first off, i tried to search a good zanpaktou thread but couldn't find none, and also i don't know if any of yous ever thought this about Zanpaktous and their relation to heavenly guardians and Five elements which define their classes.
-First off we got Hitsugaya Toushirou, and we know from the anime that his soulslayer is a water-ice type and the incarnation of one of the heavenly guardian, from the look it, it looks like a dragon and we could tell that it is Seiryu, a blue green dragon, God of the East and Water
-Second we got the Soukyoukou, when released take the form of a phoenix which probably is Suzaku, God of the south and fire.(ps: i was gonna put captain yamamoto's because his soul slayer is a fire-type but the soukyoukou looked like the phoenix so i went with it)
-Third we got Genbu, black land turtle alternatively combined with a snake(has a snake head), God of the North and earth.
-Fourth we got Byakko, White tiger, God of the West and wind.
Now according to Japanese philosophy, the five elements are: Chi(earth), sui(water), Ka(fire), Fu(wind), Ku(void). Miyamoto Musashi's famous text Gorin no sho (The Book of Five Rings), in which he explains different aspects of swordsmanship by assigning each aspect to one of these elements.
Id say that Zangetsu belongs to Ku(void). In Japanese phylosophie Kū, is the highest of all the elements,and is most often translated as "Void", but also meaning "Sky" or "Heaven", represents those things beyond our everyday experience, particularly those things composed of pure energy. Ichigo shoots strong energy with his sword and that technique is getsu gatenshou which is moon sky fang charge or charge toward the sky or charge toward the heaven.when he switches to bankai zangetsu shoots a black(usually the color of void) getsuga.
Even in western philosophy the five elements are Earth, water, fire,Air and Aether. Aether means void and it is at the center of these five elements in western philosophy. Aristotle included it as a fifth element on the principle that nature abhorred a vacuum. Aether was also called quintessence(fifth element).
Now i can't say that zangetsu has any relationship with the Genbu one of the four heavenly creatures, even though it is a black turtle with a snake head and gen means black. But in japanese Budhism philosophy Genbu's counterpart is known as Tamonten, the most popular and powerful of the Shitenno (the Four Buddhist Protectors of the Four Directions). Tamonten is also known as the Black Warrior and is also called Bishamonten; like the tortoise, his imagery corresponds to north, winter, and black.
In Japanese Buddhism, the Four Guardian Gods (Jp. 四天王 shitennō), also known as the Four Kings of Heaven, are deities who protect the Dharma. They are known as the Lokapalas (Sanskrit "world-protectors"), a set of four Hindu (Vedic) deities adopted by Buddhism:
Jikokuten (持國天, also 治國天), protector of the east
Zojoten (増長天), protector of the south
Komokuten (廣目天), protector of the west
Tamonten (多聞天, also known as Bishamon or 毘沙門, protector of the north(genbu's counterpart in japanese budhism) and ruler of the yakshas)