I would like to consider how tempo was written about in the XVI century and attempts to estimate the speed of the standard tempo that musicians thought of as unexceptional. The sources are more than somewhat ambiguous on this matter, so recourse is made to examining seventeenth-century sources, which are much more explicit. Analysis of the latter indicates that tempos in earlier music seem to have been rather slower than those felt appropriate by modern scholars and performers and gives a better perspective on what sixteenth century tempos might have been.
Fundamental to the question of tempo is how it was thought of by the musicians themselves. Sources from the late fifteenth to the eighteenth centuries usually related tempo to an up and down movement of the hand. The word ‘tactus’ applied to the tempo as governed by this motion as well as its indication by the time signature. Other words for tactus were measure, full stroke, mensura, compas, misura, battuta, Schlag, ictus, percussio and praescriptum. Tactus related only to tempo and not to rhythm. It included both up and down motions, a full cycle. The relationship between the tactus and the reciprocating hand movements was likened to that between the pulse and (their concept of) the reciprocating beats of the heart, called individually ‘diastole’ and ‘systole’ or ‘arsis’ and ‘thesis’. Neither up nor down hand movement was stressed more than the other; the sources are divided between those starting with an up motion and those starting with a down. The up and down motions were even (of equal duration) in common time and in triple time with three beats in each motion, or they were uneven in triple time with one motion twice the duration of the other.
It was usual in common time to notate the full time of a tactus with a semibreve Calla semibreve’ or ‘integer valor notarum). Alternatives were to notate it with a breve ‘alla breve’ or `proportio dupla’, also called ‘diminution’) or with a minim Calla minima’, also called ‘augmentation). The ‘alla breve’ notation was preferred when one wanted to avoid having to write too many short notes when the music was fast, or to impart an aura of learning. With these alternatives, the time duration of each hand motion, if equal, was fixed, and the differences were whether it was notated by one minim, semibreve or crotchet in common time (or three of these in triple time) in ‘alla semibreve’, ‘alla breve’ or ‘alla minima’ respectively. In triple time when the hand motions were of unequal duration, the quicker of the motions corresponded to one of these, the slower to two, and the total time of the tactus (both motions) was the same as when the motions were equal. There were time signature notations and fancy Latin names for each of these possibilities.
This was the simplest theoretical position, with one standard tactus for all notated music. It was followed when different voices in a polyphonic composition used different notation. It could also be followed in successive sections of a composition, but there were alternatives. One was that the notation and tempo remained constant, but the rate of hand movement could be doubled or halved. This created ambiguity in how the time signature related the notation to the hand movements. The other was that one could take the tactus somewhat faster than that which was considered to be the standard. A faster tactus for fast division was recommended by Luis Milán (1536), and this was mentioned by Mace (1676) as a common fault amongst most performers, including master musicians.