The subject of tempo — the basic pace at which a piece of music is rendered — has long been at the heart of debates on interpretation in Western music. Choices of tempo have been fundamental to the role of the orchestral conductor, and those choices have only been accentuated by the emergence of historical performance styles. Especially in their infancy, tempi were the very touchstone of HIP Beethoven performances, and are apparently still an obligatory discussion topic in any review. When considering the subject, it may be helpful to divide tempo into two aspects: "relative" & "absolute" tempo, mirroring the same terms applied to pitch. In this way, we can describe a relative tempo as one section of music being twice as fast as another, etc. This is obviously directly related to rhythm per se, but operates on a larger scale. It is similar to the idea of note values and so directly affects the "geometric structure" of the music and the way it fits together. In this sense, returning to the pitch analogy, relative tempi are akin to interval relationships. An absolute tempo is a precise speed, presumably by metronome or other reference, and does not affect the internal geometry of the piece so much as its absolute "size" or length.
The latter remark on absolute tempo understates the complexity of the issue. Although the issue of transposing pitch is more complicated because of physical breaks in instrument ranges & timbres, the issue of "transposing" tempo is basically similar. It would be difficult to make an argument that a small percentage change in tempo, one way or the other, makes an important difference in the musical essence of a piece, provided the relative relationships are identical. However, just as in pitch, there are underlying facts of physiology which make larger differences in tempo able to cause a musical utterance to be perceived differently. Exactly what "larger" entails is a more difficult question, and we will be content to leave a rather large gray area on that matter. One thing is certain, namely that the human body has its own natural pace, varying somewhat between individuals, and that as tempi fall differently within those parameters, they are perceived differently. This is clearly the motivation for the early vague tempo indicators of "happy" or "walking" or "slow" or "fast" as these are natural human terms. The same orientation is found in the slow, medium, fast tempo indications of Indian classical music and elsewhere.
Issues regarding relative tempi are likewise stated baldly in the opening, when in fact their structural role is rather more contentious. The basic premise is that, in general, precise tempo relationships are as structurally significant as precise note value relationships. In other words, they are often very important and often not particularly important, depending on the style and function of the music, as well as their position within the same piece. That is to say that rubato is indeed often appropriate in Romantic music, as are ritardandi in some specific sections of Baroque music, etc. To take the other extreme, in a series of divisions, if one section is to be played twice as fast, it needs to be precisely twice as fast, or one will end up with rhythmic slop in the end. As opposed to pitch relationships, these tempi are not heard simultaneously, so there is an implication here that the mind & body can remember or internalize them. What we call this is keeping the "pulse" of the music, and anyone with a good sense of rhythm can do it easily enough. Because music training prioritizes pitch, not without reason, even some professional musicians do not have a good sense of rhythm, unfortunately. Actually, tempi can be heard "simultaneously" sometimes, as for instance a minim pulse can shift to the crotchet after both have been established, etc.
Regarding the Beethoven metronome markings, one basic question is whether they are truly intended as absolute tempi or rather as a convenient means by which to precisely indicate a number of relative tempi. I am not equipped to discuss that question further, but it illustrates the distinction. I am mostly interested in music where precise relationships are important, and so must remark first of all that without a consistent pulse against which it is set, something like a sequence of two minims & a crotchet does not have enough context to establish a real rhythmic contour. I think this is clear. Tempo in the white mensural system itself is all about relative values, and so the next basic contention is that with few exceptions these are important and precise. I claim that one major failing of many conspicuous Franco-Flemish polyphony performances is not holding pulse or "tactus" across tempo markings. Complaints by Josquin and others not only agree, but indicate that the failing is historical as well, due in part to the basic difficulty of the music. Ideas on precision in rhythm & tempo are also important in Indian classical music, for instance, and especially in older styles such as dhrupad, where a precise poetic rhythm is part of what is called a "literal rendering" of verse. When it comes to older Western styles, and especially pre-mensural music (and even, in my opinion, many styles of early mensural music), a more flexible rhythm is often more appropriate. This puts even more stress on keeping a pulse, although it makes it easier to do so while deemphasizing tempo shifts per se.
The more complicated example of mensuration in Ockeghem & Josquin presents the challenge of unifying a freedom of line with an important structural pulse. One might suggest a more straightforward modern parallel in the ineffable quality of "swing." Together with ornament, this is perhaps the cornerstone of musical interpretation as such, and proceeds next to questions of articulation. To put it quite simply, to properly articulate a musical line, one must deviate slightly from the stated note values while maintaining the pulse and structural rhythms. In many cases, the note values are only a guide to the real rhythm of articulation which is rather more detailed than the notation system allows. Needless to say, one must understand which is which. One crutch for this has been the bar line, so that one always returns precisely on the main beat, but can deviate slightly to articulate off beat. This is clear enough. However, for earlier music without these specific rhythmic implications in bar line form, the idea of a regular beat is often simply wrong. The interaction is more complicated and must be approached as such, in order to preserve continuity over longer spans while retaining the structural role of relative tempo. This statement cannot be emphasized strongly enough.
The last major point concerns the articulation of pulse itself. It need not follow the mechanical precision of a metronome, although that is a safe way to get something decent. As discussed previously, Chinese literary music is one area where pulse is given a sophisticated and individual treatment. However, the main point here is that it has to be a pulse, a sensible physiological pulse. It can vary somewhat, but it takes a real master to carry off anything but a single steady rate of change. It is possible to achieve a special resonance with the music by letting the activity carry the pulse one way or the other. In the case of Franco-Flemish polyphony, no one has achieved anything like this, and of course to even attempt it, one should demonstrate the ability to render the entire piece strictly, including slurs and articulation as discussed. Although the structural role of relative tempo and continuity in pulse across changes is important and often overlooked, there are certainly full stops over which no precise continuity is implied. At this point, absolute tempo concerns come back into play, and so one must choose suitably in order to allow precise tempo shifts without straining the credibility of the absolute value. In this sense, tempo becomes a direct extension of rhythm.
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