Since this was one of the principal "epiphanies" that led him to focus on the stylistic aspects of music, the testing of this hypothesis became one of the earliest goals of Cantometrics. Drawing upon the "Ethnographic Atlas," a database compiled by ethnologist George Murdock, containing, among other things, data pertaining to the role of women in a number of different societies, Lomax found correlations that did, indeed, appear to confirm his initial hypothesis. Of particular interest is a graph appearing on p. 167 of Folk Song Style and Culture, with "productive complementarity" as the horizontal axis, and mean percentage of polyphonic singing as the vertical. The graph progressively rises from left to right, indicating a growing tendency, worldwide, for polyphonic vocalizing as the participation of women in food producing activities, according to Murdock's ratings, increases (M and N indicate male domination for such tasks, D and E rough equality of males and females and F and G almost exclusively female participation):
Interestingly, there is hardly any difference between female polyphony (scored line) and polyphony generally (solid line), indicating that the differences between "men's songs" and "women's songs" (an issue that has received much attention over the last 25 years or so) may matter less than differences in the way women are treated in the society as a whole.
While many of the relationships Lomax found between song style and social structure remain, in my opinion, either problematic or difficult to assess, his correlations between male-female "complementarity" and aspects of song style such as polyphony, tonal blend and vocal tension have always seemed more convincing. While it's not clear whether such a correlation can be regarded as truly universal, it does seem to hold for large portions of both Africa and Europe.
Lomax's notion of complementarity seems quite close to Gimbutas' idea of the matristic -- a "balanced society" where women and men live and work together on a more or less equal basis. Lomax described this type of society as follows: "[W]here women take a leading recognized part in the central activity of a society, such as supplying the main source of food, they assume, at least in this respect, a complementary, or more or less equal, interactive relationship with men. . . People tend to sing in wide voices in societies where women are most secure in their productive and sexual roles and where, therefore, they are freest to relate fully to the males" (pp. 199-200).
While Lomax often writes as though he sees a cause and effect relationship between sexual and vocal tension, complementarity and polyphony, etc., he also associates polyphonic vocalizing and wide, relaxed voices with the same "Old Europe" that Gimbutas associated with the earlier, matristic societies that dominated all of Europe prior to the advent of the Indo-Europeans. Which raises a fascinating question: are we dealing with a rather Freudian situation, where tensions between men and women, sexual and otherwise, lead to the development of a particular musical style? -- or do the differences, both sexual and musical, reflect the contrast between two periods of human history, the early matristic, complementary, polyphonic culture of Africa and Old Europe vs. the later patriarchal, repressive, violent, monophonic culture of the Indo-Europeans?