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Review: God Save the Double! Author(s): Mauro Lo Monaco and Sergio Vinciguerra Source: Dance Research: The Journal of the Society for Dance Research Vol. 24 No. 1 (Summer 2006) pp.

1 Review: God Save the Double! Author(s): Mauro Lo Monaco and Sergio Vinciguerra Source: Dance Research: The Journal of the Society for Dance Research Vol. 24 No. 1 (Summer 2006) pp Published by: Edinburgh University Press Stable URL: Accessed: 21/12/ :43 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use available at. JSTOR's Terms and Conditions of Use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the JSTOR archive only for your personal non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars researchers and students discover use and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR please contact support@jstor.org. Edinburgh University Press is collaborating with JSTOR to digitize preserve and extend access to Dance Research: The Journal of the Society for Dance Research.

2 God Save the Double! REPLY BY MAURO LO MONACO AND SERGIO VINCIGUERRA To the Author Thanks for your letter. Clear criticism always stimulates people to make their ideas clearer and to formulate them in a more comprehensible form. I have the feeling that the hypothesis according to which the term 'double step' takes its origin from the verb 'to double' is facing some opposition: not for the double in itself but for the possibility that the extension of this concept can be used also for explaining the origin and the way of performing the 'doppin sul pie\ None of us of course has direct experience of these steps and of the way of dancing in the fifteenth century Still we amateurs and scholars can propose hypotheses which are formulated by connecting both knowledge (of objective data related to the object of our research - in this case the 'doppin sul pie') and intuitions (unconscious connections). After we must gather elements as many as we can that fit and oppose the hypothesis and on this base we can elaborate a thesis. If we are lucky enough we can try to extract a rule or law and eventually we must check how much it fits with the objective data that generated the hypothesis. The simpler the law the wider is the context in which it works. The problem then is not to list all the possible solutions existing for a number of different situations but to state what is the underlying law that can resolve all of them. In this sense the variety of solutions you proposed for performing 2 and 3 'doppi in sul pie' and for 4 Contrapassi (assuming that this late term does not indicate a different way to name 3 'doppin sul pie' or 3 contrapassi) perplexes me. Moreover none of the solutions proposed for the Bassadanza can work in Quadernaria. Actually I find even more difficult to accept the continuous changing of accents. In your solution (1) the first doppio begins on the first count the second one on the fourth and the third one on the third count of the second measure of Bassadanza. The upbeat of the next step has to be shared with the last step of the sequence of 3 'doppin sul pie\ In the solution (2) the doubles begin on the first and fifth count of the first measure and on the third count of the second measure. These solutions are summarised in figure 1 where I used the same symbols you used in your formulas: 'upper case is used to indicate a full step of two counts;

3 GOD SAVE THE DOUBLE! 67 lower case for a shorter step of one count; and a point to mark the upbeat'. In the upper part of the picture you find a scheme showing two measures of Bassadanza with their division in imperfect time and major prolation consisting of minims. In the lower part two measures of Quadernaria that with the only exception of the ballo Jupiter are always divided into four semibreves or the equivalent. (I suggest to leave the discussion of this point for the future if you agree.) The columns below the notes show which step is performed during that note. Of course the brevis of Quadernaria is 1/6 shorter than that of Bassadanza. Bassadanza Q it tt /T\ /f\ /T\ /t\ in m in m sempio ;!_; i i i I ill doppio - ; L r l_jj"j ; j j j 2 d'sul pie(i) I L j r l+cj _! r I I i - I II I 3d'sulpie(1)- LJ jr j l+cj L r l+cj L I r! +-! 2 d'sul pie(2) - j I j r j I j c j I! r j I j j!! j 3d'sulpie(2). j I j r j I j c! I! r! I! c I I I r! I I 4 cotitrapas - j I j r j l+c j I j r j l+c I I j r j l+c j I I r I l+- 3 d'sul pie +r +c +r +c +r +c..i lo'o'o'o'o'o'o - e-l Quadernaria C ^^^tr^^ ^""^T^^ Going back to the beats and their relationship with the steps I wish to report Domenico's and Cornazano's words concerning the rhythm of Bassadanza and Quadernaria: Cornazano lor: Di Bassadanza ogni tempo si divide in quattro parti el vodo e una cioe elprimo moto surgente poi ciaschun degli trepassi che si f anno ne consuma uno quarto che viene a compire quatro... (every tempo of Bassadanza is divided in four parts...). Domenico 4v:... Advisandote che la quadernaria sonandola le sue bote del tenor e vannopiu equaleper distantia che quelle de la bassadanza (and playing Quadernaria please note that the beats of the tenor are at a more equal distance than those of Bassadanza). Translating it in modern notation we can consider Quadernaria as a 4/4 time with one beat at each minim and Bassadanza as a 6/4 time with the beats consisting of semibreve - minim - semibreve - minim. Both have four beats but those of Quadernaria 'are at a more equal distance than those of Bassadanza. In figure 2 you find our solution for performances of sempio doppio 2 and 3 'doppin sulpie' in Bassadanz and Quadernaria. The symbols used are those you suggest while the white notes indicate the position of the beats and the black the count without beat. Of course the dots in Quadernaria do not indicate any upbeat but prolongation of the last step.

4 68 MAURO LO MONACO AND SERGIO VINCIGUERRA Bassadanza ( tt tt /K /f\ /K /K iu iu Ui Ui sempio i L i! i ; ; j jj j j doppio - L : j r j L j! i 2 d'sul pie L r L r L j j 3 d'sul pie - L r L j r j L r j L j! V V i V VI 0 0 O 5 O 0 5 O O ' O Quadernaria C u n Looking at the picture it is relevant that all the steps maintain their position no cutting or overlapping of steps occur and according to Domenico all the steps sono in lopieno (correspond to a beat). Domenico 3r: Lui dice die dodice motti sono in Voperar de questa arte. De li quali ne cava nove naturalli e tri accedentalli. Li nove naturalli operati sono in lo pieno e li tri accindentalli operati sono in lo vuodo... dico vuodo il tacere dico pieno lo dire dico vuodo tra un tempo e Valtro dico pieno in nel tempo instanti. (He says that twelve movements are in this art... nine naturalli and three accidentali. The nine naturalli are performed upon a beat the three accidentalli upon upbeat....) There is a bulk of evidence suggesting that our hypothesis according to which the term 'doppio' takes its origin from the concept of 'doubling a passo sempio' and not from a step that is twice as long discloses a simple rule which can explain why: When the same rule is extended for a second or third doubling it generates sequences of 2 and 3 'doppin sulpie' with a mensural value of 1 + 1/2 and 2 measures respectively. Doubles in a sequence of two or three can maintain their value of one measure each when they are described with a regular change of foot but add only half a measure to the second and to the third double if they are described as 'on the same foot'. 'Doppi in sul pie" can be performed in Bassadanza as well as in Quadernaria without losing the relation between step and beat. The performance of these steps is very easy and natural. At least the authors find this rule convincing.

5 GOD SAVE THE DOUBLE! 69 REPLY BY DIANA CRUICKSHANK (Translator) I have always considered that the one clear distinction between the passo doppio in bassadanzand in quadernaria was the relative difference in the inherent and essential rhythm of the step-unit. In bassadanza the doppio has a long first step - equal to two of the six beats of the tempo a shorter second step - using the third beat only - and another (third) step taken on the fourth beat which has a pause after it. In practice this is filled by the lowering of the heels and the movimento which introduces the next doppio. In quadernaria these three steps are evened out - one on each beat of the first three - followed by a fourth beat which is often filled with other embellishment such as difrappamento or some other movement as requested in the various choreographies. One case worthy of mention occurs in La Fia Guielmina for two as described by Domenico where he indicates that the complete step comprises three sempi e due continentie the one - tempo though some will argue that this is a 'one-off' and not therefore applicable as a general statement since the step is not classified as a doppio. Although Wilson may feel 'short-changed' by this interpretation of the steps I feel equally uneasy in the face of this levelling out of the rhythm of the steps or the increased speed of his version of the doppio in quadernaria. That the step as it occurs in 'Iupiter' is described as presto might equally well be taken as descriptive of my truncated step with the cambiamento being performed on the same beat as the third step and in the case of three contrapassi the loss of the final or ninth step of the group. What makes this particularly attractive to me is that in bassadanza that very concluding step is permitted within the 1 V2 tempi thus leaving the dancer with the correct foot free for the next movement.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. On the Bound for a Pair of Consecutive Quartic Residues of a Prime Author(s): R. G. Bierstedt and W. H. Mills Source: Proceedings of the American Mathematical Society, Vol. 14, No. 4 (Aug., 1963), pp.