First, what I've been able to discern suggests that HIP tempos in Bach tend to be more historically defensible than slower mainstream ones. Below I suggest that certain tempos prevalent in HIP Bach ignore notational distinctions and are, as a result, less histo Second, while this article focuses on cases where the opposite pertains, I do not aim to be prescriptive. Historically dubious tempos may have more than enough artistic effectiveness to justify their use. I question only the idea that certain HIP choices are more historically grounded.

Part One: Time signatures and tempo
A number of scholars have argued recently that time signatures conveyed basic tempo information for Bach. Clearly, the musical world he grew up in used time signatures this way. George Houle concludes that 17^th century notational conventions 'required composers to use meter signs uniformly to indicate both metrical structures and tempos'. He notes that by the end of the century (when Bach was being trained), genres and Italian tempo words were conventionally used to modify or clarify the tempo implications of time signatures, but that signatures remained the primary indicators. As for 18th-c. German writers, a number of them, such as Sperling (1705), Mattheson (1712), Heinichen (1728) and Quantz (1752) explicitly mention links of time signatures with tempos. While such linkages were neither perfectly systematic nor uniformly observed, they are present in German sources from Bach's years as a composer.
Did Bach himself associate time signatures with tempos? At least two sources suggest as much. One is a 1738 thoroughbass manual in the hand of C. H. Thieme, a Bach student and choir member; the title page lists Bach as the author. Much of the book replicates the 1700 treatise, Die Musicalische Handleitung by F. E. Niedt, who appears to have studied in the late 1690s with Bach's older cousin Johann Nicolaus Bach. Niedt's approach to teaching bears certain broad parallels to what we know of Bach's own, leading a translator to speculate that 'it is possible that Part I is a record of the Bach family's teaching techniques'. One may question that notion, wonder about the extent of Bach's role in the 1738 manual, and doubt that a treatise by a minor predecessor captures the practices of Bach. Still, it is worth noting that in the chapter on tempo both Niedt and the 1738 manual discuss two time signatures (C and 2), and say explicitly that the signatures have differing implications for tempo. The books say nothing to suggest that these are the only such associations of tempo and time signature. Indeed, the laconic nature of the chapter makes clear that it is not meant to be exhaustive; so does Niedt's comment that he presupposes that the student will know about time, to which Bach (if it is he) adds 'because no one can give them knowledge of metre [Tact] all at once.'
What might Bach have said if he had expanded on this topic? A well-known treatise purports to tell us. Die Kunst des reinen Satzes in der Musik by J. P. Kirnberger, who studied with Bach from 1739 to 1741, details how time signatures convey information about tempo. Kirnberger claimed that in this book he sought 'to reduce the methods of the late Joh. Seb. Bach to principles, and to lay his teachings before the world to the best of my powers'. One may doubt the claim, and note that Kirnberger's principles are probably systematized beyond anything one would find in Bach's teaching or practice (which in some cases Kirnberger seems to contradict). But it is nonetheless reasonable to suspect that Bach taught Kirnberger at least some of these associations between time signature and tempo, or at least the general principle of such associations.
That Bach associated signatures with tempos seems, given the above evidence, more likely than otherwise. Bach is often said to have surpassed contemporary norms for notating ornamentation and articulation; if so, it would be characteristic of him to notate some instructions about tempo as well. Yet tempo words are not common in his scores. The implications of time signatures might explain why.
In 18^th-century sources such as Mattheson, Rameau, and Kirnberger we find another 17^th-century principle, which underlies the idea of time signatures implying tempo: that note values have intrinsic speeds. Quavers were, for example, by nature faster than crotchets. Thus - a point of significance to this paper - the signature 3/4 would have tempo implications similar to C, because its denominator is the same note value. The crotchet speed of both signatures would be roughly equivalent.
In 18^th century usage, tempo implications of time signatures could be modified by many other factors, such as Italian tempo words (discussed in Part Two, below), vocal texts, genre, and affect. Also, as Kirnberger, C. P. E. Bach, and others explain, unusually small prevailing notes - such as demisemiquavers in common time - tend to slow the tempo (an example is 'Komm, süsses Kreuz' from the St. Matthew Passion). Unusually large prevailing note values - as in a piece in 3/8 with no notes faster than quavers - tend to indicate a faster-than-usual tempo.
Performers may have good reasons for disregarding composers' tempo notations, of course; I argue only that such notations are more common in Bach than is sometimes believed. But if his time signatures did imply something about tempo, what tempos did they imply? Let us look at the most common of the signatures, C, whose tempo implications were central.

The tempo ordinario and historical performance
According to writers such as Penna (1684) and Brossard (1703), the tempo of a common-time movement with no modifying factors was called the tempo ordinario - the plain or ordinary tempo (also known in Germany as schlechte Tact, which Mattheson,for one, explicitly relates to the C signature). Handel appears to have used the term similarly, since some of his works, e.g., Messiah and op. 4/2, contain movements in C marked 'a tempo ordinario' as well as others marked Allegro, which are presumably faster. For Heinichen, too, Allegro clearly indicated a speed that was faster than ordinary.
Bach does not, in any surviving sources, use the term tempo ordinario. (He did sometimes use the term tempo giusto, as did Handel in some works.) But Bach's cousin and associate J. G. Walther, in his 1732 Musical Lexicon, for which Bach served as an agent, defines tempo ordinario in the terms given by Penna and Brossard. It refers to the signature C, in which all the notes are played in their 'natural and normal values.' Robert Marshall writes, 'There is no doubt about the relevance of the tempo ordinario to a proper historical understanding of tempo in Bach's music.'
Two sources close to Bach discuss the time signature C in other terms, but these are compatible with the tempo ordinario convention just discussed. Niedt says C is 'dignified' and contrasts it to the 'fast and lively' French signature, 2. The 1738 treatise changes the adjective to 'slow' (langsam); we don't know if the substitution is by Bach or Thieme, and 'slow' may be meant mainly to contrast with the high speed of the French signature. And Kirnberger distinguishes two kinds of common time. The 'great 4/4' is indicated with the adjective 'grave' and is notated by the ratio 4/4; it is of 'extremely weighty tempo and execution' and is 'emphatic.' It is used in church pieces and fugues in place of the (by the 1770s) outmoded 4/2 signature. But the far more common 'little 4/4' metre - which is notated with C - 'has a more lively tempo and a far lighter execution' than the great 4/4, yet 'is still somewhat emphatic.' Walther, Niedt, and Kirnberger, then, all ascribe tempo implications to the signature C, which in every case are more or less 'ordinary', explicitly so with Walther (as with Mattheson).
Are there arguments against Bach's ascribing such a tempo significance to C? One involves the signature ¢, which was often held to be an exception to the idea of intrinsic speeds. Sperling (in 1705) says that while 'many' treat ¢ as faster than C, many others ignore the distinction. His observation is not unique. Those who believe that Bach fell into Sperling's latter group note that in some Bach scores the two signatures are exchanged in some way. Sometimes a score with semiquavers will be marked C in one incarnation (the Sanctus of the B Minor Mass) and ¢ in another (the score and most parts of the 1724 Sanctus). And in some movements (again, in the 1724 Sanctus) certain parts or staves are marked C while other parts or staves have ¢.
Yet such inconsistencies do not necessarily imply that the two signatures meant the same thing to Bach. In some cases, inconsistencies may suggest that time signatures were an inexact way of conveying tempo, and that it was difficult to determine which signature to use in every case. Also, different members of an ensemble may have needed different promptings, as shown by Bach's frequent practice of notating tempo instructions only in certain parts. And Bach's decision might change according to his judgment of the moment (indeed, modern composers often change their views about the tempos of their own music). The Sanctus might have seemed fast enough to require ¢ in 1724, but seemed slightly less rapid in 1748. Some authors suggest that Bach's tempo in French overtures slowed over these decades, which may explain his tendency to move from ¢ to C in notating them. Thus Bach might sometimes have changed these signatures precisely because they had different implications for tempo.
Another factor is that of accuracy among copyists. Many instances exist of possible inaccuracy. For example, the duet 'Wir eilen mit schwachen' from BWV 78 seems to require a faster-than-ordinary tempo; yet most of the surviving parts, copied by Johann Andreas Kuhnau, are in C. (This is the signature found in modern editions.) But two parts by the composer himself sruvive, and they show ¢ - a signature that better suits the movement, it would seem. It is possible that Kuhnau's C was a careless error, which Bach did not bother to correct since he himself was conducting, and that when he began to copy parts he used the correct signature. In summary, inconsistencies do not, as is sometimes claimed, disprove the idea that C and ¢ had different tempo implications for Bach.
If a plain C or-by the principle of intrinsic speeds, 3/4-time signature with no modifying factors implies an 'ordinary' tempo, how fast would 'ordinary' be? Period discussions of a basic standard tactus use such comparisons as the normal human pulse; this and other historical comparisons variously suggest tempos between MM60 and MM85. George Stauffer suggests for Bach a tempo ordinario of crotchet=MM72, the pace of a normal pulse. Marshall points out that Bach was said more than once to take a lively tempo, implying that his tempo ordinario was at the fast end of the range implied by period discussion. Thus Marshall suggests a tempo ordinario for Bach of approximately ± =MM80.
Still, Marshall notes, 'It cannot be sufficiently emphasized that the tempo ordinario, whether defined as ± =MM80 or anything else, was by no means a fixed metronome point but rather…encompassed a fairly generous amplitude. This is already clear from its traditional association with such a variable standard as the human pulse'. Indeed, musicians know that numbers fail to capture what makes a tempo 'work'; two performances with identical metronome marks can feel as if they have different speeds, and performances at differing MMs can feel as if they have a similar speed. In practice, the speed of Bach's tempo ordinario would no doubt depend on the acoustics, instruments, phrasing and accentuation involved, the affect of the piece, the text, and the whims of the day. Still, within a certain range numbers convey differences that one feels and hears. Thus Marshall posits a range, in the neighborhood of MM72 to MM88, 'or even further in each direction.' (I would posit a range from about MM65 to MM95. Again, these numbers are not entirely to the point The tempo ordinario would be defined by a feeling of not being very extreme in either direction, and thus its measured MM might still be outside my posited range in a given piece). Still, nowhere in the literature has anyone has argued that it was as fast as, say, ± =MM115, which usually feels faster than ordinary.
The implication might be something like the following: when we have a carefully notated Bach source - a set of autograph parts, for example - and a movement is in C with no modifying factors such as unusual note values (or perhaps such as special considerations of genre), it may imply that Bach, at the time of preparing the source, did not have an extremely fast or slow tempo in mind.
What do such considerations suggest about HIP Bach performance? On the one hand, the concept of tempo ordinario often does seem to justify the 'briskness' of HIP tempos. The chorus 'Herr, unser Herscher' in the St. John Passion is in ordinary C, and thus the tempos of Slowik (MM75) or Parrott (MM72) appear to have more historical justification than the weighty tempo of Richter (MM57). Might Bach himself have sometimes taken the chorus as slowly as the latter conductor? Might there be reasons not to care? Of course. I argue only that the notation seems to imply something on the faster side.
On the other hand, an aria from the same work, 'Ach, mein Sinn,' is in ordinary 3/4 time, with no modifying factors such as a tempo words. Thus, whatever one's artistic judgement of rapid HIP tempos (which are as fast as MM115; see Table 1), they seem to lack historical justification, while the ± =MM77 of Britten or the MM90 of Jochum and Richter seem better supported by the notation. The slower tempos in this aria may also be implied by (an arguable) reference to the sarabande topos, and by the meaning of its text.

Table 1 Speeds of recorded performances of 'Ach, mein Sinn' from the St. John Passion
period-instrument
Christopher ± = 115
Scholars ± =113
Herreweghe ± = 113
Gardiner ± = 111
Parrott ± = 106
Slowik ± =105
Suzuki ± = 105
Sorrell ± = 103
Koopman ± =98
Kuijken ± =9 6
median ± =105.5
modern-instrument
Scherchen ± = 98
Jochum ± =90
Richter ± =90
Britten ± =77
median ± = 90
C is by far the most common time signature in Bach. A survey of recordings suggest that few early-music performers observe the idea that movements in C, when not subject to the modifying factors discussed above, fall within a range of, say, ± =MM65 to 95. I would not for a moment suggest that HIP musicians begin to limit their tempos thus, and I would not do so even if the above arguments had quite explicit historical support, or if all the Bach sources were reliable indications of his performance intentions.
Thus I am happy to continue to hear and play the Bb-minor prelude in the Well-Tempered Clavier Bk. 1 at well below ± =MM65. That Prelude may seem the sort of fatal exception that disproves the approach to time signatures discussed above. But such apparent exceptions may reflect modern prejudices. Consider the turba movements in the St. John Passion. While most of these are in C or 3/4, HIP performers take them at a median tempo of MM109, well above the ordinario range; mainstream performers often take them just as quickly. We may find it difficult to imagine these turbae being taken more slowly, given their dramatic character and our long experience with them. Yet Britten takes them at an average of MM92-within the ordinario range-and his turbae have all the power and variety that one finds in faster recordings. I do not mean to say that HIP conductors should emulate Britten, or that faster turbae (which can be powerful) are unjustifiable. I claim only that the turbae do not undermine the idea of C or 3/4 typically indicating a speed somewhere in the tempo ordinario range. I further question the assumption, if anyone is making it, that those who take faster speeds in the turbae are more historically accurate than Britten; an examination of German Baroque Passion settings does not support this viewpoint.

Part Two: Tempo Words: The significance of 'Andante'
John Butt observes that 'Many gurus of performance practice still interpret [Italian tempo words in Bach] literally as moods rather than tempo indications.' Yet Baroque German sources, he notes, contradict the gurus. From Praetorius on, these sources typically call for the use of Italian tempo words specifically to indicate tempo. If some sources also relate some words to character, none state that Italian tempo words have to do with mood more than speed. Why that belief became common among early-music performers is an interesting question, which this article will not examine, but it did not result from overwhelming evidence.
Consider sources close to Bach. In Niedt's treatise (and the related 1738 manual) the brief chapter on tempo includes the sentence, 'If it is to be played fast, the composer expressly writes underneath: allegro or presto. If it is to be played slowly, this is indicated by writing adagio or lento underneath.' Also, in a 1706 second volume (not copied in the Bach-circle text), Niedt gives definitions of Adagio, Allegro, Andante, Largo, and Presto that have to do purely with tempo; in only one case, Allegro, is there additional mention of character.
The tempo definitions in Walther's 1732 Lexicon often derive from the 1703 Dictionaire of Brossard, with modifications. Despite Walther's familial relationship and documented contact with Bach, one may question whether the Lexicon is an infallible guide to Bach's own usage; but again, its definitions may be relevant evidence. Some, like Presto and Lento, deal more or less exclusively with speed: Largo, for example, is 'very slow [sehr langsam], as if expanding the measure'. Three other definitions (Adagio, Andante, Allegro) deal with character, but also, unambiguously, with speed. Walther gives a literal translation (lebhaft) of the Italian Vivace, which might or might not refer to speed.
Other sources related to Bach state unambiguously that Italian time words are used to indicate tempo. These include the Musikalischer Trichter (1706) by Martin Fuhrmann, who later heard and appreciated Bach, and (after Bach's death), C.P.E. Bach's Versuch (1753-1762), and Kirnberger's Die Kunst des reinen Satzes.
As for the evidence of Bach's scores, Marshall argues that these suggest a hierarchy of tempo words, from slowest (Adagissimo) to fastest (Prestissimo). That Bach also associated tempo words with character, may be suggested by movements in which he combined two markings; but Marshall notes only two such combinations - Allegro e presto and Vivace ed allegro-and only the latter occurs more than once. In each case the words combined have speed implications that are neither unrelated nor contradictory. Also, Stauffer mentions 49 cases where Bach gave different tempo markings to different simultaneous parts (e.g., Lente and Adagio), suggesting that the markings in question were more or less equivalent. But none of this implies that Bach's tempo words were primarily concerned with character. Both external and internal evidence suggests that they primarily indicated tempo.
Did any Italian tempo words indicate character and not tempo for Bach? Stauffer has recently argued that this is true of Vivace, although Marshall and others disagree. And - quite influentially - such commentators as Willi Apel, Fritz Rothschild, Nikolaus Harnoncourt, and David Fallows have stated that Andante in Bach (to quote Fallows in New Grove) is 'not a tempo designation'. It seems, says New Grove, 'to have been fully accepted as a tempo designation only with Leopold Mozart (1756)'. Fallows says that the Andante marking in Prelude 24 of the Well-Tempered Clavier (WTC) Book 1 is simply 'an instruction for clear performance of the running bass, and a warning not to play inégale'.
But Bach sometimes uses the term Andante for movements without running or quaver bass lines. In some of these movements, the bass line involves held breves and semibreves (as in BWV 10/6). In at least one case, Andante applies to a motet-style fugal passage in minims (the last ten bars of BWV 12/2) that continues the style and texture of the preceding music. Andante can only refer to tempo in this instance, and, similarly, in the final bars of BWV 21/2.
One might argue that in most (but not all) of these movements the motion is such that Andante could refer to a steadiness or evenness of execution; Bach often uses Andante in movements with at least one line, usually the bass, moving in continuous quavers (or semiquavers). But even in these cases Andante could, of course, refer to tempo as well.
Opponents of that view sometimes point to composers like Corelli and Handel, who use the term Andante in conjunction with other tempo words, e.g. Andante largo or Allegro andante. In these cases, Andante may perhaps to refer to execution or character (and perhaps functions literally as a verb). But it is by no means clear that Andante does not indicate tempo here; and in any case, the use of Italian tempo words in other countries, particularly Italy, may not be relevant to the conventional use of these words in northeast Germany. For that, we would do better to turn to the sources closer to Bach.
These leave no doubt that Andante moderated the tempo. Niedt, for example, describes Andante as being 'gantz langsam'. In a posthumous second edition of Niedt's book, Mattheson changed Niedt's description to 'nicht zu langsam nicht zu geschwinde' with a footnote mentioning the earlier description and saying that the musical reader 'shall decide whether this is right or wrong'.Even Mattheson's revision indicates that for him, too, the term has tempo implications that preclude great speed. Fuhrmann categorizes Andante among the slow tempo markings. Walther strays from Brossard by adding that Andante is 'somewhat faster than an Adagio' ('etwas geschwinder als adagio'). Since Walther considers an Adagio to be 'langsam', his comparison clearly indicates that Andante slows the tempo to something below the ordinary. Finally, Kirnberger gives a list of Italian tempo markings that, he says, modify the tempo implications of time signatures and note values. It seems to begin at the slow end of the tempo spectrum (with Largo) and end at the fast end (with Presto) - and Andante is on the slow side, faster than Adagio and slower than Allegro.
The unanimity of these sources (as well as his own usage) suggests that for Bach, the term Andante slowed the tempo somewhat compared to what it would be without the marking. Marshall speculates that a speed in the broad neighborhood of ± =MM60 would suit a common-time movement marked 'Andante'. Once again, however, the Andante tempo would be defined by feeling rather than by a specific metronome mark; Andante should feel more relaxed than ordinary.
HIP performers sometimes treat Andante this way, but at other times treat it as if it does not affect the tempo. In, for example, Prelude 24 of the Well-Tempered Keyboard, Book 1, ten HIP performers I surveyed took a median tempo of ± =MM87, while ten pianists had a more moderate median of MM70.(See Table 2 below.) One may or may not prefer the faster tempo (I feel that the fastest HIP performances, reaching MM100, undermine the expressive implications of the dissonances); but the average pianists' tempo in this prelude has more historical support. The 'Andante' that Bach wrote over this prelude would, by the above evidence, relax the tempo somewhat compared to the tempo ordinario that the C signature implies.
Similar logic applies to the 'Et in unum' of the Mass in B Minor. Here again we have a duet in common time; the Andante marking may be considered cautionary, warning musicians not to play it as quickly as a movement in common time would normally go. But while mainstream performers take a median tempo of MM67 - a historically plausible Andante tempo - HIP performers take a median tempo of MM76, that of a tempo ordinario, which (to speak subjectively) often feels too jaunty to qualify as an Andante.
There are other reasons for taking the 'Et in unum' at less than an ordinary tempo. One could, perhaps, argue that an unhurried pace helps the singers declaim the imitative writing most effectively. Moreover, the movement has an enormous amount of text; at a fast tempo it 'often sounds gabbled, almost like a patter aria'.One could also compare tempos in this movement to those in the 'Christe eleison'. That movement, too, is a common-time duet with a quaver bass line, but it has no tempo marking. Thus, its notation the notation of the 'Christe' suggests a tempo no slower than the 'Et in unum', and probably noticeably faster. Yet all but a few EM recordings take the 'Et in unum' perceptibly faster and the others take the two movements at more or less identical tempos.

Part Three: Genre: The Crucifixus
Another element that might modify the tempo implications of time signatures was genre. But applying that principle can be tricky. Misreadings of genre sometimes lead HIP performers to historically dubious tempos.
An example is the 'Crucifixus' of the B Minor Mass. Four very distinguished EM performers - Harnoncourt 1968, Leonhardt, Herreweghe 1997, and Brueggen - take the 'Crucifixus' far faster than their colleagues, either HIP or mainstream. Harnoncourt, at [half note]=MM76, holds the studio speed record [he is far slower in his 1986 recording].
Harnoncourt in 1968 explained his speed by saying that the 'Crucifixus' (which is in 3/2) is a dance, a passacaglia. He added, 'it may well seem strange to us that, in this of all places, Bach has chosen a dance form'. A different dance form has been posited for this movement by Thomas Hoekstra, who asserts that it is a sarabande; he suggests a tempo in the mid-60s, since that would fit estimates of the tempo of that dance.
The basic lament notes are indeed reached on the second beat of each bar; but that does not make the 'Crucifixus' an actual sarabande, to be played at a tempo that would allow one to dance. The sarabande is marked by many attributes, including phrasing and rhythm, not present here. A baroque movement in a triple metre with a significant second beat is not necessarily a sarabande, much less a danceable one. (And, of course, actual dance topics need not imply danceable tempos in Bach's music, even in named dances.)
The passacaglia attribution is more plausible, but still does not imply a fast tempo. For one thing, this movement is not simply a passacaglia. It has a more specific topos, a descending minor tetrachord ostinato, which during the mid-17th century (as Ellen Rosand writes) 'came to assume a quite specific function associated almost exclusively with a single expressive genre, the lament'. It still had this association for Bach, who used it in the early Capriccio on the Departure of His Beloved Brother, with the title, 'Ist ein allgemeines Lamento der Freunde'. To this movement in 3/4 he gave the tempo marking Adagiosissimo, which Robert Marshall has identified as the slowest of all his tempo markings. The slow tempo was not idiosyncratic: the lament was associated with a slow tempo.
Alexander Silbiger writes, 'it is still not clear to what extent the seventeenth century identified the descending tetrachord ostinato with the passacaglia dance-genre.'Wye J. Allanbrook is more certain about the 18th century: she states that the descending tetrachord lament had lost any dance implications whatsoever. Even if one regards the Crucifixus as a passacaglia, its metre (as well as its lamento topic) would still imply a slow tempo. Silbiger notes that a 'slower tempo for the passacaglia is sometimes suggested by a meter based on larger note values (e.g., 3/2 rather than 6/4 or 3/4)'.
A final argument for a slow tempo in the Crucifixus is that Bach gave its model, BWV 12/2, the tempo marking Lente.

Part Four: Do HIP Performers Selectively Favour Evidence for High Speed?
One can come up with other examples in which the fast new tempos favoured by HIP performers seem to have less historical support than the slow ones once favoured by mainstream performers. But it is not the case the historical performers as a group have always played Bach faster than mainstream performers, or that they have selectively favoured evidence for high speed whenever it is available.
For one thing, a majority of HIP performers take certain movements as slowly as their mainstream predecessors, in spite of evidence that could easily be used to support a faster tempo. One example is the 'Et incarnatus', in which the median HIP tempo (± =MM50) is only four points faster than the traditional median. Yet the movement is in ordinary 3/4, and has no markings to indicate a slow tempo; if one wished, one could plausibly argue that it is a tempo ordinario movement. Admittedly, Stauffer notes that 'the text, the b-minor mode, and the expressive slurring' (one might add, also, the suspensions) slow the tempo in the 'Et incarnatus'; but one can give these matters their due without slowing below the tempo ordinario range. Rifkin and René Jacobs take the Et incarnatus at ± =MM66-67, yet their slurs sound expressive and their suspensions have sufficient weight.
In another example, the Sanctus, most of the HIP tempos fall into two distinct groups. One group (including nine conductors) has a median tempo of ± =MM64, barely faster than the median mainstream tempo of MM60. The other group, with six conductors, takes a much faster median tempo of MM78. The latter accords with Marshall's estimate of the tempo ordinario - the tempo suggested by the movement's notation in C with triplets (again, an earlier version has ¢ with triplets). Indeed, Bach could probably have notated the movement in 12/8 (unless one holds that the timpani should not be assimilated with the prevailing triplets); for reasons of intrinsic note-value speeds, Marshall argues that 12/8 would imply a tempo approximately a third slower than what is implied by C.
That the slower tempo is more common than the fast one in both movements among HIP performers is no cause for outrage. But it does show that HIP performers have not always favoured evidence for faster speeds, even when such evidence can be found easily. The Benedictus and Agnus Dei arias are two additional examples; in the latter, several prominent HIP recordings are so slow as to move at eight to the bar. Here, then, are four movements in which a majority of HIP performers have ignored convenient evidence for a faster tempo.
Another reason to qualify the belief that HIP performers always favour evidence for speed is that in some works and genres HIP performers have played significantly more slowly than their mainstream predecessors and colleagues. An example is Book 1 of the Well-Tempered Keyboard, in which a group of ten pianists take median tempos that are on the whole about 9 percent faster than ten period-instrument recordings. While the period instrument players are significantly faster in eight movements, usually serious ones like the minor-key fugues in c#-, d-, f#-, g#- and bb, the pianists are significantly faster in 20 movements, usually fast ones like the Prelude in c minor. This pattern suggests that what motivates HIP tempo choices is something other than a global taste for speed.

Perhaps it might be taken as evidence for the thesis that a central motive for HIP performers is to be different from the mainstream. Perhaps this desire arises as a reaction to specific performance traditions. Harpsichordists may be reacting against pianists and the Bischoff/Czerny tradition, while HIP conductors may react against previous choral traditions, which tended to seek weight and gravity. There will, of course, be many exceptions to the generalizations in the previous sentence; but reaction against the mainstream may well motivate some of the fastest performances of the Kyrie 1, the 'Et in unum', and the 'Crucifixus', among others.
We might also consider the role of performance media and fashions of playing. It could be that harpsichordists play more slowly than pianists in fast movements because harpsichordists cannot emphasize strong beats with dynamics, and instead use preceding articulatory silences. If harpsichordists played with pianistic styles and speeds, they might sound mechanical. Moreover, harpsichordists tend to place greater rhetorical weight on smaller motivic units. Also, while I used the Crucifixus as an example of a movement that has sometimes been played quickly based on mistaken ascription of a dance genre, considerations of dance have often slowed tempos, especially in keyboard music.
It is often suggested that traditional choral recordings have been slower than EM recordings because of the limits on speed caused by huge choruses. However, the evidence undermines the belief. In the fastest choral movements, mainstream recordings with large choruses (e.g., the B Minor Mass of Solti, or the St. John Passion of Scherchen) can be every bit as fast as the quickest early-music recordings.
Another hypothesis might be that influential individual performers, e.g., Leonhardt, create tempo traditions among students; a preliminary statistical investigation, however, fails to confirm this hypothesis either in the Mass or in the WTC.
Perhaps, also, period-keyboardists simply tend to favor a narrower spectrum of tempos than pianists do. If so, one might wonder if their circumspection reflects an attempt to apply the idea of the tempo ordinario in movements in C or 3/4, and otherwise to interpret time signatures according to intrinsic note values. But this idea could account for only eleven of 28 tempos in which the two groups differ significantly in WTC 1.
One general influence on the cases examined in this article may be musicological advice. Influential musicologists such as Robert Donington have told performers that time signatures had no tempo implications in Bach, that Andante was not a tempo marking, even that Bach's notation generally did not indicate tempo. If such advice turned out to be mistaken, performers who thought they had historical sanction would be mistaken as well.

Conclusion: Authenticity and Tempo
Donington is indisputably correct when he says that 'the right tempo for a given piece of music is the tempo which fits, as the hand fits the glove, the interpretation of that piece then being given by the performer,' and when he adds that 'the limits within which the right tempo for any particular piece of music may vary are surprisingly wide.' Such matters as the performance's character, pulse, and phrasing all play a role in making a given tempo work. Even if we were able to reconstruct Bach's systems of tempo notation with a fair degree of confidence, then, we should hardly expect performers to be bound by it. Indeed, composers' own tempos in performance vary widely from one occasion to another.
On the other hand, Andrew Parrott has argued that when musicians take account of historical data 'new possibilities emerge, even if old ones fall by the wayside'. The same might be said of criticisms of HIP trends: even when attempts at debunking have failed, they have sometimes suggested new possibilities to performers. Thus I hope that the arguments in this paper, however they are judged in the long run, will serve to stimulate performers rather than to constrain them.
I am very grateful to Alyson Ahern, Jonathan Bellman, John Butt, Robert Cammarota, Matthew Dirst, Laurence Dreyfus, Don Franklin, George Houle, Michael Marissen, Robert Marshall, Daniel Melamed, Andrew Parrott, Joshua Rifkin, and Eric Van Tassel for their comments on this paper.