The standard joke amongst heralds is that heralds do not pun--they cant. In essence, to cant arms is to make a visual play-on-words (or pun) on someone's name or title by use of heraldic charges. Canting is a strict form of allusive arms, known as Armes Parlantes. Armes Parlantes refers to alluding to one's name, title, office, or estate via one's armorial bearings. There are many examples of this in period--although many of the cants are lost on us since we do not have the proper medieval context. What follows are some canted arms from period and from the SCA as examples of how canting has been done.
Sir Robert de Setvans (formerly Septvans)'s funerary brass (c.1307) displays on his surcoat, shield, and ailettes (collectively) seven winnowing fans.
Sir Roger de Trumpington, (c.1289) Azure, crusilly and two trumpets palewise Or.
Thomas Corbet of Caus (d. 1274) Or, two Corbies sable.
Odinel Heron: Azure, three herons Argent.
John Cammel of Queen Camel in Somerset's(1418): Azure a camel passant argent.
William Shakespeare: Or, on a bend sable a spear Or.
Hasely of Suffolk bore Argent, a fess gules between three hazel nuts Or.
Cockerell, of London bore: Or, a cross between four cocks gules.
A plethora of period armory contains varieties of fish as plays on surnames. For example, a pike or luce (the fish) can be found in the arms of Lucy, Lucas, and Pyke. A word of caution, though, many of these names and fish are somewhat obscure to the modern vocabulary, and it is quite obvious that the many of the blazons are contrived--at a distance, a fish is just a fish.
From the reign of Henry III, we find the Count of Tierstein's arms contain a hind (a female deer--also known as a tier), and Nicholas de Kennet had three dogs on his armory--a kennet being a type of dog.
The arms of Sir Thomas Harris of Shropshire consist of Or, three herrisons azure, (herrisons being another name for hedgehog) and his crest is a golden hedgehog.
De Ferres: Argent, six horseshoes sable. Horseshoes are made of iron, ferrum, in Latin.
As noted above, some of the fish cants on names are a bit obscure: sole for Desoles, roaches (a type of carp, not the insect!) for Roche, garvin fishes a small Atlantic fish for Garvie, etc.
Many arms contain references to the armiger's station, occupation, estate, or some other item of note about that person. Classic examples abound in ecclesiastic armory. As St. Peter is the keeper of the gate to Heaven, many church officials alluded to this relationship by having keys or regalia of their office on their personal armory. Cardinals and bishops are well-known for this type of armory.
Many people choose symbols that are considered characteristic of themselves (although the Victorian heralds attempted to codify the characteristics of many charges, this is a fruitless exercise). Lions were quite popular because the King of Beasts was known for ferocity, bravery, and strength. Key events in a person's life can be summarized with symbols--the obvious examples being the saints and martyrs: St. Sebastian's arrows, St. Andrew's cross, St. Catherine's wheel, etc.
Catherine Carnimirie von Westphalia: Per fess azure and vert, on a cross Or a Catherine's wheel sable.
Corwyn Wodewarde: Or, a bend sinister between a legless corbie close sable and a wodehouse statant affronty proper, within a bordure sable. Corbie/Corwyn and a wodehouse is now referred to as a "wildman".
Eldred Ælfwald: Argent, semy of pine trees vert, a mug gules foamed Or. "Aled red, Ale wald" This is an example of a very contrived cant, but it still works because it is close to how the name is supposed to be pronounced.
Logan Blackwoulfe: Quarterly gules and argent, a wolf rampant reguardant sable between four crescents in saltire counterchanged, a bordure embattled sable. A black wolf.
Matsudaira Kentarou Toshiyori: (Fieldless) A fan conjoined in pale with another inverted argent, each charged with a Japanese pine tree that in base inverted purpure. Matsu is Japanese for pine tree.
Dragon-related cants are rather popular in the SCA:
Alrekr der Drache: Per pale argent and sable, a double headed wyvern displayed, a bordure rayonny counterchanged.
Basil der Drache: Azure, a pall inverted between two basil leaves and a dragon segreant, a bordure argent.
Drachenwald, Kingdom of: Or, three pine trees gules, overall a dragon passant, all within a laurel wreath sable.
Bruce Draconarius of Mistholme: Azure, on a chief embattled argent a dragon couchant azure winged sable.
Nottinghill Coill: Or, a wake knot issuant by its base ends from a mount vert, overall a laurel wreath counterchanged. This one is pretty obvious. The mount is a type of hill, and the wake knot is a double cant for "Notting-" and "Coill". "Coill" is Gaelic for forest or wood.
Apart from Officers' badges, allusive arms are somewhat rare in the SCA, but I do know of a few that immediately spring to mind:
Windmasters' Hill, Barony of: Per chevron azure and vert, in chief twin aeoli addorsed and conjoined at the nape, and in base a winged cat passant extended with wings elevated and addorsed, all argent, the whole environed of a laurel wreath Or. This is a good example of both a cant and allusive arms. The two aeoli (the winds) and the per-chevron field division provide the cant. The winged cat is allusive to Kitty Hawk--the site of the Wright Brothers' first flight.
Eldred Ælfwald: Azure, three wheels, on a chief argent a dragon statant azure. Eldred received his AoA for providing transportation between an event site and parking area.
Elspeth Hinds: Per bend dovetailed argent and azure, a hind's head and a unicorn's head counterchanged. The dovetailed field division is allusive to Elspeth's father's occupation of carpenter. The hind's head, of course, is a cant.
Hannah Cameron: Argent, a fox rampant gules maintaining a torch proper and on a chief vert three garbs Or. Garbs are sheaves of wheat, and the whole of Hannah's armory is a Biblical reference.
Jaelle of Armida: (Fieldless) A snail guardant contourny argent. Jaelle's retirement title from being the Triton Principal Herald is "Argent Snail Herald".
As with puns, the more subtle a cant is, the better. Some cants are obviously quite contrived and lose their effectiveness.
While canting is a sound, medieval practice, the use of several pictures as a rebus for a long name or phrase usually leads to poor design practice because of the diversity of charges. There are a very few, rare, good examples of someone "who got away with it," but in the end, a good design is worth much more than a bad pun. (example: Azure, semy of conches argent, a bar between ten deer Or (a "Semi-conscious Bartender)
Another thing to watch out for is whether or not the armory ends up being offensive. Some of the borderline ones that have been registered include:
Artorius Conchobhar: Per bend sinister potenty vert and argent, and gules, a dunghill cock rising, wings addorsed within a bordure wavy Or.
Kathleen Erin-go-burne-the-Bragh: Vert, a chalice argent containing flames Or. This one is becoming more obscure, but it was funny when it was registered in the early 1970's.
A quick and obvious way to cant your arms is look for elements of your name that are also used as heraldic charges and/or tinctures. If your name contains an occupational byname, the tools of the trade can readily be used as charges on your armory. Likewise, if you have a name that relates to an animal, then the animal can be used. Allusive arms are more elusive J . With a bit of work, you can probably find something that will appeal to you and symbolize your best characteristics.
Don't forget that line treatments and field divisions can be used to devise or assist making a cant or allusive arms--see Windmaster's Hill and Elspeth Hinds' armory for examples.
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Brooke-Little, J.P. An Heraldic Alphabet. London: Robson Books, Ltd. 1996. ISBN: 1-86105-077-1
Fox-Davies, A. C. A Guide to Heraldry. England: Bonanza Books. 1969. ISBN: 0 517 46893X
Friar, Stephen, and John Ferguson. Basic Heraldry. New York: W. Norton & Company. 1993. ISBN: 0-393-03463-1
Grant, Francis J., ed. A Manual of Heraldry. Edinburgh: John Grant Booksellers, Ltd. 1948. Neubecker, Ottfried. Heraldry: Sources, Symbols, and Meaning. London: Tiger Books International. 1997. ISBN: 1-85501-908-6
Woodcock, Thomas, and John Martin Robinson. The Oxford Guide to Heraldry. Oxford: Oxford University Press. 1988. ISBN: 0-19-211658-4