(1) The 15th- and 16th-century term for a beat, i.e. a unit of time measured by a movement of the hand, first discussed in detail by Adam von Fulda (De musica, 1490). One tactus actually comprised two hand motions, a downbeat and an upbeat (positio and elevatio, or thesis and arsis). Each motion was equal in length in duple time (tempus imperfectum); in triple time (tempus perfectum) the downbeat was twice as long as the upbeat.
In theory the tactus in 16th-century music measured a semibreve of normal length (integer valor notarum), a breve in diminution (proportio dupla), and a minim in augmentation. Gaffurius (Practica musice, 1496) wrote that one tactus equalled the pulse of a man breathing normally, suggesting that there was an invariable tempo then of M.M. = c60–70 for a semibreve in integer valor. However, in the 16th century (as Dahlhaus, 1960, pointed out), it was possible for the tempo of the tactus to vary, depending on the interpretation of the mensural conditions. The diminution in tempus perfectum diminutum (), for example, was understood as a reduction of the time value of the notes by one third and not by half, so that the tactus alla semibreve became two thirds of the usual length. Furthermore, there are some isolated cases in which verbal instructions indicate a change of the speed of the tactus: for example, in Luys Milán’s El maestro (1536) he indicated that the tactus should be fast or slow with the expressions apriessa and espacio respectively. From the possibility to divide the tactus while the value of the notes was retained (i.e. to beat twice as fast) there followed the distinction between a larger and a smaller tactus (Martin Agricola, Musica figuralis deudsch, 1532). Hence in tempus imperfectum diminutum (C) the tactus maior constitutes a breve and the tactus minor a semibreve; in tempus non diminutum (C) the unit is correspondingly able to contain a semibreve or a minim. At the turn of the 16th century the tactus was seen primarily as a measure of the semibreve, which could by now be faster or slower: according to Michael Praetorius the tempus imperfectum diminutum corresponded to a tactus celerior, the tempus non diminutum to a tactus tardior (Syntagma musicum, iii, 1618, 2/1619). The mensural concept of tactus continued to have an effect on music theory until the 18th century; Mattheson especially held unwaveringly to the definition of tactus as a dual unit of thesis and arsis.
See also Conducting, §1 and Performing practice, §I, 4 and Tempo.
(2) The verb tangere was used from the Middle Ages onwards to mean ‘to touch an organ’ or, more generally, any keyboard instrument. From this, tactus came to mean a formulaic musical unit that was particularly constitutive for cantus firmus settings, determining the progress of such keyboard pieces. German organ treatises of the 15th century (e.g. D-Mbs Clm 7755, ed. in Göllner, 1961) teach how a musical work may be constructed on a given tenor by the use of prewritten ornamented figures, in a rhythmic-melodic movement from one concordance to another, the initial harmony being emphasized and the final sonority prepared each time. In so far as each tactus represents, in its relationship to a single note of the cantus firmus, a metrical unity whose length is determined by the prescribed ‘beats’ of the movement (e.g. quatuor or sex notarum), which is also marked by analogous tablature-lines, this instrumental structure is closely related to the modern concept of metre. In some sources the sample exercises as a whole – and in the Buxheimer Orgelbuch (D-Mbs Cim.352b) even entire pieces – are called tactus. After Conrad Paumann, organ teaching became more influenced by vocal composition and the elementary tactus procedure was replaced by new techniques of formulation; however, the principle of working to such formulae remained important for instrumental music. Thus, in terms of musical history, it is likely that the modern bar system is also related to these older practices of instrumental performance.
(3) Giorgio Anselmi (De musica, 1434), used the word to mean the Fret on a lute or clavichord, and also the keys of a clavichord or organ (see Key (ii)). Gaffurius (De harmonia musicorum instrumentorum opus, 1518) followed Anselmi’s example.
See also Rhythm, §II, 5.
G. Schünemann: ‘Zur Geschichte des Taktschlagens’, SIMG, x (1908–9), 73–114
G. Schünemann: Geschichte des Dirigierens (Leipzig, 1913)
W. Apel: The Notation of Polyphonic Music, 900–1600 (Cambridge, MA, 1942, rev. 5/1961; Ger. trans., rev., 1970)
C. Dahlhaus: ‘Zur Theorie des Tactus im 16. Jahrhundert’, AMw, xvii (1960), 22–39
C. Dahlhaus: ‘Zur Entstehung des modernen Taktsystems im 17. Jahrhundert’, AMw, xviii (1961), 223–40
T. Göllner: Formen früher Mehrstimmigkeit in deutschen Handschriften des späten Mittelalters (Tutzing, 1961)
A. Auda: Théorie et pratique du tactus (Brussels, 1965)
J.A. Bank: Tactus, Tempo and Notation in Mensural Music from the 13th to the 17th Century (Amsterdam, 1972)
C. Dahlhaus: ‘Die Tactus- und Proportionenlehre des 15. bis 17. Jahrhunderts’, Geschichte der Musiktheorie, ed. F. Zaminer, vi (Darmstadt, 1987), 333–61
A.M. Busse Berger: Mensuration and Proportion Signs: Origins and Evolution (Oxford, 1993)
C. Bockmaier: Die instrumentale Gestalt des Taktes: Studien zum Verhältnis von Spielvorgang, Zeitmass und Betonung in der Musikgeschichte (Tutzing, forthcoming)
HOWARD MAYER BROWN/CLAUS BOCKMAIER