In traditional societies, myth and ritual are two central components of religious practice. Although myth and ritual are commonly united as parts of religion, the exact relationship between them has been a matter of controversy among scholars. One of the approaches to this problem is "the myth and ritual, or myth-ritualist, theory", which holds that "myth does not stand by itself but is tied to ritual".

Ritual from myth
Leaving the sphere of historical religions, the ritual-from-myth approach often sees the relationship between myth and ritual as analogous to the relationship between science and technology. The pioneering anthropologist Edward Burnett Tylor is the classic exponent of this view. A ritual always presupposes a preexisting myth: in short, myth gives rise to ritual.

E. B. Tylor
Against the intuitive idea that ritual reenacts myth or tries to persuade mythical beings, many 19th century anthropologists argued the opposite position: that myth and religious doctrine result from ritual. This is known as the "primacy of ritual" hypothesis.

Myth from ritual (primacy of ritual)
This view was asserted for the first time by the bible scholar William Robertson Smith.

William Robertson Smith
In his essay "The Ritual View of Myth and the Mythic," Stanley Edgar Hyman makes an argument similar to Smith's:
"In Fiji [...] the physical peculiarities of an island with only one small patch of fertile soil are explained by a myth telling how Mberewalaki, a culture hero, flew into a passion at the misbehavior of the people of the island and hurled all the soil he was bringing them in a heap, instead of laying it out properly. Hocart points out that the myth is used aetiologically to explain the nature of the island, but did not originate in that attempt. The adventures of Mberewalaki originated, like all mythology, in ritual performance, and most of the lore of Hocart's Fijian informants consisted of such ritual myths. When they get interested in the topology of the island or are asked about it, Hocart argues, they do precisely what we would do, which is ransack their lore for an answer."
Here Hyman argues against the aetiological interpretation of myth, which says that myths originated from attempts to explain the origins (aetiologies) of natural phenomena. If true, the aetiological interpretation would make myth older than, or at least independent of, ritual--as E.B. Tylor believes it is. But Hyman argues that people use myth for aetiological purposes only after myth is already in place: in short, myths didn't originate as explanations of natural phenomena. Further, Hyman argues, myth originated from ritual performance. Thus, ritual came before myth, and myth depends on ritual for its existence until it gains an independent status as an aetiological story.

Stanley Edgar Hyman
The famous anthropologist Sir James George Frazer claimed that myth emerges out of ritual during the natural process of religious evolution. Many of his ideas were inspired by those of Robertson Smith.

James Frazer
The classicist Jane Ellen Harrison and the biblical scholar S. H. Hooke regarded myth as intimately connected to ritual. However, "against Smith," they "vigorously deny" that myth's main purpose is to justify a ritual by giving an account of how it first arose (e.g., justifying the Adonis worshipers' ritual mourning by attributing it to Adonis's mythical death)

Jane Ellen Harrison and S. H. Hooke
Not all students of mythology think ritual emerged from myth or myth emerged from ritual: some allow myths and rituals a greater degree of freedom from one another. Although myths and rituals often appear together, these scholars do not think every myth has or had a corresponding ritual or vice versa.

Myth and ritual as non-coextensive
The classicist Walter Burkert states that myths and rituals were originally independent.

Walter Burkert
Like William Smith, the anthropologist Bronislaw Malinowski argued that myths function as fictitious accounts of the origin of rituals, thereby providing a justification for those rituals: myth "gives rituals a hoary past and thereby sanctions them." In other words, not all myths are outgrowths of ritual, and not all rituals are outgrowths of myth.

Mircea Eliade
Mythography,
Religion and mythology,
Aitiology
People:
Walter Burkert