In this chapter, I ask the question of whether theproportional relationships so integral to theRenaissance and to Praetorius's teachings can beapplied to the triple and compound metersconstructed later in the Baroque era, such etc.Coupling both treatise evidence with themathematical logic inherent in the fractional signs,I propose here that each time signature wasunderstood as related to another in a network ofmeters, called the “terraced tempo system” in thisstudy. This system is presented as largely active inthe German Baroque. However, because of certainadditions and changes to the characteristics of cand ¢ late in the Baroque period, we finally see theutter disintegration of the proportional system.This chapter is therefore divided according to thefollowing points:

• 1. TEMPO RELATIONSHIPS BETWEEN THE TRIPLE ANDCOMPOUND METERS. Continuing the discussion begunin chapter 1, we will see which triple meters wereslow and which were faster.

• 2. PROPORTIONAL RELATIONSHIPS. By extrapolatingon early seventeenth-century theory of proportionand placing this alongside later teachings onmetric equivalencies, a model can be created thatallows for each time signature to have its own setof proportional meters.

• 3. PROPORTIONAL RELATIONSHIPS AT THE END OF THEBAROQUE. Certain elements related to the smallallabreve and ccreated changes in the Baroque proportional systemso that each signature no longer had its fullcohort of proportional meters, as it used to. Thiscreated gaps in the proportional system, signalingthat it was no longer fully in use.

Performer's Corner

Figure 3.4 further below in this chapter contains ashort-cut of sorts, showing which time signaturesare strictly proportional to each other in a measure= measure relationship, and which are related by theratio 1.5:1. In this case, the measures of allsignatures in each column have the same duration,while all the signatures in each successive columnare approximately 1.5 times (not two times!) fasterthan the previous. This provides valuable data forinterpreting the vast numbers of meter changes inthe repertoire approached in parts 2 and 3.

Figure 3.4, however, does not explain the changes theproportional system incurred at the end of theBaroque era: these are reflected in yet anotherchart in figure 3.8, which shows how some meters nolonger had a complete set of proportionalmeters.