Figure 1 attempts to illustrate the substance of ... eight points. The abscissa is to be understood as a rank scale of increasing "distance" from Ego, the ordinate then showing increasing suitability as sexual or marriage partner.
The concept "distance" in the graph can be interpreted in various ways, chiefly the following (see Murdock, 1949, p. 314 sq.) :
a) Kinship distance. The scale begins with first-degree relatives, i.e. members , of the nuclear family. Next come relatives of the second and third degree, followed by members of a "Lineage", i.e. those persons whose relationship to Ego is still just traceable, and finally, all such persons with whom Ego still feels himself (more or less mystically) related, without however being able to substantiate this feeling - so-called sibs or clans. The abscissa range further to the right represents all those persons not felt to be related.
b) Cultural distance. Grouped on the left are members of Ego’s own tribe or nation, with whom he identifies, also from a cultural point of view. There follow, within his own society, varying sub-cultures (e.g. social classes) and cultures (e.g. castes), and members of an alien nation and culture.
c) Geographical distance. The term "distance"; can also be taken literally. The scale then begins with members of Ego’s own community, "neighbours" in the strict and wider senses of the word, and extends to the right expressing increased geographical remoteness.
d) Physiognomical distance. This factor is not distinguished by Murdock, but is blended in with the other scales. The physiognomical scale would begin, on the left, with partners phenotypically more or less similar to Ego; there follow members first of related and then of alien race, until finally the borderline of the species is reached, beyond which non-human life begins.
The monotonously descending dash-dot curve in Figure 1 can be interpreted as a positively-shaded "we";-feeling, the amplitude of the curve over a given abscissa point indicating the strength of preference for the choice of an individual located at that point as marriage or sexual partner.
If this "endogamy gradient" - or, as Murdock has proposed, "gradient of ethnocentrism" - were alone effective, then indeed extreme incest among members of the nuclear family would be the favourite form of marriage. In fact, however, there is a second gradient plotted over the same scales, ascending monotonously from left to right; this we call, again after Murdock, the "exogamy gradient".
Supposing the two forces, symbolized by the two gradients, approximately multiply each other, then we obtain as product an inverted U-curve, showing the degree in which individuals are preferred as sexual or marriage partners. The left-hand descending portion of the curve is designated as endogamy taboo or incest taboo if applied primarily to marriage or to sexual intercourse, respectively. The descent of the curve towards the right represents the bestiality taboo at the latest, although here in certain cases narrower boundaries are drawn, e.g. class, caste or race barriers.
It is shown schematically in Figure 1 that the four scales of "distance" span, as a rule, different regions of the abscissa. The scale of "kinship distance", for example, always begins at the left, ascending flank of the preference curve - denoting the permanent existence of a particularly close degree of relationship with which sexual contact is forbidden. The "cultural distance"scale, on the other hand, usually commences at the point on the abscissa directly under the peak of the preference curve: i.e. maximum cultural "proximity" will as a rule define the most favoured spouse. But here too, there are occasional exceptions, for example the status-group exogamy of certain Indians, that is, the obligation of people of rank to choose a partner from a lower class (Murdock, 1949, p. 266).
Similarly, for the "physiognomical distance" one should at first proceed from the supposition that the typical features of one’s own race lie at the apex of the preference curve. It is not yet clear, however, what conditions obtain if the scale is extended still further to the left into the area of individual physiognomical similarity with Ego. Upon this differing reports have been made, in which for some features (e.g. the Kretschmer constitutional types) a certain preference is shown for contrasting partners. With the majority of features, nevertheless, there seems to be a preference for similarity. Geneticists speak of homogamy or assortative pairing (cf. Lerner, 1968, p. 261; Knussmann, 1965). We shall not pursue this issue further, as in any case no social rule concerning the left-hand termination of the physiognomical scale seems to exist.
Norbert Bischof (1972)