Mean-tone.

A system of temperament or a tuning of the scale, particularly on instruments lacking any capacity for flexibility of intonation during performance, which differs from the equal-tempered system normally used on such instruments today. In its most restricted sense the term refers, like its German equivalent mitteltönige Temperatur, to a tuning with pure major 3rds (frequency ratio 5:4) divided into two equal whole tones (whereas in Just intonation there are two sizes of whole tone corresponding to the ratios 9:8 and 10:9); to achieve this the tuner must temper the 5ths and 4ths, making the 5ths smaller and the 4ths larger than pure by a quarter of the syntonic comma, hence the label ‘1/4-comma mean-tone’, a more specific name for the same kind of tuning.

A broader and equally legitimate use of the term (dating back to such 18th-century writers as Sauveur and Estève) includes any Renaissance or Baroque keyboard tuning in which a major 3rd slightly smaller or, more often, slightly larger than pure is divided into two equal whole tones (see Table 1). In 2/7-comma mean-tone temperament, for example, the major 3rds are 1/7-comma smaller than pure, whereas in 2/9-comma mean-tone they are 1/9-comma larger and in 1/6-comma mean-tone they are 1/3-comma larger. In each case the major 6th (or minor 3rd) is perforce tempered the sum of the amounts by which the major 3rd and 4th are rendered larger than pure; and a 12-note scale will include one sour ‘wolf 5th’ considerably larger than pure because the other 11 are tempered more than enough to make a ‘circle’ of identical 5ths as in equal temperament. Hence the tuner about to set a mean-tone temperament must choose not only a particular shade of mean-tone (e.g. 1/4- or 1/5-comma) but also a particular disposition (e.g. with the wolf 5th at C–A, G–E or D–B).

In all mean-tone temperaments the diatonic semitone is larger than the chromatic semitone, so that E is higher than D, A higher than G and so forth; and a diminished 7th (e.g. G–F) is larger than a major 6th (A–F), a diminished 4th (G–C) larger than a major 3rd (A–C), etc. Triads generally sound more resonant in a mean-tone temperament than in equal temperament, though in varying degrees depending on the musical style, the instrument, the acoustical circumstances and the precise shade of mean-tone used. The most resonant shades are generally those in which the major and minor 3rds are tempered least; but these (2/7- or 1/4-comma mean-tone) also have the largest diatonic semitones and hence the lowest leading notes. Although some 17th-century musicians considered the large diatonic semitone of 1/4-comma mean-tone to be, as Mersenne (1636–7) put it, one of the greatest sources of beauty and variety in music, most musicians today would be likely to prefer the smaller diatonic semitones of equal temperament or Pythagorean intonation; a modern connoisseur might therefore find in 1/5- or 1/6-comma mean-tone a nice compromise between the relative virtues of 1/4-comma mean-tone and equal temperament. For the history of mean-tone temperaments in performing practice, see Temperaments, §§3 and 6; see also Padgham, Collins and Parker (1979).

Various shadings of regular mean-tone temperament correspond closely to certain divisions of the octave into more than 12 equal parts. A number of 18th-century theorists aware of these manifold possibilities sought to show that some particular division of the octave with intervals approximating to some shade or other of mean-tone was better than all the others. In the 16th and early 17th centuries Salinas, Costeley and Titelouze had used the 19-tone division (equivalent to 1/3-comma mean-tone), and in 1691 Christiaan Huygens had advocated the 31-part division (corresponding to 1/4-comma mean-tone), which Vicentino may have used in the 1550s (see Lindley, 1982). Sauveur (1701) preferred the 43-part division (corresponding to 1/5-comma mean-tone); Henfling (1710) and Smith (1749) the 50-part division (corresponding to 5/18-comma mean-tone); Telemann (1743) and Romieu (1758) the 55-part division (corresponding to 1/6-comma mean-tone); and Riccati (1762) the 74-tone division (corresponding to 3/14-comma mean-tone). Estève (1755) said that the most perfect system was ‘between that of 31 and that of 43’, by which he meant some shade of mean-tone between 1/4- and 1/5-comma.

The term ‘mean-tone temperament’ and its Italian equivalent systema participato have sometimes been used to refer to certain schemes in which only the seven naturals of the keyboard (and perhaps not even all of them) conform to any of the regular mean-tone patterns discussed above; the characteristics of such irregular tunings are described in Temperaments, §§4 and 7, and in Well–tempered clavier.

BIBLIOGRAPHY

PraetoriusSM, ii

L. Rossi: Sistema musico (Perugia, 1666), 58

J.B. Romieu: ‘Mémoire théorique & pratique sur les systèmes tempérés de musique’, Mémoires de l’Academie royale des sciences (Paris, 1758)

A.R. McClure: ‘Studies in Keyboard Temperaments’, GSJ, i (1948), 28–40

J.M. Barbour: Tuning and Temperament: a Historical Survey (East Lansing, MI, 1951, 2/1953)

K. Levy: ‘Costeley’s Chromatic Chanson’, AnnM, iii (1955), 213–63

M. Lindley: ‘Early 16th-century Keyboard Temperaments’, MD, xxviii (1974), 129–51

M. Lindley: ‘Fifteenth-century Evidence for Meantone Temperament’, PRMA, cii (1975–6), 37–51

C.A. Padgham, P.D. Collins and G.K. Parker: ‘A Trial of Unequal Temperament on the Organ’, JBIOS, iii (1979), 73–91

M. Lindley: ‘Chromatic Systems (or Non-Systems) from Vicento to Monteverdi’, EMH, ii (1982), 377–404

For further bibliography see Temperaments.

MARK LINDLEY