A trope or tropus may refer to a variety of different concepts in medieval, 20th-, and 21st-century music.
The term trope derives from the Greek τρόπος (tropos), "a turn, a change", [1] related to the root of the verb τρέπειν (trepein), "to turn, to direct, to alter, to change". [2] The Latinised form of the word is tropus.
In music, a trope is adding another section, or trope to a plainchant or section of plainchant, thus making it appropriate to a particular occasion or festival.
From the 9th century onward, trope refers to additions of new music to pre-existing chants in use in the Western Christian Church. [3]
Three types of addition are found in music manuscripts:
In the Medieval era, troping was an important compositional technique where local composers could add their own voice to the body of liturgical music. These added ideas are valuable tools to examine compositional trends in the Middle Ages, and help modern scholars determine the point of origin of the pieces, as they typically mention regional historical figures (St. Saturnin of Toulouse, for example, would appear in tropes composed in Southern France). Musical collections of tropes are called tropers.[ citation needed ]
Tropes were a particular feature of the music and texts of the Sarum Use (the use of Salisbury, the standard liturgical use of England until the Reformation), although they occurred widely in the Latin church. Deus creator omnium, was widely used in the Sarum Use and is in the form of a troped Kyrie:[ citation needed ]
Deus creator omnium, tu theos ymon nostri pie eleyson,
tibi laudes coniubilantes regum rex magne oramus te eleyson,
laus, virtus, pax et imperium cui est semper sine fine eleyson,
Christe, rex unice, patris almi nate coeterne eleyson,
qui perditum hominem salvasti, de morte reddens vite eleyson
ne pereant pascue oves tue Jesu, pastor bone, eleyson.
Consolator spiritus supplices ymas te exoramus eleyson.
Virtus nostra domine atque salus nostra in eternum eleyson,
summe deus et une, vite dona nobis tribue misertus nostrique tu digneris eleyson. [4]
O God creator of all things, thou our merciful God eleyson,
we pray to thee, O great king of kings, singing praises together to thee eleyson,
to whom be praise, power, peace and dominion for ever without end eleyson,
O Christ, sole king, O Son coeternal with the kind Father eleyson
who saved mankind, being lost, giving life for death eleyson
lest your pastured sheep should perish, O Jesus, good shepherd eleyson.
Consoler of suppliant spirits below, we beseech thee eleyson,
O Lord, our strength and our salvation for eternity eleyson,
O highest God, grant to us the gifts of eternal life and have mercy upon us eleyson. [5]
The standard Latin-rite ninefold Kyrie is the backbone of this trope. Although the supplicatory format ('eleyson'/'have mercy') has been retained, the Kyrie in this troped format adopts a distinctly Trinitarian cast with a tercet address to the Holy Spirit which is not present in the standard Kyrie. Deus creator omnium is thus a fine example of the literary and doctrinal sophistication of some of the tropes used in the Latin rite and its derived uses in the mediæval period.
In certain types of atonal and serial music, a trope is an unordered collection of different pitches, most often of cardinality six (now usually called an unordered hexachord, of which there are two complementary ones in twelve-tone equal temperament). [6] Tropes in this sense were devised and named by Josef Matthias Hauer in connection with his own twelve-tone technique, developed simultaneously with but overshadowed by Arnold Schoenberg's.
Hauer discovered the 44 tropes, pairs of complementary hexachords, in 1921, allowing him to classify any of the 479,001,600 twelve-tone melodies into one of 44 types. [7]
The primary purpose of the tropes is not analysis (although it can be used for it) but composition. A trope is neither a hexatonic scale nor a chord. Likewise, it is neither a pitch-class set nor an interval-class set. A trope is a framework of contextual interval relations. Therefore, the key information a trope contains is not the set of intervals it consists of (and by no means any set of pitch-classes), it is the relational structure of its intervals. [8]
Each trope contains different types of symmetries and significant structural intervallic relations on varying levels, namely within its hexachords, between the two halves of an hexachord and with relation to whole other tropes.
Based on the knowledge one has about the intervallic properties of a trope, one can make precise statements about any twelve-tone row that can be created from it. A composer can utilize this knowledge in many ways in order to gain full control over the musical material in terms of form, harmony and melody.
The hexachords of trope no. 3 are related by inversion. Trope 3 is therefore suitable for the creation of inversional and retrograde inversional structures. Moreover, its primary formative intervals are the minor second and the major third/minor sixth. This trope contains [0,2,6] twice inside its first hexachord (e.g. F–G–B and G♭–A♭–C and [0,4,6] in the second one (e.g. A–C♯–D♯ and B♭–D–E). Its multiplications M5 and M7 will result in trope 30 (and vice versa). Trope 3 also allows the creation of an intertwined retrograde transposition by a major second and therefore of trope 17 (e.g., G–A♭–C–B–F–F♯–|–E–E♭–C♯–D–B♭–A → Bold pitches represent a hexachord of trope 17). [9]
In general, familiarity with the tropes enables a composer to precisely predetermine a whole composition according to almost any structural plan. For instance, an inversional twelve-tone row from this trope 3 (such as G–A♭–C–B–F–F♯–D–C♯–A–B♭–E–D♯) that is harmonized by the [3–3–3–3] method as suggested by Hauer, will result in an equally inversional sequence of sonorities. This will enable the composer, for example, to write an inversional canon or a mirror fugue easily (see example 1). The symmetry of a twelve-tone row can thus be transferred to a whole composition likewise. Consequently, trope technique allows the integration of a formal concept into both a twelve-tone row and a harmonic matrix—and therefore into a whole musical piece. [10]
In music, a tone row or note row, also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.
In musical notation, an accidental is a symbol that indicates an alteration of a given pitch. The most common accidentals are the flat and the sharp, which represent alterations of a semitone, and the natural, which cancels a sharp or flat. Accidentals alter the pitch of individual scale tones in a given key signature; the sharps or flats in the key signature itself are not considered accidentals.
In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions, such as duration, dynamics, and timbre.
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.
In music theory, a trichord is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.
In music, the mystic chord or Prometheus chord is a six-note synthetic chord and its associated scale, or pitch collection; which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin. Scriabin, however, did not use the chord directly but rather derived material from its transpositions.
In music, a hexachord is a six-note series, as exhibited in a scale or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ and χορδή, and was also the term used in music theory up to the 18th century for the interval of a sixth.
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."
In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.
In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation, or multiplicative operations. These may produce reorderings of the members of the set, or may simply map the set onto itself.
Josef Matthias Hauer was an Austrian composer and music theorist. He is best known for developing, independent of and a year or two before Arnold Schoenberg, a method for composing with all 12 notes of the chromatic scale. Hauer was also an important early theorist of twelve-tone music and composition.
Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and vice versa. This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone row successively, "[t]he inversion of the prime series in reverse order from last pitch to first."
A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.
An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords, when expressed in prime form. In set theory notation, these are [0,1,4,6] (4-Z15) and [0,1,3,7] (4-Z29). Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b). The interval vector for all all-interval tetrachords is [1,1,1,1,1,1].
Fritz Heinrich Klein was an Austrian composer.
In music, the "Ode-to-Napoleon" hexachord is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonaparte Op. 41 (1942) by Arnold Schoenberg. Containing the pitch-classes 014589 it is given Forte number 6–20 in Allen Forte's taxonomic system. The primary form of the tone row used in the Ode allows the triads of G minor, E♭ minor, and B minor to easily appear.
In music, an all-interval twelve-tone row, series, or chord, is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11. A "twelve-note spatial set made up of the eleven intervals [between consecutive pitches]." There are 1,928 distinct all-interval twelve-tone rows. These sets may be ordered in time or in register. "Distinct" in this context means in transpositionally and rotationally normal form, and disregarding inversionally related forms. These 1,928 tone rows have been independently rediscovered several times, their first computation probably was by Andre Riotte in 1961.
In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. For example, zero through five and six through eleven. On C:
A Sermon, a Narrative and a Prayer is a cantata for alto and tenor singers, a narrator, chorus, and orchestra by Igor Stravinsky, composed in 1960–61. It belongs to the composer’s serial period, and lasts a little over a quarter of an hour in performance.
The tone clock, and its related compositional theory tone-clock theory, is a post-tonal music composition technique, developed by composers Peter Schat and Jenny McLeod. Music written using tone-clock theory features a high economy of musical intervals within a generally chromatic musical language. This is because tone-clock theory encourages the composer to generate all their harmonic and melodic material from a limited number of intervallic configurations. Tone-clock theory is also concerned with the way that the three-note pitch-class sets can be shown to underlie larger sets, and considers these triads as a fundamental unit in the harmonic world of any piece. Because there are twelve possible triadic prime forms, Schat called them the "hours", and imagined them arrayed in a clock face, with the smallest hour in the one o'clock position, and the largest hour in the 12 o'clock position. A notable feature of tone-clock theory is tone-clock steering: transposing or inverting hours so that each note of the chromatic aggregate is generated once and once only.
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