The Eloquent Body: Dance and Humanist Culture in Fifteenth-Century Italy

Appendix 2. The Use of Mensuration Signs as Proportion Signs in the Dance Treatises

Appendix 2. The Use of Mensuration Signs as Proportion Signs in the Dance Treatises In explaining how Domenico uses mensuration symbols and proportion signs, I rely on three assumptions. The first of these is breve equivalence.1 The second assumption is that factors of two are not notated, which is consistent with the recorded music. For example, the assumption that one breve (or bar) of has to equal two breves (or bars) of is confirmed when the music and choreography are put together, as X tempi of quaternaria misura always coincides with 2X breves’ worth of music. The third assumption is that Domenico’s description of the proportions is concerned with what is happening at the minima level. Domenico’s concern is a practical response to the demands of the dancer, since the three movements of a doppio step occur on minima beats. In the theoretical section of his treatise Domenico often reminds the reader that bassadanza misura is the basis of the other three misure, whose speeds are derived from it. The appellation given to bassadanza misura, that is, major imperfect or , must therefore be the reference point for the other proportions. Domenico then says that saltarello misura is major perfect, or . When the sign for major perfect, , is used as a proportion sign after the mensuration of , the proportion of 2:3 (or sesquialtera) is produced (assuming breve equivalence), as is shown in figure 8. The ratio of 2:3 between bassadanza and saltarello is the same ratio that results from the description of saltarello misura as two-sixths faster than bassadanza misura. Elsewhere the ratio of bassadanza to piva is given as 1:2 (or proportio dupla). Domenico gives the sign of minor perfect, , to piva, but the ratio of to does not give the ratio of 1:2. It is at this point I must assume that Domenico did not notate factors of two. This does not seem unreasonable, as exactly doubling or exactly halving the speed is the easiest proportion for musicians to perform. Support for this assumption, albeit indirect, is found in Bobby Wayne Cox’s article on the sign in another manuscript.2 Cox’s argument is well summarized by Eunice Schroeder, who emphasizes Cox’s point that “the original use of [was] as a convenient way of writing in the next higher level of note values in order to avoid flagged semiminims,” and “only incidentally does Appendix 2 159 Figure 8. Relationship between bassadanza and saltarello misure appear to mean twice as fast as .”3 The point of Cox’s argument is the scribes were not portraying proportio dupla by the sign , but simply wanted to avoid writing flagged semiminima. Thus, if in one manuscript practice it was not considered especially important to notate proportio dupla, then it is easier to assume it was not so important in other manuscript practices as well. This is the case, for instance, in the dance Rostiboli gioioso in the ballo repertory. The notes for the first three musical sections of this dance are all semibreves , but for the choreography to fit the music, they must all be played at the speed of minima. John Caldwell has also pointed out that it is unnecessary to account for factors of two; since “major prolation in the fifteenth century normally implied augmentation, it is actually unnecessary to assume diminution of the minor perfect mensuration [ ] here.”4 Therefore, if one assumes that factors of two were not notated, one breve of is equal to two breves of (as is shown in figure 9) and proportio dupla is achieved on the minima level. Thus the relationship is between and . Figure 9. Relationship between bassadanza and piva misure 160 Appendix 2 Figure 10. Relationship between bassadanza and quaternaria misure Domenico describes the relationship between bassadanza and quaternaria misura as to . The ratio of to , however, causes the music to slow down, not speed up, as four minima are played in the time of six. But Domenico is quite definite that quaternaria is faster than bassadanza misura, and so one has to assume that one breve of is equal to two breves of ; that is, a stroke is missing from the sign (see figure 10). Once allowance has been made for this factor of two, then the bassadanza to quaternaria ratio on the minima level is 6:8 or 3:4, another one of the commonly used proportions...