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I compiled all comments, and answered your comments: Are you wanting too much? There has never been the one optimal obligatory clearly superior solution for church architecture. Each general plan has advantages and disadvantages, besides being subject to custom and tech or $$ limits.
The church must be structurally sound, and with no modern ways to calculate stuff, they had to be conservative - extra support, wider walls, etc, especially when they wanted to go bigger, better, more amazing.
It also has to inspire, to help to elevate the heart, generally, to show an image of heaven. These two always go together. The selling spin of an architect may be a really useful idea for a preacher, and vice versa. Even the original Roman basilica basic plan is described by Vitruvius as an image of “Order, grandeur and harmony”. It was an image of the State suitable for a civic building, but isn’t this also a valid image of heaven? At least they had to make do with it, because the other common building plan, the pagan temple, was not suitable for christian worship.
The cross-shaped church with transepts was/is an option. Among others. Not different from any architectural endeavor, where the architect has to balance requisites and limitations with taste and preferences from his clients and from himself.
You could put a big tower over the crossing, but most (continental) gothic churches have tower(s) in the west facade.
Towers involve big $$, customs… Hard to see a pattern. Probably it depends more on $$ and purpose: bells? Watchtowers? Desire to embellish more the façade to be seen from the square, or to be seen from a distance?
The transept faces can hold nice big round windows, but that alone does not seem so important to me.
Transept can also include doors, easing faster/safer entrance/exit. Separate doors + elaborated portals + big window + separate portion of roof = more opportunity to beauty here… But, yes, it is ONE solution among various...
The transept makes the church cross-shaped, which is of course symbolically nice. However, the cross is really only visible in the bird's eye view or on a plan, while on the ground it is less clear and often obscured by the buttresses, extra chapels, a cloister etc. So it's not clear to me that this is really that important.
Com’on, even a child looks at a cross shaped church and understands the shape. From inside AND from outside. Even more when the shape is relatively simple, with no overtly elaborated external supports or arcboutants.
It makes the separation of the choir form the nave more obvious. On the other hand, transeptless churches also manage to clearly delineate choir and sanctuary without problem. And of course, conceptually, one first defines the choir (I'd suppose), and then the placement of transept and chapels follows.
Again, cross-shape is ONE solution among many. But lateral chapels are important. There were many more priests than needed for public masses. AND, many unemployed priests. Those could make a living by being paid to say private masses. To pray for the dead of some family, etc, or to the dead buried at the same chapels. Also, in peregrination churches, a group of peregrines with a priest could use a lateral chapel. More ordinarily, a traveling priest could arrive and ask to say mass at unusual times. Or, in big priestly meetings, every priest would need to say mass, and concelebration was nonexistent or very rare. With many lateral altars, all of these issues have trivial solutions.
Lateral chapels and altars may have been an important basic project requisite, don't subestimate them.
The transept will in principle stabilize the long walls of the nave...
Again, cross-shape is ONE option to help stability, not the only one. And remember that gothic arcboutants, etc, were not available before the gothic era.
However, the transept and crossing tend to clutter the interior, which is much cleaner without. Then, the transepts seem to create a lot of essentially dead space where you don't see much of the mass. Many churches have some side altars there, but at least in the churches I've visited, it often seems like they don't really now what to do with the transept areas (one of them may be the main entrance).
the comment about lateral chapels is valid for side altars too. And, is dead space bad? Yes. But a little bit… It is not so bad. When you go to the mass everyday, or even every week, if one day you get behind the columns and are blind, it is not a big deal. I have done this many many times. And the older rite had even less visible parts than today’s. Moreover, I do not think zero dead space is achievable with more than one nave.
Generally, there does not seem to be a standard use for the transept AFAIK, as opposed to nave for laypeople and choir for clergy. In the comments, Luiz indicated that there would be groups of worshippers which require separate seating, so maybe these spaces are not that useless - but is that common?
I gave as examples pupils, nuns, or sick people, which do not apply to usual parochial churches. And, in some place/times during the middle ages, man and women seated separately. Then, transepts again would be ONE solution, among many.
Can’t people just follow taste or preferences, or choose one solution for no really super-intelligent reason, just because of habit, or because uncle bob’s village had a beautiful church like that?
Let's look at other options (the Roman Basilica I have already covered):
A greek cross is a much more perfect image of Ap 7: the angels from the 4 corners of the earth; the host before the lamb - it is an image of people from all directions coming to the altar of the Lamb, an image of heaven and/or of the universality of the church. This imagery is still present but less obviously in a cross-shaped church with transepts. The Gent Altarpiece has a good visual representation
And greek crosses were not as common in the West as in the East. A circular shaped church, such as the Templar churches… It still has some of the Ap 7 imagery, but it emphasizes an idea of community, of all equal brothers around the altar. Convenient for a small church for a military order. But less important for a normal church, besides the architectural difficulties to scale - who wants circular domes everywhere? Yet there are some circular churches.
Gothic: it did not fully abandon the Basilica theme, but emphasized another layer --> sursum corda, look above: verticality, lightness, and light. A cross shape would be still pretty much valid.
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An answer from French Wikipedia (perhaps not very different from what has already mentioned in the comments and the answer by @Luiz):
Outre le côté symbolique de la croix latine, le transept tient aussi un rôle technique de premier ordre en participant à la solidité de l'édifice, à la manière de deux arcs-boutants géants. Il augmente également l'espace intérieur de l'église et joue son rôle ordinaire de lieu de passage marquant la séparation liturgique entre le chœur des religieux à l'est et la nef des fidèles à l'ouest. Enfin, en démultipliant le nombre et la surface des murs, il permet, sans préjudice pour la stabilité de l'ensemble et grâce à ses fenêtres, d'apporter un éclairage latéral au sanctuaire ainsi que des portes supplémentaires qui régulent la circulation intérieure2.
In addition to the symbolic side of the Latin cross, the transept also plays a major technical role by contributing to the solidity of the building, like two giant flying buttresses. It also increases the interior space of the church and plays its ordinary role as a place of passage marking the liturgical separation between the choir of religious to the east and the nave of the faithful to the west. Finally, by increasing the number and surface area of the walls, it allows, without prejudice to the stability of the whole and thanks to its windows, to provide side lighting to the sanctuary as well as additional doors which regulate interior circulation.
The Answer in Italian Wikipedia is also of interest (as Italians also have some expertise in building Catholic Churches):
All'incrocio tra navata e transetto si trova spesso un elemento decorativo o strutturale, atto a sottolineare il ruolo architettonico svolto dallo stesso; non è raro, infatti, specie in età medievale, che l'altare maggiore si trovi proprio in tale corrispondenza. Esso può assumere le forme di una cupola (è il caso del Duomo di Milano), una torre (come nella Cattedrale di Salisbury) o di una guglia (come nella Cattedrale di Notre-Dame a Parigi).
L'orientamento della navata trasversale, cioè il transetto, è determinato da quello principale della navata centrale, che prevedeva originariamente la facciata a ovest e l'abside ad est, seguendo cioè il corso del sole. In questa configurazione, comune in Italia fino al XIII secolo, la chiesa veniva detta orientata.
Le potenzialità della struttura, che interrompe le serie strutturali della navata, generalmente articolate in cappelle laterali o navate minori illuminate da finestroni, vengono spesso sfruttate per favorire l'ingresso e l'uscita dei fedeli dall'edificio: ecco allora apparire, anche in corrispondenza del transetto, maestose facciate, spesso ricche di richiami ornamentali e architettonici alla facciata principale, e portali laterali, solitamente in corrispondenza delle singole navate in cui è suddivisa la navata trasversale.
At the intersection between the nave and the transept there is often a decorative or structural element, designed to underline the architectural role played by it; it is not uncommon, in fact, especially in the Middle Ages, for the main altar to be found precisely in this correspondence. It can take the form of a dome (as is the case of the Milan Cathedral), a tower (as in the Salisbury Cathedral) or a spire (as in the Notre-Dame Cathedral in Paris).
The orientation of the transverse nave, i.e. the transept, is determined by the main one of the central nave, which originally included the façade to the west and the apse to the east, i.e. following the course of the sun. In this configuration, common in Italy until the 13th century, the church was said to be oriented.
The potential of the structure, which interrupts the structural series of the nave, generally divided into side chapels or minor naves illuminated by large windows, is often exploited to facilitate the entry and exit of the faithful from the building: here it then appears, even in correspondence of the transept, majestic facades, often rich in ornamental and architectural references to the main facade, and lateral portals, usually in correspondence with the individual naves into which the transverse nave is divided.
Similarity to the Latin cross
The collection Le transept et ses espaces élevés dans l’église du Moyen Age (XIe-XVIe siècles). (The transept and its elevated spaces in the Middle Ages church (11th-16th centuries). Provides wealth of information on functional and esthetic role of the transept and, importantly, how these evolved over centuries. In particular, the introduction provides extended comment on the role of the cross-like shape (interestingly, term transept infiltrated French only in the XIX-th century - up to then the term was crux):
Au Moyen Âge, lorsqu’il s’agit de désigner cette partie de l’édifice, les exégètes de l’église emploient le plus sou- vent le mot « crux », de forte signification symbolique puisque les fidèles se voient ainsi rassemblés sous le signe du Christ crucifié, leur modèle. Lorsqu’elle est cruciforme, l’église reproduit plus exactement la forme du corps humain: le sanctuaire en est la tête, le transept les bras et les mains, la nef les membres inférieurs. Dans un édifice pensé en tant qu’équivalent matériel de l’Ecclesia spirituelle, rassemblant (physiquement et symboliquement) les fidèles, l’organisation des espaces correspond à celle de la société: le sanctuaire, soit l’emplacement de l’autel, est celui du clergé qui « prie, prêche, chante, et administre les choses saintes », tandis que la nef est réservée au peuple qui « écoute et qui prie ». L’utilisation du mot « crux » pour qualifier et désigner la structure architecturale souligne la valeur hautement symbolique de ce vaisseau pour les chrétiens, une structure qui apparaît dès le développement de la première architecture chrétienne au IVe siècle, à Saint-Pierre de Rome notam- ment mais également à Saint-Paul-hors-les-Murs. Soumise à une organisation longitudinale des espaces, l’église l’est aussi dans un rapport de latéralité: les hommes, « plus fermes dans la foi » et donc plus résistants aux assauts de la tentation, occupent la partie sud de l’édifice, la plus exposée, tandis que les femmes, plus faibles et moins résistantes aux tentations, doivent se tenir dans sa partie nord.
In the Middle Ages, when it came to designating this part of the building, church exegetes most often used winds the word “crux”, of strong symbolic meaning since the faithful see themselves gathered together under the sign of Christ crucified, their model. When it is cruciform, the church more exactly reproduces the shape of the human body: the sanctuary is the head, the transept the arms and hands, the nave the lower limbs. In a building designed as the material equivalent of the spiritual Ecclesia, bringing together (physically and symbolically) the faithful, the organization of spaces corresponds to that of society: the sanctuary, i.e. the location of the altar, is that of the clergy who “pray, preach, sing, and administer holy things", while the nave is reserved for the people who "listen and who pray.” The use of the word “crux” to qualify and designate the architectural structure underlines the highly symbolic value of this vessel for Christians, a structure which appears from the development of the first Christian architecture in the 4th century, at Saint-Pierre in Rome in particular ment but also in Saint-Paul-hors-les-Murs. Subject to a longitudinal organization of spaces, the church is also in a laterality relationship: men, “firmer in the faith” and therefore more resistant to the onslaught of temptation, occupy the southern part of the building, the most exposed, while the women, weaker and less resistant to temptations, must be held in its northern part.