numbers. In this last group of 10, seen as 1 + 2 +3 + 4, we have the 1 as Divine Fool, the 2 as the end of time (Judgment and World), the 3 of the Celestials (Sun, Moon, and Star), and the 4 of the spheres of the elements, going from Death as earth, Temperance as water, Piscina’s "Demoni’" as air and the Tower as Fire.

Alternatively, in another Neoplatonic way of seeing Temperance as portrayed in the Tarot, it represents the lower part of the air, which Ficino has as the level just above earth (Ibid). ). The lower air is the region inhabited by the soul immediately after death, with what Plotinus and Ficino after him called the "airy body" (Ficino, Commentary on the Phaedrus, trans. Allen, p. 75). The soul in that body can enter our dreams and appear as ghosts. Below it was the "earthy body" (Ibid.) and above it the "fiery body" and others (Plotinus Enneads, 4.3.9: "a soul leaving an aerial or fiery body for one of earth"; see also,4.3.15, both at From that perspective the soul would be the liquid on the card traveling between two containers.

Finally, is it certain that the type-A Tarot is an exception to the division 1 + 4 + 7 + 10? The A order in Bologna had the "four papi," all with the same trick-taking power; that sounds very much like Alain's group of four. In that order the three moral virtues are all in the third group, which Alain associates with the number 7. That is the number traditionally associated with the virtues, the 4 cardinal and 3 theological. Putting all three before the Hanged Man makes him 13th; the third group then has eight cards and the fourth group nine including the Fool. That is why Alain says that the "arithmological" schema does not fit the A order.

But if the Hanged Man is made the beginning of the 4th group, then everything comes out according to Alain’s formula: the last two groups are then 7 and 10. Is that wrong, conceptually? The theme of the last section is ascent to heaven. In the early type A cards (the “Charles VI,” the Rosenwald Sheet, the Rothschild Sheet), the man is shown clutching bags of coins. That suggests Judas and his “30 pieces of silver” for which he betrayed Christ. But Judas's betrayal is what leads to the crucifixion, and without the crucifixion, there is no admittance to heaven. In that way the card is not only the moment of failed trial of types B and C, but also involved in the ascent to heaven, which is the theme of the last section. The division 1 + 4 + 7 + 10 in that case still holds for the A order.

In fact Dummett's rationale for his three groups, that of cards' staying within a certain range in the order, cannot specify by itself which group the Hanged Man is in, any more than it can specify in which group Death is in, because ithe Hanged Man's position relative to the card above it does not change from one order to another. If a card at the dividing line is invariably in the same place in the sequence, the dividing line can be before it just as well as before or after its successor. So Dummett puts Death in the last group in The Game of Tarot (Dummett 1980, p. 399), and Il Mondo e L'Angelo, 1993 (p. 174), and in the next to last group in "Tarot Triumphant," 1985 (p. 47). The same can be said for the Hanged Man, which immediately precedes Death in all the orders except the Sicilian.

However that a Hanged Man was chosen and put where it is would seem to be dictated by the nature of the card it precedes, so that if there is also an image of Death, the image of a man about to die will be most likely put before it. If so, it is likely that Death at the dividing line would have been prior to the Hanged Man in that situation, so that the A sequence’s order in that respect would be later than the B sequence’s. This is not to say that the B sequence is earlier, just that the placement of a Hanged Man immediately before Death in the sequence is likelier to have occurred there first, if Alain’s hypothesis is correct.

As for the Sicilian placement of the Hanged Man after Death, the Tarot was most likely introduced there in 1663-4 by a particular 17th century governor (Dummett 1980, p. 376); unlike all the other early A-order Hanged Men, this one holds no money bags: nor is he hanging from his ankles, the characteristic pose of the traitor. The allegory has been lost.

I do not think it is too radical an idea to make Judas part of the road to salvation. After all, for salvation to be possible at all, Christ had to be a sacrifice to atone for man’s Original Sin. It is the same for the Devil: for humanity to be worthy of heaven, it must resist evil, and not simply do good. Both the Devil and Judas play their part in salvation. Also, it isn’t just Judas. It is anyone who has betrayed his Lord for material gain. That merely makes his load especially heavy on the ascent.

If all three orders can fit Alain’s division into 1 + 4 + 7 + 10, then it becomes not merely a way of justifying a division into thematic groups, but also a possible explanation for the similarities and differences among the three regions’ orders. If they recognized 22 as a pentagonal number divided in that way, and also the meanings of the groups so derived, that can explain why the game designer would have arranged the cards in such a way as to respect those groups. Alain’s proposal in this way explains why the Bateleur is always first and the Hanged Man just before Death (excepting in both cases the Sicilian): the latter card maintains a consistent number in each group, even when the placement of the virtues changes. This is more than Dummett’s and Hurst's theory can offer.

As for how the card makers would have known to think in such terms, Alain in his essay shows that Pythagorean arithmology was then part of learning mathematics in general, a discipline any card maker would have to know in order to lay out his sheets and run his business. I will give an example of the Pythagorean slant in arithmetic books shortly. As far as accounting for the variability in the order only within the groups, we have the Pope and Death –including, in A, impending death - as natural dividing lines beyond which the groups change in character.

5. Aditional historical precedents for seeing the sequence in such "arithmological" terms

Alain in his footnote 1 focuses on the revival of interest in Plato during the time of the early Tarot. That is certainly part of the story, since Plato had a positive attitude toward Pythagoreanism and used it in his dialogues, notably the Timaeus. The interest in Plato stimulated interest in Pythagorean works themselves, some of which were already available throughout the Middle Ages, as well as books by Christian authors applying the Pythagorean ideas, including John of Salisbury and others. In the Preamble I discussed Nicholas of Cusa in such terms, and in this essay passages in Plato and Ficino applied to the Tarot by Piscina. 

Throughout the Middle Ages, Pythagoreanism was an integral part of what was considered arithmetic. Below is an excerpt from Joannes Martinus, Arithmetica, 1526, on "plane" and "solid" numbers (Heninger 1974, p. 73): In the medieval trivium the subject of arithmetic was seen in the terms of Nichomachus's treatise, as an extension of geometry, including theorems involving series of so-called triangular, square, and pentagonal numbers.The case illustrated shows a series of "solid" numbers using pyramids with an ascending order of plane figures as their base.

In relation to the Tarot in particular, another Pythagorean analysis of the deck was given by Guillaume D’Oncieu in 1584 Savoy, part of a lengthy presentation on each of the ten primary numbers and the groups of things falling under them (for the original and translation, see Vitali, n.d. [no date] 2). When D’Oncieu speaks of a “quaternary” of 56 cards being made "ternary" by the addition of the 21 trick-taking cards and the Fool, he has in mind the Pythagorean meanings of these terms, the mundane world including the divine. Also, his reference to the number 27 as a quaternary number is a Pythagorean notion; it is the fourth in the series 1, 3, 9, 27, as enumerated by the Pythagorean teacher Timaeus in Plato’s dialogue of that name (I thank Steve Mangan for this last, at

In addition, an explicitly Pythagorean analysis of the ordinary deck was given by Jean Gosselin in 1582, in a book whose title begins La signification de l 'ancien jeu des chartes pythagoriques (The meaning of the ancient game of Pythagorean cards). Having presented the rudiments of Pythagorean musical theory, Gosselin introduces the section by saying (pp. 31-32; for the original French, see Appendix I at the bottom of this web-page):
After having explained, as clearly as has been possible for us, the proportions of numbers and the consonances and Harmonies that arise from them, it is appropriate to declare the secrets hidden in this game of cards - which was invented and put into use by a few men learned in Pythagorean Philosophy: Considering that the Pythagoreans say that there are very great secrets of nature hidden in numbers; And also that the greatest victory in the game of cards consists in the number thirty-one, which by its parts contains a most excellent Harmony, as we demonstrate presently.
Then comes his application of Pythagoreanism to the cards, and in particular to a game called Trente et Un, Thirty-One. Here I will summarize his presentation and add in parentheses what I think are the Pythagorean principles involved.

1. Gosselin observes (pp. 33-34, 35) that no card, including the court cards, exceeds in points the number 10, which is 1+2+3+4. (This relationship between 4 and 10 is the famous Pythagorean Tetratkys.)

2. The four suits of the cards correspond to the four elements (p. 31). (That there are four elements is an assumption of Pythagorean and most other ancient philosophies. But in general, Pythagoreans looked for relationships and commonalities between the members of different natural groups of the same number. An oft-repeated story about Pythagoras was that in listening to blacksmiths’ hammers, he noted that the tones varied according to the weights of hammers producing them, and that the same tones produced by strings varied according to the same ratios in weights applying tension to the strings (Nichomachus, Manual of Harmonics, Ch. 6; Iamblichus, Life of Pythagoras, Ch. 26; Macrobius, Commentary on the Dream of Scipio, II.1.8-12). Accordingly, Pythagoras was depicted listening to hammers, e.g. by Luca della Robbia, 1437-1439, on the campanile of Florence cathedral (author’s photo below, taken at the Museo del Duomo, with the museum’s placard). Identifying which ratios were harmonious was part of Pythagorean musical theory. In general, Pythagoreans saw number as the key to understanding numerous phenomena.)
3. Between the French suit of Tiles (floor tiles?) and Earth there is the commonality of supporting heavy things. Between Pikes and Fire there is the commonality of penetrating, and being the most penetrating of its group. Hearts (in our bodies) are in a relationship of dependence on Air. Clover is in a relationship of dependence on much Water. (pp. 31-32.) (This is a process of analogy between one thing and another familiar in medieval allegory. For example snakes were a sign of Prudence because Jesus said, as the Vulgate rendered Matthew 10:16, “estote ergo prudentes sicut serpentes “therefore be as prudent as serpents”. The analogy is facilitated by the commonality of “four” between suits and elements. Moreover, the four suits in card games play a similar role to the four elements in ancient physics: just as particular things were combinations of elements in different proportions, so the hands dealt the players contained the suits in different proportions, as Gosselin explains on pp. 38-40.)

4. Regarding the "most excellent harmony" (p. 31) in the game, Gosselin observes that in music the “by adding of diapasons (octaves), one above the other, the result is always a perfect consonance – which does not happen in other consonances of music” (p. 37). A diapason exists when two sounds vibrate in a ratio of 2:1. It is a “perfect” consonance in that two notes an octave apart sound like the same note, just higher or lower in pitch. Thus a series of four diapasons, starting from unity, is 1 to 2, 2 to 4, 4 to 8, and 8 to 16. (p. 37). (This is an application of Pythagorean musical theory to the "4" of the game. The ratio “2” represents the octave, 4 the second octave, 8 third octave, and 16 the fourth.)

5. Adding these ratios together, starting from unity, is the sum of 1+2+4+8+16 +31, which is also the perfect number of points in the game of Trente et Un, Thirty-One (p. 36). The sum of a note plus its four octaves is their combination into one harmonious whole. (This is an application of the geometric proportions expressed in the four “perfect consonances” of Pythagorean music theory to the game of Thirty-One.)

6. Thus the game of Thirty-One, by making 31 its best hand (“the one who gains 31 points or comes closest to it claims victory”), corresponds to a “great and admirable harmony, because just as there are certain temperaments between the qualities of the four Elements in all natural things, there exists between the numbers of thirty-one great harmony.” (p. 36). Here we might ask why the series to be added up should stop at 4 octaves, as opposed to 5, 6, or an indefinite number. It may simply be related to the number 4 of the elements and suits: a harmony of 4 octaves adds up to 31. On the other hand, a passage in Macrobius suggests another answer. In the course of explaining the basics of Pythagorean harmony, he says (section II.i.24, Stahl et al translation p. 189):
And so the consonant chords are five in number, the fourth, the fifth, the octave, the octave and fifth, and the double octave. This number of consonant chords has to do only with the music that the human breath can produce or the human ear can catch; beyond this there is still the range of celestial harmony, which reaches even four times the octave and fifth.
What is of interest is the “range of celestial harmony”. According to the translators’ note to this sentence, Macrobius’s number “four” here was “Because twenty-seven was the largest number in the construction of the World-Soul (see above,, and note), and because, according to his statement in the next paragraph, there would be four octaves and a fifth in twenty-seven and a half tones.“ Section is Macrobius’s discussion of the so-called Platonic Lambda, where the World-Soul is constructed, starting from unity, by the numbers 2, 4, and 8 on one side and 3, 9 and 27 on the other. Section II.i.25 says that an octave has six tones, and the ratio known as the fifth has 3.5 tones, making 27.5 tones in all, or 4.7 octaves. So just as the universe has four elements, four octaves is the extent of the range of its “perfect consonances”. 

I conclude that specifically Pythagorean considerations, and not just the four elements, clearly did play a major role in Gosselin’s argument. That is not to say that his argument is convincing. First, that there are four suits may be for different reasons: the four sides of the cards, for example, or what makes for the most interesting games. Second, the inventors of French suit-signs may have had other reasons for choosing the signs they did. Current thinking is that the French signs were adaptations, for ease of stenciling, of German suit signs (Dummett, Game of Tarot, pp. 22-23). But the French signs of Tiles and Clovers are not just simplified Bells and Acorns, and the German names (for Leaves, Acorns, Bells, and Hearts) are quite different, except for Hearts. Could the four elements have been a consideration? I do not have a better theory. Third, the inventors of the game of Trente et Un may have had other reasons for choosing the number 31, having to do with what makes a good game. Again I do not have a better theory. Fourth, as to why the court cards were given the point value of 10, it makes for easier addition of points. But again, Pythagoreanism is not ruled out.”

6. Conclusion

In Section One I summarized the arguments in favor of Dummett’s three groups five, five and eight, excluding the three virtues and the Fool, as well as some of its difficulties.

In Section Two I also defended Alain’s four groups in relation to traditional Classical and Christian Pythagorean significations of 1, 4, 7 and 10 for defining the groups in question.

In Section Three I discussed the arguments for and against putting the Fool at the end of the sequence. The examples were all in the B region, except for the C region after a descendent of the ruling family in the major B region city, Ferrara, played a role in the production of the first known rules in French. In meaning it can fit in either place. The earlier documentation in Ferrara suggests that the four groups dictated by the pentagonal series would likely have first applied to the Tarot in Ferrara.

In Section Four I examined the issue of whether Alain’s four groups applies to all three regions of the early Tarot or just one or two. Alain only defends it for the B order, whereas I see it as applying easily to C and even to A, although with a different dividing line between the third and fourth groups. In fact a desire to keep the last two groups as 7 and 10 could explain why the Hanged Man is there, always just before Death, precisely a subject, as a person about to die, that belongs before Death and so allows all three virtues to be in the third group and still have 7 in that group and 10 in the fourth. In such a case, however, the A arrangement for the whole in terms of the four groups would be later than the B. Finally, that the pentagonal number's groups start with 1 could explain why the Bagatto is always first and therefore qualifies as a group in Dummett’s sense: it is the first group’s sole member.

In Section Five I gave an example of a standard textbook of the time discussing series of numbers in terms of the geometrical figures they made, similar to that of pentagonal numbers. I also gave examples of Pythagorean thinking similar to that used by Alain applied either to the trumps or the suits by authors during the early period of the Tarot, namely Guillaume d’Oncieu, 1584, and Jean Gosselin, 1582. These are in addition to Francesco Piscina, 1565, discussed in Sections 2-4, who applied Pythagorean mathematical ideas to the Tarot from Plato’s Timaeus and Ficino’s commentary on Proclus’s In Timaeum.


ALBERTSON, David, 2014. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford U. Press, New York, 2014.

ATHANASSAKIS,Apostolos, and WOLKOW, Benjamin, 2013, translators and editors. The Orphic Hymns. Johns Hopkins Press, Baltimore. Introduction online in Google Books

AUGUSTINE of Hippo. On Christian Doctrine. Originally 397 c.e. as De Doctrina Christiana,

BOUGEAREL, Alain, n.d. Tarot and Neo-Pythagoreanism: The numerogical structure of the Tarots Also in Italian, translated by Andrea Vitali, same site, click on Italian flag top right. Originally in French.  

CAPELLA, Martianus, 1992. The Marriage of Philology and Mercury. Translated by William Harris Stahl and Richard Johnson, with E. I. Burge. Vol. 2 of Martianus Capella and the Seven Liberal Arts, Columbia University Press, New York. Relevant pages in Google Books. Originally in Latin, 410-429 c.e., as De nuptiis Philologiae et Mercurii, text online.

CHRISTIAN, Paul [Jean-Baptiste Pitois], 1863. L'Homme Rouge des Tuileries [The Red Man of the Tuileries], par l'auteur, Paris. Online in Gallica.

DANTE Alighieri, 2000. Divine Comedy, revised edition, translated by James Finn Cotter. Forum Italicum, Stony Brook, New York. Relevant passage online at

DECKER, Ronald, 1999. "Number Symbolism and the Tarot Trumps," in The Playing Card, 27:5 (March-April 1999), pp. 192-193, 202-207.

DECKER, Ronald, 2013. The Esoteric Tarot: Ancient Sources Rediscovered in Hemeticim and Cabala, Chapter 5, Numinous Numbers. Theosophical Publishing House, Wheaton, Illinois. Online in Google Books.

DECKER, Ronald, DEPAULIS, Thierry, and DUMMETT, Michael, 1996. A Wicked Pack of Cards: The Origins of the Occult Tarot. Duckworth, London. 

DEPAULIS, Thierry, 2013. Le Tarot Révélé: une histoire du tarot d'apres les documents [The Tarot Revealed: A History of the Tarot According to the Documents]. Musée Swisse du jeu, La Tour-de-Peilz, Switzerland. 

DUMMETT, Michael, 1980. The Game of Tarot: from Ferrara to Salt Lake City. Duckworth, London. Relevant chapter online at

DUMMETT, Michael, 1985. "Tarot Triumphant," FMR [journal], Milan, pp. 46-53. Online at

DUMMETT, Michael, 1993. Il monde e l’angelo: i tarocchi e la loro storia [The world and the angel: the tarot and its history], Bibliopolis, Naples. Relevant passage translated into English by Michael S. Howard at

DUMMETT, Michael, 2004. "Where do the virtues go?," The Playing Card 32:4, pp. 165-167. Posted online at

ETTEILLA [Jean-Baptiste Alliette], 1783. Manière de se récréer avec le jeu de cartes nommées tarots, 4pour servir de troisième Cahier a cet Ouvrage [Way to amuse oneself with the playing cards called tarots, serving as the third Notebook of this Work]. By the author, Amsterdam/Paris. Online in Gallica. Translation at

ETTEILLA [Jean-Baptiste Alliette], 1785a. Manière de se récréer avec le jeu de cartes nommées tarots, pour servir de premier Cahier a cet Ouvrage [Way to amuse oneself with the playing cards called tarots, serving as the first Notebook of this Work]. By the author, Amsterdam/Paris. Online at Starts on p. 215 of scans there.

ETTEILLA [Jean-Baptiste Alliette], 1785b. Manière de se récréer avec le jeu de cartes nommées tarots, pour servir de second Cahier a cet Ouvrage [Way to amuse oneself with the playing cards called tarots, serving as the second Notebook of this Work]. By the author, Amsterdam/Paris. Online at For transcription and translation of some passages see, post entitled "Etteilla on the cards as a whole II."

FICINO, Marsilio, 2008. Commentary on the Phaedrus. In Commentaries on Plato, Vol. 1: The Phaedrus and Ion, ed. and trans. by Michael J. B. Allen. Original work published 1484 or 1485. Google Books.

FICINO, Marsilio, 2010. Compendium in Timaeum [Commentary on In Timaeus], translated by Arthur Farndell in All Things Natural: Ficino on Plato’s Timaeus, London: Shepheard-Walwyn. First published in Ficino’s Opera [Works]  in 1491. Online at

GEBELIN, Court de, 1781.‘"Du Jeux des Tarots." In Le Monde Primitif, analyse et comparé avec le monde moderne, Vol 8, Tome 1, etc. ["On the Game of Tarot," in The Primitive World, analyzed and compared with the modern world, Vol. 8, Part 1, etc]. By the Paris, pp. 365-394, online at, translated by Steve Mangam,

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HENINGER, S. K., 1974. Touches of Sweet Harmonies: Pythagorean Cosmology and Renaissance Poetics, Huntington Library, San Marino, California.

HOPPER, Vincent Foster, 1938. Medieval Number Symbolism: its Sources, Meaning and Influence. Columbia University, New York. 2000 reprint by Dover Publications, Mineola, New York.

HOWARD, Michael S., 2012. Neopythagoreanism in the Tarot: Sola-Busca, Etteilla, Waite, at

HOYLE, Edmund, 1765. Mr. Hoyle’s Games of Whist, Quadrille, Piquet, Chess and Back-Gammon, Complete, 14th edition. Printed for Thomas Osborne, Henry Woodfall, and Richard Baldwin, London. Online in Google Books.

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KATZENELLENBOGEN, Adolph, 1964. Allegories of the Virtues and Vices in Medieval Art, from Early Christian times to the Thirteenth Century, trans. Alan J. P. Crick. W. W. Norton & Co., New York. Originally published 1939 by the Warburg Institute, London.

KIRSCH, Edith, 1994. "Bonifacio Bembo's Saint Agostino Altarpiece." In Studi di Storia dell'Arte in Onore di Mina Gregori, ed. Elisa Acanfora; pp. 47-49. Silvana Editoriale, Milan.

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LA MAISON ACADEMIQUE, contenant les jeux, 1659. Paris, Chez Estienne Loyson, at

LEVI, Eliphas [Alphonse Constant], 2001. Transcendental Magic, its Doctrine and Ritual. Translation by E. A. Waite of Dogme et Ritual de la Haute Magie, originally published in two parts 1855-1856 (per Waite on p. xxiii). Weiser, York Beach, Maine. Online in Google Books.

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MOAKLEY, Gertrude, 1966. The Tarot Cards Painted by Bonifacio Bembo for the Visconti-Sforza Family, an Iconographic and Historical Study. New York Public Library, New York. Online at elsewhere.

NICHOLAS of Cusa, 1997. Selected Spiritual Writings, translated by H. Lawrence Bond.. Paulist Press, New York. In Google Books. Passage cited originally in De docta ignorantia, 1440 Rome, 

NICHOMACHUS of Gerasa, 1926. Introduction to Arithmetic, translated by Martin Luther d’Ooge, Macmillan, New York. Originally in Greek, 1st or 2nd century.c.e. Online in Google Books and HathiTrust.

NICHOMACHUS of Gersa, 1994. The Manual of Harmonics, translated by Flora R. Levin, Phanes Press, Grand Rapids, Michigan.  Originally in Greek, 1st or 2nd century c.e. Partially online in Google Books.

PAPUS [Gérard Encausse], 1889. Le Tarot des Bohémiens: le plus ancien livre du monde, a l’usage exclusif des initities. chez l'auteur, Paris. Online at

PAPUS, 1896. The Tarot of the Bohemians, the most Ancient Book in the World, for the Exclusive Use of Initiates, translated by by A. P. Morton. George Redway, London. Online in Original work in French, 1889, Online at

PAPUS, 1911. Le Tarot des Bohémiens (2me édition augmentée): le plus ancien livre du monde, a l’usage exclusif des initities. Hector et Henri Durville, Paris. Online in Gallica.

PISCINA, Francesco, 2010. Discorso sopra l’ordine delle figure de Tarocchi [Discourse on the Order of Figures in the Tarot]. In Explaining the Tarot, Two Italian Renaissance Essays on the Meaning of the Tarot Pack, edited and translated by Ross Caldwell, Thierry Depaulis and Marco Ponzi, Maproom Publications, Oxford, pp. 10-29. Original text published 1565 by Leonardo Torrentino, Monte Regale, Piedmont.

REGLES dv iev des tarots, 1637. Anonymous, but written by the Abbé Michel de Marolles, who also had it printed at Nevers. Transcribed by Thierry Depaulis at

STANFORD Encyclopedia of Philosophy 2017. "Plato's Timaeus", at

STEELE,  Robert, 1900. "A Notice of the Ludus Triumphorum and some Early Italian Card Games ; with some Remarks on the Origin of the Game of Cards." Archeologia, or miscellaneous tracts relating to antiquity, vol. 57 (January 1900), pp. 185-203.Online in Google Books.

TANZI, Marco, 2011. Arcigoticissimo Bembo : Bonifacio in Sant'Agostino e in Duomo a Cremona. Officina Libraria, Milan.

TEIKEMEIER, Lothar [‘Huck’], 2016. Tarot History Forum post of Aug. 16, at

THEOLOGY of Arithmetic [Theologumena Arithmeticae], 1988. Translated by Robin Waterfield, Phanes Press, Grand Rapids, Michigan. Authorship attributed at first to Iamblichus, then Nichomachus of Gerasa, but in fact is unknown, ancient Greek, 4th-5th century c.e,, brought to Italy c. 1460.

VITALI, Andrea, 2005. "I Tarocchi in Letteratura I: I documenti più importanti" ["The Tarot in Literature I: The most important documents"], with English translation by Michael S. Howard (click on British flag at upper right of the page],

VITALI, Andrea, 2018."La Scala Mistica nel 'Sermo de Ludo': Un esempio del concetto “Ludendo Intelligo” (Giocando Imparo)," ["The Mystical Staircase in the 'Sermo de Ludo': An example of the concept "Ludendo Intelligo" (Playing and Learning)"], with English translation by Michael S. Howard»,

VITALI, Andrea, n.d. [no date] "Ganellini seu Gallerini -Il gioco delle Minchiate a Genova, Roma e Palermo (secc. XVII - XVIII)" ["Ganellini seu Gallerini -The game of Minchiate in Genoa, Rome and Palermo" (17th - 18th centuries)"], with English translation by Michael S. Howard,

VITALI, Andrea, n.d. 2. "Tarotica – 1584: La Quaterna dei Tarocchi fra Mistica e Gioco" ["Tarotica – 1584: The Quaternity of the Tarot between Mysticism and Game"], with English translation by Michael S. Howard,

VITALI, Andrea, n.d. 3. "Trattato del gioco delle Minchiate: Un documento sul gioco delle Minchiate del 1716" ["Treatise on the Game of Minchiate: A document on the Game of Minchiate dated to 1716"], English translation revised by Michael S. Howard,




[30] Déclarer le signification des images et des caractères du jeu des cartes: et comment le dit jeu nous représente la composition de chaque chose naturelle

Après avoir expliqué le plus familiairement qu'il nous a été possible les proportions des nombres, les consonances et Harmonies qui en proviennent, il convient de déclarer (errata première transcription donnée comme 'énoncer') les secrets qui sont cachés en ce jeu des cartes - lequel a été inventé et mis en usage par quelques hommes savants en Philosophie Pythagorique. Attendu que les Pythagoriques [errata première transcription donnée comme 'Philosophes'] affirmaient qu'il y a de très grands secrets de nature cachés sous les nombres. Et aussi

[31]que la plus grande victoire du jeu des cartes consiste au nombre de trente et un,
lequel selon ses parties contient une très excellente Harmonie comme nous le démontrons présentement.

Premièrement, il convient de considérer qu'en un jeu de cartes vulgaires, il y a quatre manières de caractères qui sont carreaux, trèfles, coeurs et piques. Lesquels nous représentent les quatre Eléments dont toutes choses naturelles sont composées.

Ces Eléments sont situés et disposés au monde selon l'ordre suivant.

La Terre est le plus pesant de tous et au milieu des trois autres Eléments, soutient sur soi et en soi, toutes choses pesantes; l'Eau est moins pesante que la Terre et est répandue à l' alentour de la Terre en plusieurs endroits. L' Air est plus léger que l' Eau - c'est pourquoi, il environne l' Eau et la Terre.Et le Feu qui est le plus léger de

[32] tous, est par-dessus l' Air - lequel il environne de toutes parts et touche le ciel de la Lune.

Les carreaux qui sont peints sur les cartes signifient la Terre : car tout comme la Terre soutient toutes choses pesantes, de même les carreaux sont propres à soutenir les choses pesantes que l'on met dessus eux.

Les trèfles qui sont peints sur les cartes nous représentent l' Eau car le Trèfle est une herbe qui croît en milieu humide et se nourrit de l'eau qui l'arrose.

Les coeurs qui sont peints sur les cartes nous signifient l'Air - c'est que nos coeurs ne peuvent pas vivre sans air.

Les piques qui sont peints sur les cartes nous représentent le Feu parce que le Feu est le plus pénétrant des quatre Eléments à l'instar des piques qui sont des instruments de guerre très pénétrants.

Et de chacun des caractères cités sont  

 marquées treize cartes en un jeu qui valent, somme toute, cinquante deux cartes. C'est, à savoir:
- l' image d'un Roi qui est peinte sur une carte avec l'un des dits caractères [carreau ou coeur ou trèfle ou pique]
- l'image d'une Reine qui est peinte sur une autre carte avec l'un des dits caractères
- l'image d'un Valet qui est peinte sur une autre carte avec l'un des dits caractères.

Il s' en suit qu'il y a autant de rois que de reines et de valets en un seul jeu de cartes qu'il y a d' Eléments dans la Nature - soit quatre Rois, quatre Reines et quatre Valets.

Chacune de ces quatre Images est accompagnée comme cela a été dit d'un des quatre caractères ci-dessus décrits, ... au nombre de dix. Et chacune des autres cartes qui ne sont pas marquées de figure humaine, mais seulement de quelques uns de ces caractères [carreaux, coeurs, trèfles ou piques] signifient autant d'uni- 

-tés qu'il y a de caractères peints sur la carte.

Le nombre ne dépasse jamais dix.

J'estime avec grande raison que c'est parce que le nombre de dix a des propriétés admirables, principalement touchant les consonances de musique qui procèdent des nombres dont il est composé : lesquels sont un, deux, trois et quatre qui ajoutés les uns aux autres tous ensemble valent dix.

   En quoi, il convient de noter que:
- entre un et deux, il y a un Diapason (comme cela a té dit aurapavant) ainsi qu'entre deux et quatre
- entre deux et trois, il y a un Diapente
- entre trois et quatre, il y a un Diatessaron
- entre un et trois, il y a un Diapason Diapente
- entre un et quatre, il y a deux fois le Diapason.

Par cela il est manifeste que les principales consonances de Musique Pythagorique et

Diatonique sont comprises dans le nombre de dix.

Ce n'est donc pas sans grande raison qu'il n'y a aucune carte en ce jeu qui contienne plus de dix - semblablement, et que, chaque image peinte sur ces cartes avec son caractère soit de dix précisément.

Et à ce propos, il faut savoir que par le nombre des cartes les Anciens entendaient les degrés des qualités de chaque Elément.

Desquels nombres, une des personnes (qui jouent à ce jeu) en prend le plus qu'elle peut, selon la coutume du jeu, sans excéder trente et un, afin d'acquérir, pour elle, le dit nombre de trente et un, ou à tout le moins, de s'en approcher au plus près, plus que nul des autres qui jouent avec elle, car c'est en l'un de ces eux points (31 ou valeur s'en approchant le plus) que consiste la victoire et le gain du dit jeu des cartes.

Or, si nous voulons savoir la raison pour laquelle les Anciens ont

constitué la grande victoire du jeu des cartes au nombre de trente et un plutôt qu 'en un autre nombre tel que vingt huit lequel est un nombre parfait ou bien trente qui est le nombre des degrés d'u signe céleste (zodiaque de 360° : 12 = 30°) voire en quelque autre nombre plus grand ou plus petit, il convient de considérer que le nombre de trente et un est composé par l'addition des cinq premiers nombres de la proportion Géométrique double : c'est, à savoir, un, deux, quatre, huit et seize[31 = 1+2+4+8+16] Lesquels nombres ainsi disposés en progression Géométrique sont une très grande et admirable harmonie.

Car tout comme 'il y a certains tempéraments entre les qualités des quatre Eléments en la composition de toute choses naturelle, il existe entre les nombres dont trente et un est composé une harmonie très excellente laquelle contient qua-

-tre fois le Diapason.

En effet, il y a
-entre un et deux, un Diapason
-entre deux et quatre, un autre Diapason
-entre quatre et huit, encore un autre Diapason,
-et, entre huit et seize, un autre Diapason.

Ainsi donc, il est manifeste qu'il y a autant de fois le Diapason qu'il y a d'Eléments dans la Nature.

Davantage, il convient de considérer que (le) Diapason consonance parfaite comprend en fait, toutes les simples consonances de Musique qui sont: Diapante, Diatessaron, Tierces et Sextes.

Pareillement, en additionnant précisément plusieurs Diapasons ensemble l'un au-dessus de l autre, il en résulte toujours une consonance parfaite - ce qui n'advient pas à autre consonance de Musique.

Et pour cause de ce que nous avons dit antérieurement, les quatre Eléments, en la composition de toute choses nature-

 -lle, gardent entre eux la grande harmonie susdite : ou aussi, ils s' approchent bien près de cette harmonie.

Quelqu'un pourrait dire et objecter qu'il faudrait (si cela était vrai) que toutes choses naturelles eussent meilleures qualités et mêmes tempéraments pour que les quatre Eléments gardent entre eux semblables harmonies en la composition de chaque chose naturelle. Ce à quoi, nous faisons la réponse suivante.

Pour que les quatre Eléments en la composition de toute chose naturelle gardent entre eux cette grande harmonie ou quelques consonances qui s'en approchent, il n'est pas nécessaire que toutes choses naturelles soient de même tempérament et complexion. Car en chacune des choses naturelles, un même Elément ne domine pas sur les trois autres Eléments.

Ainsi en une choses naturelle, un Elément a

 l'avantage sur les trois autres Eléments tandis qu' en une [autre] chose naturelle, de diverse qualité, c'est un autre Elément qui domine sur les autres trois ; néanmoins, les qualités des quatre Eléments sont tellement proportionnées et ont une telle harmonie ensemble qu'ils s'accordent en la génération et composition de chaque chose naturelle.

Et quand cette harmonie se corrompt, cette chose naturelle (dont elle est Harmonie) périt et se finit.
Les différences des tempéraments et complexions des choses naturelles, diverses, sont très bien représentées par la différence des caractères des cartes qui signifient les quatre Eléments.

C'est ainsi que:
- il advient parfois qu'un de ceux qui joue, gagne et acquiert une certaine harmonie de nombres des cartes qui signifient les quatre Eléments dont la plus grande partie est représentée

par Carreaux qui signifient la Terre : par quoi ils dénotent qu'il y a plus de Terre en la chose naturelle par ceux représentés qu'il n'y a de nul autre Elément.
- Et quelques autres fois, un de ceux qui jouent acquiert en jouant une autre harmonie dont la plus grande partie des nombres de cette dernière, est représentée par Trèfles - lesquels signifient l' Eau : par quoi cette harmonie montre qu'il y a plus d' Eau, en la plus naturelle représentée ;
- et ainsi faut-i juger de toutes les autres différences qui se trouveront en chaque harmonie et aux proportions qui sont sous-jacentes [au-dessous de] à ces harmonies. Lesquelles différences sont en très grand nombre, tout comme les choses naturelles de diverses espèces en ce monde.

Ce sont là les principales significations de l'ancien jeu de cartes lequel mérite bien d'être.


p. 30
The meaning of the images and the characters of the game of cards: and how the said game represents the composition of each natural thing.

After having explained the most common proportions of numbers, the proportions of numbers and the consonances and Harmonies that arise therefrom, we are now ready to state the secrets which are hidden in this game of cards - which was invented and put into use by a few men learned in Pythagorean philosophy: Considering that the Pythagoreans say that there are very great secrets of nature hidden in numbers. And also

p. 31
of the number thirty-one, which is the number of victory in that so-named game of cards, (1) and which according to its parts contains a most excellent harmony, as we will demonstrate presently.

Firstly, we must consider that in a common set of cards there are four suits whose emblems [suit-signs] are tiles [diamonds], clovers [clubs], hearts and pikes [spades]. These we take to represent the four elements of which all natural things are composed. These elements are located and arranged in the following order.

Earth is the heaviest of all and is in the middle of the other three elements, and supports on and in itself all heavy things. Water is less heavy than Earth and surrounds it in several places. Air is lighter than water and surrounds Water and Earth. And Fire, which is lightest of

p. 32
all, is above the air – which it surrounds on all sides and touches the heaven of the moon.

The tiles [diamonds] that are painted on the cards signify Earth because just as Earth supports all heavy things, so tiles support the heavy things that one puts on them.

The clovers [clubs] which are painted on the cards represent Water, because clover is a grass that grows in wet environments and is nourished by Water.

The hearts which are painted on the cards represent Air, for our hearts cannot live without air.

The pikes [spades] which are painted on the cards represent Fire, because Fire is the most penetrating of the four elements just as pikes are the most penetrating instruments of war.

And each of these suit signs are

p. 33
also marked on thirteen of the fifty-two cards of the game. Namely:

 - The image of a King is painted on a card with each of the said suits (tiles, hearts, clovers or pikes).
- The image of a Queen is painted on another card with each of the four suits.
- The image of a Jack is painted on another card with each of the four suits.

It follows that there are as many times kings, queens and jacks in a single deck of cards as there are of Elements in Nature – four Kings, four Queens and four Jacks.

For each of these four emblems [suit-signs] there are a further ten cards. These other cards do not have a human figure on them, but only as many of the emblems [tiles, hearts, clovers, pikes] to signify as many un-

p. 34
its as there are emblems on the card.

The number does not pass ten.

I believe with good reason that this is because the number ten has admirable properties, principally touching the consonances of music proceeding from the numbers of which it is composed: being one, two, three and four which added all together equal ten.

To which it should be noted that:
- between one and two there is a Diapason (as has been explained above), and also between two and four
- between two and three there is a Diapente
- between three and four there is a Diatessaron
- between one and three there is a Diapason Diapente
- between one and four, there is twice the Diapason.

By this is clear that the main consonances of Pythagorean Music and

p. 35
Diatonics are included in the count of ten.

Therefore, it is not without great reason that no card in this game contains more than ten – similarly each painted image with its emblem is ten precisely [i.e. each court figure counts as ten in the game of 31].

And in this regard, you should know that by the number of the cards the ancients heard the degrees of the qualities of each Element.

Which numbers, the player of this game [Thirty-One], seeks the highest score he can, in order to reach, but without exceeding, the number 31. Or at least to get closer to the number 31 than any other player, for the one who gains 31 points or comes closest to it claims victory and the gains of said game of cards.

[See Note 1: the value of the Courts is Ten and that of the number cards, the number of emblems painted on the card: 1,2,3,4,5,6,7,8,9,10.]

Now if we want to know why the ancients made

p. 36
thirty-one the victorious number in this game, rather than any other number such as twenty-eight, which is a perfect number, or thirty, which is the number of degrees of a celestial sign, or in some other number, greater or smaller, it should be considered that the number thirty-one is the sum of the first five numbers in double Geometric proportion, that is, one, two, four, eight and sixteen [1+2+4+8+16=31].

In this geometric progression of numbers there is a great and admirable harmony, because just as there are certain temperaments between the qualities of the four Elements in all natural things, there exists between the numbers of thirty-one great harmony, containing the

p. 37
the Diapason four times:

- between one and two, a Diapason;
- between two and four, another Diapason;
- between four and eight, yet another Diapason;
- and between eight and sixteen, another Diapason.

Thus, it is clear that there are as many diapasons as there are Elements in Nature.

Further, it should be considered that the diapason includes in fact all the simple musical consonances, which are the Diapante, Diatesseron, Tierces and Sextes. Similarly, by adding diapasons together, one above the other, the result is always a perfect consonance – which does not happen in other consonances of music.

And as we said previously, the four elements, in the composition of all natural

p. 38
things, maintain between them this great harmony, or else approach very closely to it.

Someone might object and say that, if true, all natural things should have the best qualities and same temperaments because the four elements would maintain the same harmonies in all natural things. To which we make the following response.

For the four elements in the composition of all natural things to maintain this great harmony or approach this consonance, it is not necessary that all natural things are of the same temperament and complexion, because in each of the natural things, the same element does not dominate over the other three elements.

In one natural thing, one element has

p. 39
the advantage over the other three elements, while in another natural thing, of varying quality, another element is dominant over the other three. Nevertheless, the qualities of the four elements are so proportionate and have such harmony together, that they accord in the generation and composition of every natural thing.

And when this harmony is corrupted in any natural thing, it perishes and ends.

The differences of temperament and complexions of the variety of natural things, is represented by differences of the emblems of the cards that signify the four elements.

Therefore, it sometimes happens that one of those who plays, wins and acquires a certain harmony of numbers in which there are more

p. 40
Tiles [Diamonds], which signify earth. than any other of the four suits, by which is indicated that there is more earth in the natural thing represented by them than of any other element.

Another time a player may acquire a harmony of numbers in which the greater part of the numbers is represented by Clovers [Clubs] – signifying Water, whereby this harmony of number shows there is more water in the thing represented. And thus must be judged all the other differences which will be in each harmony and the proportions which underlie them. These differences are numerous, as with all natural things and diverse species of the world.

These are the main meanings of the ancient game of cards, which well deserves to be.