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Horst Brunner

(Ger. Barform)

A term denoting in musicology the three-part form AAB. The sections are called first Stollen (pes; A), second Stollen (pes; A), together forming the Aufgesang (frons), and Abgesang (cauda; B). German terms are normally retained because the concept of bar form was first introduced into musical terminology through Lorenz’s investigations into the form of Wagner's works. It is based on an incorrect use of the word ‘Bar’ in Die Meistersinger von Nürnberg. In Act 3 scene ii Walther von Stolzing sings the first stanza of his Prize Song, which has AAB form. Hans Sachs then sings: ‘Das nenn’ ich mir einen Abgesang! Seht, wie der ganze Bar gelang! … Jetzt richtet mir noch einen zweiten Bar’. Bar here means ‘a tripartite stanza’. In this Wagner was not in full accord with the terminology of the German Meistersinger of the 15th to 18th centuries from whom the word comes....



Howard Mayer Brown

revised by Claus Bockmaier

(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...


Laurenz Lütteken

(from Gk. isos: ‘identical’ and melos: ‘melody’; Ger. Isomelie)

A term coined by Heinrich Besseler for the melodic resemblances in the upper parts between different sections of certain isorhythmic motets of the first half of the 15th century. Isomelic recurrence may take place at the beginning of successive taleae and may involve transposition, as in the triplum of Du Fay’s Rite maiorem (ex.1). Since color and talea do not normally overlap in 15th-century motets (by contrast with earlier practice), isomelic resemblance may also be found at the beginning of successive colores, as in the triplum of Du Fay’s Fulgens iubar (ex.2). Isomelism of this kind, also found in music of the Old Hall Manuscript (see Bukofzer), is not related to the cantus firmus. (In this special meaning of coloration, the term was used by E. Reeser.) Isomelism was once regarded as highly significant, but its importance has since been disputed. Scholars at first interpreted it as a product of conscious compositional procedure: either as a means of ‘symbolizing’ isorhythmic structures, and hence clarifying them (Besseler), or simply as a device which could be inserted in order to mark off isorhythmic sections (Bukofzer, Eggebrecht, Reichert). At the other extreme, Sanders regarded it as a mere by-product of motet composition. More recently, an intermediate view has gained acceptance (see Finscher and Laubenthal)....


Clive Greated

(Adolf )

(b Würzburg, Aug 11, 1888; d Düsseldorf, Dec 20, 1956). German engineer and acoustician . He studied electrical engineering (1906–8) and law (1908–11), and received the doctorate from Karlsruhe (1921) before working in the radio industry. In 1930 he was appointed lecturer and in 1935 professor of musical acoustics at the Berlin Musikhochschule. His experiments in electronic music resulted in several instruments, including an amplified harpsichord (1936, in collaboration with Hanns Neupert), electronic bells and, most importantly, the Trautonium, developed in 1930 and used by, among others, Hindemith, Höffer, Genzmer and Julius Weismann, all of whom wrote concertos for it, Egk and Strauss. In the late 1940s Trautwein worked in Paris in aviation research; he then set up a school of composition in Düsseldorf which in 1950 became part of the Robert Schumann Conservatory. He published a trautonium method (Trautoniumschule, 1936...


Julian Rushton

(Fr. quart de tonGer. VierteltonIt. quarto di tono)

An interval half the size of a semitone. The term was used by some 17th- and 18th-century theorists to denote the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g. D♯–E♭). In most contexts, however, it refers to an interval of of an octave, or 50 cents.

Quarter-tones form part of the enharmonic genus of ancient Greek music theory (see Greece §I, and Diesis); they have also been discussed in the context of medieval plainsong (see Gmelch), and were considered by Hothby in the late 15th century (see Reaney) and by Coprario in the early 17th (see Field). Interest in them increased steadily during the 19th and 20th centuries. The ‘Aphorismen’ of Heinrich Richter, published in 1823 under the pseudonym ‘Amadeus Autodidactos’, ventured to propogate quarter-tone music, and Johanna Kinkel urged the emancipation of the interval in her essay of 1853. The Russian futurist painter Mikhail Matyushin (...



Richard L. Crocker

(Gk.: ‘song’)

A group of more than five or six notes sung to a single syllable. The term may be applied universally, but has been most used in reference to medieval European music, particularly chant. ‘Melismatic’ indicates one end of a spectrum; the other is ‘syllabic’, or one note to each syllable. An intermediate category, with several notes to a syllable, is sometimes termed ‘neumatic’.

The word ‘melisma’ existed in ancient Greek but was not much used; it meant, vaguely, ‘song’, and conveyed none of the sense given above. (Liddell and Scott’s Greek–English Lexicon cites one instance in which it meant ‘lyric poetry’.) The current technical meaning seems to have been superimposed upon the word by German scholars in an effort to create a term for what was a puzzling feature of Gregorian chant. In the latter context the term has been used in two ways that are distinct but closely related through a characteristic train of thought. The meaning that is logically first is abstract and generic, easier to grasp in German than in English: ...



Miloš Velimirović

(Gk.: ‘sound’)

A technical term in Byzantine chant, usually translated ‘mode’ or ‘modality’.

There is considerable difference between the Eastern and Western European understanding of modality. In the West, the term ‘mode’ most often means a scale or ‘octave species’; but an ēchos depends rather on a ‘mood’, which is in turn dependent on the types of melody found in that ēchos. When systematized by theorists, these melody-types do produce different ‘octave species’ or scales; this is of secondary significance, however, compared to the melodies themselves. An ēchos in fact consists primarily of a repertory of melodic formulae together with some melodic motifs and even melody-types.

These categories overlap at times: a melody-type may be a melodic formula, but a melodic formula may be only part of a melody-type. The motif is the smallest of these units and occurs as a subdivision of the larger structural elements, the formula and the melody-type, the latter being the largest of the three. Some of these elements may appear exclusively in a single ...


Mark Lindley


When pitch can be intoned with a modicum of flexibility, the term ‘just intonation’ refers to the consistent use of harmonic intervals tuned so pure that they do not beat, and of melodic intervals derived from such an arrangement, including more than one size of whole tone. On normal keyboard instruments, however, the term refers to a system of tuning in which some 5ths (often including D–A or else G–D) are left distastefully smaller than pure in order that the other 5ths and most of the 3rds will not beat (it being impossible for all the concords on a normal keyboard instrument to be tuned pure; see Temperaments, §1). The defect of such an arrangement can be mitigated by the use of an elaborate keyboard.

In theory, each justly intoned interval is represented by a numerical ratio. The larger number in the ratio represents the greater string length on the traditional ...


M. Jennifer Bloxam

(Lat.: ‘fixed melody’; Ger. fester Gesang; It. canto fermo)

A term, associated particularly with medieval and Renaissance music, that designates a pre-existing melody used as the basis of a new polyphonic composition. The melody may be taken from plainchant or monophonic secular music, or from one voice of a sacred or secular polyphonic work, or it may be freely invented. Cantus firmus composition is now understood to encompass a wide range of rhythmic and melodic treatments of an antecedent tune within a new polyphonic texture.

Early theorists used the term ‘cantus firmus’, in both its Latin and its Italian forms, with a variety of related meanings. Frobenius identified three broad stages in its usage:

(1) From the 13th century to the 17th the term had three related meanings. The original one, used by theorists from Boncampagno da Signa (Rhetorica novissima, 1235) to Zarlino (Le istitutioni harmoniche, i, 1558) and Forkel (Allgemeine Geschichte der Musik...


Gordon A. Anderson

revised by Edward H. Roesner

[Ars Veterum, Ars Vetus] (Lat.: ‘old art’)

A term used by a group of writers, mostly active in Paris in the early 14th century, to distinguish the polyphony and notation of the immediate past from the new practice of their own time, the Ars Nova (Ars Modernorum), especially that associated with Philippe de Vitry, Johannes de Muris and their circle in the 1310s and 20s. (The word ‘ars’, as understood in the Middle Ages, translates the Greek word technē, a ‘technique’ or ‘craft’, and has no aesthetic connotations.)

Among music theorists, the champion of the Ars Antiqua was Jacobus of Liège, who in his encyclopedic Speculum musice (1320s) upheld the authority of Franco of Cologne, Magister Lambertus (whom he called ‘Aristotle’) and Petrus de Cruce, and while criticizing the moderns defined the main virtues of the old practice: (1) modern composers wrote only motets and chansons, neglecting other genres such as organum, conductus and hocket (CSM, iii/7, p.89); (2) modern composers used a multiplicity of imperfect mensurations alongside perfect ones in their work, whereas the old practice, following Franco and Lambertus, adhered exclusively to perfection (CSM, iii/7, pp.86–8); (3) the moderns divided semibreves into smaller values, perfect and imperfect groups of minims and semiminims, whereas the followers of the Ars Antiqua divided breves only into semibreves in perfect mensuration, holding that the semibreve was indivisible (CSM, iii/7, pp.35–6, 51–3); (4) as a consequence, paradoxically, the rhythmic language used by the moderns was much more limited and inflexible than that of the adherents to the old practice (CSM, iii/7, pp.38–9); (5) the moderns engaged in a great deal of experimentation with notation, resulting in an inconsistent practice, whereas the followers of Franco had a clear and established tradition for notating their music (CSM, iii/7, pp.51–3); (6) the moderns indulged too much in quirky and capricious rhythmic movement,...



Harold S. Powers, Frans Wiering, James Porter, James Cowdery, Richard Widdess, Ruth Davis, Marc Perlman, Stephen Jones, and Allan Marett

(from Lat. modus: ‘measure’‘standard’ ‘manner’‘way’)

A term in Western music theory with three main applications, all connected with the above meanings of modus: the relationship between the note values longa and brevis in late medieval notation; interval, in early medieval theory; and, most significantly, a concept involving scale type and melody type. The term ‘mode’ has always been used to designate classes of melodies, and since the 20th century to designate certain kinds of norm or model for composition or improvisation as well. Certain phenomena in folksong and in non-Western music are related to this last meaning, and are discussed below in §§IV and V. The word is also used in acoustical parlance to denote a particular pattern of vibrations in which a system can oscillate in a stable way; see Sound, §5, (ii). For a discussion of mode in relation to ancient Greek theory see Greece, §I, 6.

Harold S. Powers, revised by Frans Wiering...


Ian D. Bent

revised by Anthony Pople

A general definition of the term as implied in common parlance might be: that part of the study of music that takes as its starting-point the music itself, rather than external factors. More formally, analysis may be said to include the interpretation of structures in music, together with their resolution into relatively simpler constituent elements, and the investigation of the relevant functions of those elements. In such a process the musical ‘structure’ may stand for part of a work, a work in its entirety, a group or even a repertory of works, in a written or oral tradition. The relationship between the structures and elements proposed by analysis, and experiential, generative and documentary perspectives on music, has circumscribed analysis differently from time to time and from place to place, and has aroused debate. Less controversially, a practical distinction is often drawn between formal analysis and stylistic analysis; but this is unnecessary insofar as on the one hand any musical complex, no matter how small or large, may be deemed a ‘style’; and on the other hand, all the comparative processes that characterize stylistic analysis are inherent in the basic analytical activity of resolving structures into elements....


Nors S. Josephson

(Lat.: ‘more subtle art’) The highly refined musical style of the late 14th century, centred primarily on the secular courts of southern France, Aragon and Cyprus. The term was introduced to musicological vocabulary by Ursula Günther and derives from references in (?)Philippus de Caserta's Tractatus de diversis figuris to composers moving away from the style of the Ars Nova motets ‘post modum subtiliorem comparantes’ and developing an ‘artem magis subtiliter’ as exemplified in the motet Apta caro (CoussemakerS, iii, 118); similarly Egidius de Murino referred to composition ‘per viam subtilitatis’ in his Tractatus cantus mensurabilis (CoussemakerS, iii, 127). The development of the idiom (chiefly encountered in grandes ballades) may be traced in successive, roughly chronological stages. Of these, the post-Machaut generation – De Landes, Franciscus, Grimace, Pierre de Molins, Solage, Susay (A l'arbre sec) and Vaillant – was largely engaged in developing the classical ballade style of Machaut....


Mark Lindley

Tunings of the scale in which some or all of the concords are made slightly impure in order that few or none will be left distastefully so. Equal temperament, in which the octave is divided into 12 uniform semitones, is the standard Western temperament today except among specialists in early music. This article traces the history of temperaments in performing practice and in relation to the main lines of development in the history of harmony; for additional technical and historical details see Tuning, Pythagorean intonation, Just intonation, Microtone, Mean-tone, Well-tempered clavier, Equal temperament and Interval, especially Table 1.

Since the 15th century, tempered tuning has characterized keyboard music and in Western culture the art music of fretted instruments such as the lute. Its prevalence is due mainly to the fact that the concords of triadic music – octaves, 5ths and 3rds – are in many cases incommensurate in their pure forms. Three pure major 3rds (e.g. A♭–C–E–G♯) fall short of a pure octave by approximately one fifth of a whole tone (lesser diesis); four pure minor 3rds (G♯–B–D–F–A♭) exceed an octave by half as much again (greater diesis); the circle of twelve 5ths, if the 5ths are pure, does not quite cumulate in a perfect unison; and, most important of all in the context of Renaissance and Baroque music, the whole tone produced by subtracting a pure minor 3rd from a pure 4th (C–F–D) is about 11% smaller than the whole tone produced by subtracting a pure 4th from a pure 5th (C–G–D). These discrepancies are summarized in ...


Peter Jeffery

(Gk.: ‘eightfold sound’)

The system of the eight ‘church modes’ (the ‘musical’ oktōēchos) in the medieval Latin, Byzantine, Slavonic, Syrian, Armenian and Georgian repertories of Christian liturgical chant. Also, by association, the practice of grouping chants by mode (the ‘calendric’ oktōēchos) so that they can be sung in numerical order over a period of time, usually one mode per week, proceeding to the next higher number each Sunday and beginning with the 1st mode again when the 8th is completed. And a book (the ‘liturgical’ oktōēchos) in which the chant texts are grouped by mode in numerical order to facilitate performance according to the calendric oktōēchos (see Liturgy and liturgical books, §IV, 3, (viii)); books also exist in which chants are arranged according to mode but without regard to a calendar, notably the Western Tonary and the Byzantine Heirmologion).

Although many theories regarding the origins of the eight-mode system have been proposed, the earliest genuine evidence of the musical ...


Giselher Schubert

(b Hanau, nr Frankfurt, Nov 16, 1895; d Frankfurt, Dec 28, 1963). German composer, theorist, teacher, viola player and conductor. The foremost German composer of his generation, he was a figure central to both music composition and musical thought during the inter-war years.

Hindemith descended on his father’s side from shopkeepers and craftsmen who had settled primarily in the small Silesian community of Jauer (now Jawor, Poland), where the family can be traced back to the 17th century, and on his mother’s side from small farmers and shepherds in southern Lower Saxony. While no signs of musical interest can be found among the relatives of his mother, Maria Sophie Warnecke (1868–1949), his father, Robert Rudolf Emil Hindemith (1870–1915), came from a family of music lovers. Robert Rudolf supposedly ran away from home when his parents opposed his wish to become a musician; after arriving in Hesse, however, he became a painter and decorator. As he was never able to provide a secure income for his family, the Hindemiths were forced to move frequently. Paul spent three years of his childhood with his paternal grandfather in Naumburg. He was sincerely devoted to his mother, whom he is said to have resembled closely, even in similarity of gestures, and dedicated the first volume (...


(Franz Walter)

(b Vienna, Sept 13, 1874; d Los Angeles, July 13, 1951). Austro-Hungarian composer.

His father Samuel (1838–89) was born in Szécsény, his mother (née Nachod, 1848–1921) in Prague. They came to Vienna from Pressburg (Bratislava). Schoenberg accordingly inherited Hungarian nationality, which was converted to Czech on the formation of the state of Czechoslovakia in 1918. He became an American citizen in 1941. The family was Jewish, and the three children, Arnold, Ottilie and Heinrich, were brought up in the orthodox faith. Neither parent was particularly musical; Schoenberg remembered his uncle Fritz Nachod, who wrote poetry and taught him French, as the main cultural influence of his childhood. But his sister and brother showed musical talent, and the latter, like their cousin Hans Nachod, became a professional singer. Schoenberg’s musical education began when he was eight with violin lessons, and he very soon began composing by the light of nature, imitating the violin duets by such composers as Pleyel and Viotti that he was given to learn, and arranging anything that came his way – operatic melodies or military band music – for the same combination. Somewhat later, having met a schoolfellow who played the viola, he was able to spread his wings to the point of writing trios for two violins and viola....