9. The tempo in the first half of the 18th century, especially in the organ works of Johann Sebastian Bach
‘Maatsoorten en tempo in de eerste helft van de 18de eeuw, in het bijzonder in de orgelwerken van Johann Sebastian Bach’ [Time signatures and tempo in the first half of the 18th century, in particular in the organ works of Johann Sebastian Bach], Bachs ‘Orgel-Büchlein’ in nieuw perspectief, red. P. Peeters, Voorburg 1988 (Kerkmuziek & Liturgie 1), 191-239.
The first part of this article was previously published in Het Orgel 81 nr. 6 (juni 1985), a special issue dedicated to the Internationaal Bach-Congres Groningen 19-22 juni 1985. It served as an introduction to my presentation at that congress for its parcipitants. The presentation itself is the second part of this article.
The original article in dutch you can find here (as pdf, 1.02 MB).
Summary.
1. Data concerning time signatures and tempo in the first half of the eighteenth century
The introduction sketches the development of mensural notation in relation to tempo, from the Ars Nova to the Baroque.
French data
The tempos of 3/2, 3/4, 3 and 3/8
L’Affilard 1705 gives exact information on the tempos of French dances. For those in simple triple time, the tempo is:
(The numbers are metronome marks indicating the number of counting units per minute.)
From descriptions of the tempo of these dances in L’Affilard 1702 and De Montéclair (1736), neither of whom give numbers, it appears that counting units 60 and 120 form transitions a) from ‘grave’ to ‘gai’ resp. from ‘gai’ to ‘vite’ and b) for the choice of counting unit, i.e. the chosen time signature: 3/2, 3/4 or 3 and 3/8. The values 60 and 120 are of fundamental importance; they are also found in De Saint-Lambert (1702) and Boyer (1767). Crotchet = 60, quaver = 120, etc, can be viewed as the basic note value, and minim = 60, crotchet = 120, etc. as halved note values, or values ‘alla misura breve’. The tempos of the triple time signatures are as follows:
(Vertical: the tempo of the counting unit compared with 60 and 120; horizontal: the note values compared with ‘whole’ and ‘halved’ note values.
The tempos of C and 
, 2 and 2/4, 6/4 (incl. 9/4 and 12/4, 6/8 (incl. 9/8 and 12/8)
C is always in quadruple time, crotchet = 60 or slower.
can have two meanings:
a) a duple time signature with notes ‘alla misura breve’, minim = 60, and
b) a quadruple time signature ‘à quatre temps légers’, crotchet between 60 and 120.
2 is always in duple time; however, tempo indications in the sources differ strongly. Minim = 60 seems a plausible average.
2/4 likewise has considerable variation. The two units may be ‘légers’or ‘vite’. See the following tables:
6/4 and 6/8: the sources are rather contradictory. I propose the following:
9/4 and 12/4: equivalent in tempo to 6/4 (and 3).
9/8 and 12/8: equivalent in tempo to 6/8 (and 3/8).
‘Notes inégales’; the beat of the bar
The following table indicates the note values that may be played ‘inégal’ in certain circumstances in the various time signatures:
1/16 is the shortest note value that may be performed inégal in time signatures with beats approximating ‘whole’ note values (crotchet = 60 or quaver = 120); 1/8 is the shortest note value that may be performed inégal in time signatures with beats approximating ‘halved’ note values (minim = 60 or crotchet = 120). An upper limit to the tempo of note values to be played inégale could be approximately four such notes to metronome mark 84 or two to 168.
Concerning the beats in the bar:
C and 4: quadruple beat, upper tempo limit is crotchet = 120. The faster 4/8 (quaver ≥ 120) is taken in two.
2, 2 and 2/4: duple beat, the tempo of 2 is minim = 60.
3/4 and 3: triple beat, upper tempo limit is again crotchet = 120. From crotchet = c. 90 the bar can already be taken in two dissimilar beats (long-short). The faster 3/8 also has two dissimilar beats in its lower tempo range; from quaver = c. 180 (as the average of the beats ‘à un temps et demi’ rises to 120) it is taken in one beat.
German data
Heinichen (1728) tells us how to treat ‘fast notes’ in various time signatures. He makes an important distinction, however, between such notes and ‘notes in fast passages’: e.g. in ordinary time C the ‘fast notes’ (corresponding with the ‘notes inégales’in French music) are semiquavers, while demisemiquavers only occur in ‘fast passages’.
Quantz (1752) gives a classification of tempo modifications on the grounds of his observation that more than eight ‘passage notes’ in an average beat of 80 per minute are hardly practicable. A closer examination of his data, however, reveals that his four ‘Hauptarten’ are in fact subsidiary classes of the principal classes allegro, tempo ordinario and adagio. See the following scheme (the interpolated classes are in bold):
One should bear in mind that Quantz also remarks that allegro assai ‘in former times’ was played hardly faster than allegretto ‘nowadays’. May we consequently deduce that the crotchet in ordinary allegro C, for example, was scarcely faster than 72 in the music of Bach?
In the spirit of his teacher Bach, Kirnberger (1776-1779) gives an exposition on the different time signatures. He writes that the ‘tempo giusto’ (‘just tempo’) of a piece is determined by a) the given time signature and b) the given note values. This ‘tempo giusto’ can be modified by tempo indications such as allegro and adagio. In my article I propose a method based on these principles to calculate the tempos of a number of organ works by Bach.
2. Time signatures and tempo in the organ works of Johann Sebastian Bach
The time-signature
In the French sources we see that can have two meanings, namely ‘deux temps graves’ or ‘quatre temps légers’. This seems to be valid for Bach’s organ works too.
1. - ‘deux temps graves’ (Allabreve group)
The minim is the (heavy) beat. Pieces written in this time signature can be recognised immediately by their style. (See Kirnberger’s ‘Allabrevetackt’: the shortest notes are quavers, the performance heavy and emphatic, but twice as fast as note values indicate.) The tempo ordinario of this time-signature is minim = 60; if the work in question is in a compact polyphonic style one can reduce to minim = c.54 if this is to the good of the performance. Bach gives the time signature C twice with the addition ‘alla breve’: the normal note values in C are halved.
2. - ‘quatre temps légers’ (Allegro group)
The crotchet is the (light) beat. Pieces in this time signature do not have the characteristics of the allabreve style. At first sight they have a normal semiquaver movement as in C without a stroke, but they are written in the style of the sonata allegro. One could establish the tempo of this time signature as minim = c.72 (with a maximum of minim = c.84). The pulse occurs on the first and third crotchet. At the beginning of the 18th century the indication ‘allegro’ will still have been one of character, equivalent to the French ‘gai’ or ‘léger’. There are however a number of works in which the meaning of is less clear. The allabreve tempo of the Prelude in c, BWV 546, is modified by the triplet movement to minim = c.48.
The time-signature 
This occurs only once in the organ works: in the last movement of the 2nd Sonata; tempo minim = c.72
The time signature C
In the light of French sources: ‘Quatre temps graves’, tempo ordinario crotchet = 60; Quantz’s information corresponds to this.
In many pieces with this time signature one finds a more or less continuous movement in semiquavers; in France these were the shortest notes which could be played ‘inégale’; as far as Germany is concerned one could say that they are the shortest notes allowing a varied articulation.
One could take crotchet = 60 as the basic tempo. Among the longer free organ works in particular there are many pieces in which the tempo could be taken faster than crotchet = 60. For the concise chorale preludes of the ‘Orgel-Büchlein type’ lowering of the tempo ordinario to crotchet = c.54 would seem necessary (consider the compactness of the setting, the text of the chorale).
In the case of the time signature C we find a number of works and groups of works which we can classify as ‘exceptions to the rule’, requiring special attention in respect to the tempo.
The time signature 2/4
Occurs only occasionally (first movement 3rd Sonata and 6th Sonata, last movement 5th Sonata and ’Wir glauben all . . .’ BWV 680).
In principle we can start from the tempo ordinario (crotchet = 60); in the first movement of the 3rd Sonata ‘andante’ not much slower than the tempo ordinario, in the case of the addition ‘allegro’ or ‘vivace’ crotchet = c.80.
The time signature 3/2
This occurs mainly in chorale preludes, and we find it in the ‘Orgel-Büchlein’ in particular.
In practice, a tempo just above the tempo ordinario minim = 60 seems to be required. Here too however we find a number of special cases (e.g. in the ‘Orgel-Büchlein’: ‘In dulci jubilo’)
The time signature 3/4
With the exception of a few works in which the notes have halved values (e.g. Fugue in A, BWV 536; tempo crotchet = c.108), Bach’s organ works in 3/4 time have notes in natural values. As in 4/4 time we find here a continuous semiquaver movement. Apart from passagenotes and the like, the semiquavers are the shortest notes.
As average we can take crotchet = 60 as the basis, with an increase to crotchet = c.72 for some works (and again a maximum of crotchet = c.84).
But here too a number of special cases deserve particular attention (e.g. ‘Komm, Heiliger Geist’ BWV 652, ‘An Wasserflüssen Babylon’ BWV 653, ‘Schmücke dich. . .’ BWV 654, ‘Vater unser. . .’ BWV682).
The time signature 6/4 and 9/4
We encounter the time signature 6/4 both as time signature with halved note value (e.g. second part of Fugue in E flat major), and as time signature with the notes in natural values (e.g. Fantasia in c BWV 537 and ‘Dies sind. . .’ BWV 678).
The time signature 9/4 occurs only in the last part of ‘O Lamm Gottes, unschuldig’ BWV 656, as ‘proportion bar’.
The time signature 3/8
Starting point here is quaver = c.120 (e.g. ‘Christ lag in Todesbanden’ BWV 695), to be modified in a number of cases, e.g. to quaver = c.144 in the Toccata in F, BWV 540. The tempo of the last movement of the 3rd Sonata is modified to quaver = c.118, and that of the last movement of the 4th Sonata to quaver = c.108, because of the triplet movement and the respective indications ‘Vivace’ and ‘Un poc’ allegro’.
The time signature 6/8
This time signature occurs both in its typical tempo ordinario form with running semiquavers (as basis for the tempo quaver = 120) and a ‘proportion bar’ (crotchet + quaver then has the same value as crotchet in tempo ordinario, i.e. crotchet + quaver = 60). A special problem is the Prelude in b, BWV 544, in which the tempo giusto will be considerably below quaver = 120, in practice quaver = 80 would appear to be the highest feasible tempo.
In the slow movements of the 3rd, 5th and 6th Sonatas quaver = 60 seems to be a suitable tempo, which also corresponds to the conclusions which can be drawn from Quantz’s information.
The time signature 9/8
In my opinion we are concerned here with a ‘proportion bar’ in all cases, i.e. crotchet + quaver = crotchet in tempo ordinario = 60.
The time signature 12/8
As in 6/8, roughly speaking we can distinguish two possibilities:
1) the notes in their natural values (quaver = c.120);
2) ‘proportion bar’ quaver = c.180 / crotchet + quaver = c.60.
In the middle movement of the 1st Sonata we are concerned with a ‘proportion bar’, but then in adagio tempo (quaver = c.90 / crotchet + quaver = c.30).
Proportional tempo relationships in the organ works of Bach
The investigation of three examples produces the following tempi:
1) Canzona: C minim = c.48, 3/2 minim = c.72;
2) the manual Kyrie - Christe - Kyrie preludes from ‘Klavierübung III’; 3/4 crotchet = c.60, 6/8 quaver = c.120, 9/8 quaver = c.180;
3) Fugue in E flat: C minim = c.54, 6/4 crotchet = c.108, 12/8 crotchet + quaver = c.54.
Summary: Paul Peeters
Translation: Stephen Taylor