(Fr. diapason; Ger. Mensur).
In organ pipes, the relationship between the length and diameter of a given pipe, and its progression throughout the compass of a rank of pipes. Since the 18th century, several attempts have been made to relate pipe scaling to a ‘norm’. Scale affects tonal quality: a pipe that is fairly wide in proportion to its length will have a foundational, fluty tone; one that is fairly narrow will have a thin, stringy tone. From the 15th century to the present day, numerous concepts of pipe-scaling have been propounded by theoreticians, although practical organ builders tend to employ a more empirical approach based on what ratios they have found will provide the desired consistency of timbre throughout the range of a given stop.
In string keyboard instruments, the term refers to the sounding length of the strings in relation to their pitch. Given constant tension and diameter, a string sounding an octave below another will be twice its length, but for practibility the scaling is normally shortened in the bass, as even in a harpsichord with generally short scaling (25 cm for c'' instead of 35 cm) the maintenance of ‘just’ scaling in the bass would oblige the sounding length of the C-string to exceed two metres. Most early clavichords, harpsichords and pianos retain a ‘just’ scaling for at least the upper half of their compass, and begin to shorten the scaling in the tenor range, the reduction in relative string length being compensated for by increases in diameter and, in many instances, by the use of a heavier substance for the bass strings. In the modern piano the scaling is gradually shortened throughout the range from treble to bass, one aim of this ‘tapered’ scaling being to achieve a smooth gradation of string tension and timbre throughout the instrument's compass.
See also Aliquot; Duplex scaling; Harpsichord, esp. §§2(i) and 4(iii); Organ, §III, 1.
G.A. Sorge: Die geheim gehalten e Kunst von Mensuration von Orgel-Pfeiffen (MS c1760; ed. and Eng. trans. C.O. Bleyle, Buren, 1978)
A.H. Benade: Fundamentals of Musical Acoustics (New York, 1976)
H. Henkel: ‘Zur Bestimmung der Nationalität unsignierter Kielinstrumente auf Grund der Mensurverläufe’, Aufsätze und Jahresbericht 1976 für die Freunde des Musikinstrumenten-Museums der Karl-Marx-Universität (Leipzig, 1977), 14–23
EDWIN M. RIPIN, DEREK ADLAM, BARBARA OWEN