chord , harmony, IPN, interval, interval-class (ic). key, melody, meter, mode, note, pitch, pitch-class (pc), rhythm, series, set, tonic

The level at which each concept is most often introduced is indicated by the numbers 0-4 in brackets, where 0 is pre-college level, 1-4 are various levels of undergraduate theory, and 5 is graduate level. Names of the originators of recent terms, when known, are indicated in parentheses.

* A note about set-theory: This field is divided into two branches: linear and nonlinear. It is important to keep these separate since many of the tenets of one do not apply to the other, even though they use much of the same vocabulary. Linear set-theory deals primarily with melodic lines and tone rows, i.e. pitch-class-sets that have a linear order. Nonlinear set-theory deals primarily with harmony, where the order of notes, e.g. within a chord, rarely matters. Thus, it treats them as a "simultaneous unit", like a triad.

The glossary shows which terms are applicable to which branch of set-theory, indicated (set-theory, nonlinear) or (set-theory, linear). In some cases a term is used by both, indicated (set-theory).

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absolute music. [3] music which has no associations outside itself; it has no text, and does not attempt to narrate a story, portray characters, events, impressions, etc.; e.g., Bach's fugues.

action-notation. [4] musical notation that directs the performer in a course of action without indicating the resulting sound. Syn. process-notation; e.g., John Cage's 4'33".

-ad. suffix (set-theory, nonlinear) ; [4] a set of pitch classes, the prefix of which indicates the number of pitch classes; e.g. dyad, hexad, pentad. However, the term triad has come to have a special meaning.

a cappella. [1,2] purely vocal (or choral) music, without instrumental accompaniment.

accidentals. [0] signs used in musical notation to alter notes, e.g. sharps (#), flats, naturals; however, accidentals are not key signatures.

Aeolian-mode. [0,1] a mode consisting of T-S-T-T-S-T-T (T=whole-tone, S=semitone), equivalent to the natural-minor mode. Note the difference between mode and scale.

aggregate. [4] (set-theory, linear) 1. any combination of all twelve pcs. 2. (Babbitt) a vertical combination of hexachords or smaller sets found in the use of combinatorial rows.

Alberti-bass. [0,1] a special type of chord figuration that alternates 1 5 3 5 and repeats as an accompaniment figure. It is very common in the music of the 18th century Classical style and is named after the composer Domenico Alberti, who used it frequently.

aleatory. [4] (Boulez) the European term for chance music. John Cage is the primary proponent of the use of chance in musical composition. The meaning of aleatory, however, is different from chance. Aleatory, which was a European adoption of American chance, implies the use of chance with selected aspects of control; thus, aleatory was considered, by Cage, to be a corruption of chance. The correspondence of Cage and Boulez is particularly enlightening about this. "Alea" was the original term used by Boulez in an essay he wrote which criticized the use of chance in musical composition, referring to, without naming, the practice of John Cage. Aleatory is also often mistakenly confused with indeterminacy, which refers to performance practice, rather than to composition. It is sometimes confused with improvisation, as well.

algorithm. [5] (mathematics) a repeatable series of steps used to solve problems, etc., e.g., a computer program or a process used to analyze music. The manual analysis of music using a repeating series of steps is also an algorithm.

all-combinatorial. [5] (Babbitt) (set-theory, linear) a set in which any of its transformations (P, I, R, RI and their transpositions), may occur simultaneously with any other transformation without duplicating pitch-classes (pc) before all twelve pcs have occurred.

all-interval-chord or all-interval-set. [5] (set-theory, nonlinear) a chord that contains one of each interval-class, i.e., 0146 (4-Z15), which has the interval-vector (iv), 111111.

all-interval-row. [5] (set-theory, linear) (a) a twelve-tone-row that contains all eleven directed-intervals (DI); e.g., in Alban Berg's Lyric Suite, f,e,c,a,g,d,g#,c#, d#,f#,a#,b, the DIs are: 11,8,9,10,7,6,5,2,3,4,1.

altered-chord. [3] see chromatic-chord.

alto-clef. [0,1] a C-clef that is placed so that middle C is the middle line of the staff. It is used for instruments that have an alto range, especially the viola.

ambiance or ambience. [0,4] the background noise or environmental sound.

ambit. [0] the range of pitches . It is suggested here that the International Pitch Notation, or IPN, (after the Acoustical Society of America) be the standard (A4=A440).

ametric. [4] without meter. Gregorian chant is an example of music without a meter. Metrical music became the norm after the Middle ages, although some ametrical music also occurs in the 20th century; e.g., Ives's The Cage.

anhemitonic. [4] a scale or set that lacks semitones. The "black key" pentatonic is an example.

Anstieg. [5] (Schenker: ascent) (English: mounting) the initial stepwise ascent to a tone of the tonic (3,5, or 8) where the descent in the Urlinie begins (see also Kopfton).

antimusic. [4] music in which the purpose is to overthrow conventional associations, stereotypes, or expectations, e.g., Satie's Vexations.

appoggiatura. [1] a nonharmonic-tone that is approached by leap and resolved by step, normally in the opposite direction.

arch-form. [4] a musical form that is symmetric in time and climaxes in the middle.

architectonic. [1] (literally, the architecture of music); formal structure in which large scale aspects echo small scale structures, particularly the organization of structures within structures; e.g. a binary subject in a binary form.

arpeggio. [0] a chord that is played one note at a time, rather than as simultaneous tones.

array. [4] (set-theory, linear) an arrangement of a series according to its quantitative values, i.e., smallest to largest; e.g., the interval vector.

articulation. [0,1] the manner in which notes are struck, sustained, and released. This includes legato, staccato, tenuto, etc.

atonal. [0,1] having no tonal-center, hence no key; syn. pantonal.

atonality. [0,1] noun for atonal.

attack. [0,1] the inception of a sound.

auditory-perspective. [4] the perception of the physical, geometrical location of sound sources.

Aufhaltung. [5] (Schenker: delay) a prolongation before scale step #2 (part of the dominant chord) in the Ursatz that delays the occurrence of that scale step.

augmentation. [1,2] a thematic variant that is played slower than the original theme.

augmented-sixth chords. [3] tertian chromatic-chords that evolved from the minor key and normally appear in first-inversion. They can be spelled in thirds based on the second or raised fourth degree of the key, e.g. F# A-flat C in the key of C; thus the "root" is commonly chromatic. This chord would occur in first-inversion as A-flat C F#, and is called the Italian-augmented-sixth, which is enharmonic to an incomplete dominant-seventh chord. All augmented-sixth chords contain the interval of the augmented sixth or its inversion, the diminished third. Two other forms are common. One is the "German-sixth", e.g. F#, A-flat, C, E-flat, which has simply added the seventh to the "Italian-sixth". It is enharmonic to the dominant-seventh chord. The last form is the "French-sixth", e.g. D, F#, A-flat, C, another altered seventh chord. They all normally resolve to a dominant-function chord, hence their true function is revealed as basically subdominant or supertonic, dominant-preparation chords.

Ausfaltung. [5] (Schenker: unfolding) a prolongation by means of the unfolding of intervals horizontally.

Auskomponierung. [5] (Schenker: composing out) the unfolding of the tonic triad as the fundamental structure of a tonal work. According to Schenker, the first stage of composition consists of the Ursatz, or "fundamental structure". Latter stages are achieved by various means of prolongation.

Auswicklung. [5] (Schenker: unravelling) the unravelling of intervals or chords in the Middleground levels.

authentic-cadence. [0,1] a cadence harmonic formula consisting of a stop on tonic chord preceded by a dominant-function chord; e.g., V I, or vii6 I.

avant-garde. [4] a style or music considered to be experimental or advanced.

axis. [4] (set-theory) a line or point used as a divider in a symmetric operation. Axes can exist in time, pitch, or other dimensions. e.g. a melodic inversion resulting from a reflection transformation around an axis of pitch. e.g. an upward line: c,e,f,f# can be reflected downward with an axis on c as c,a-flat,g,g-flat. If the axis were c# the inversion would be d, b-flat,a, a-flat.

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Background. (Schenker: Ursatz) [3,5] the most fundamental structural framework of a musical composition. Frequently, this takes the form of I V I in the fundamental bass (Bassbrechung) motion, combined with scale steps 3-2-1 or 5-4-3-2-1 or 8-7-6-5-4-3-2-1 in the principal voice or Urlinie.

basic-interval-pattern. [5] (set-theory, nonlinear) abbrev. bip (Forte). the normal-order of an interval-class set.

bass. [0] the lowest pitch, or the lowest note. Notice that bass is not the same as root, tonic, or fundamental, and that bass is a pitch, not a pitch-class.

bass-arpeggiation. [5] (Schenker: Bassbrechung). the fundamental bass movement in a composition, normally the roots of I V I.

Bassbrechung. [5] (Schenker: bass-arpeggiation) the fundamental bass-arpeggiation of a composition, normally the roots of I V I.

basso-continuo. [1,2] literally, continuous bass; a Baroque practice in which a bass line mechanically keeps the beat as well as supplying the foundation of the harmony.

beats. 1. [0,1] a constant unit of time that forms a background clock in music. 2. [1] difference tones whose frequency difference is below 20 Hz, resulting in separate pulses rather than a "tone". These are often used in tuning instruments.

beat-frequencies. [1] a difference-tone where the difference in two frequencies is 20 Hz or less.

best-normal-order (Forte) (set-theory, nonlinear), abbrev. BNO. [5] the most compact form chosen from a set and its inverse (see normal-order). Forte uses the BNO to the exclusion of normal-order, e.g. in his list of all sets in Appendix I of The Structure of Atonal Music (1973), thereby making no distinction between major and minor chords. I.e., C E G, a major chord, has a normal-order of 047 but C, E-flat, G (minor and the inverse of 047) has a normal-order of 037. In Forte's system there is no distinction -- both are 037, identified with the set-name 3-11 (there is no 047 in his list). Solomon (Interface, Vol. 11/2, 1982) proposes a new list that includes the inverse forms; the major chord is named 3-11B.

bimodality. [4,5] the simultaneous use of two modes.

binary. [0,1] a two part form, normally A B. Usually these parts are repeated, hence ||: A :||: B :|| or A A B B, and the first part normally moves from the tonic to the dominant, either as a half cadence or as a modulation. In a minor piece the change is normally from tonic to the relative major key. The second part then moves back to the tonic. Each part is normally subdivided into binary as well. With a four measure phrase as a basic unit, the simplest binary pieces consist of an 8-measure A section and an 8-measure B section with each section repeated. Each of these is subdivided into two 4-measure phrases. A special type of binary, the rounded-binary is very important in music, and is the proto-sonata form. The rounded-binary has the same structure as the simple binary with a repetition of part, or all, of A at the end of B. The binary form is normally an "open" form, which means that the sections are dependent upon one another. This is due mainly to the motion away from the tonic, e.g. cadencing on the dominant at the end of A. Thus, section-A sounds incomplete by itself.

block-chord. [0] an unbroken chord.

blues-progression. [4] a twelve bar sequence of seventh-chord changes in jazz based on I, IV, and V chords (there may be three or more chords). Two common progressions are I, I, I, I, V, V, I, I, IV, V, I, I and I, I, I, I, IV, IV, I, I, V, IV, I, I (all the chords add the seventh). However, other variants are possible.

blues-scale. [4] normally C, D, E-flat, E, F, F#, G, A, B-flat, C. This scale is very common in jazz.

borrowed-chord. [3] a chord that is taken from the parallel major or minor key.

Brechung. [5] (Schenker: arpeggiation)

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cadence. [0,1] a pause or stopping point. Often cadences are associated with harmonic or melodic formulae; e.g., an authentic cadence is a stop with the chords V to I. A "Landini cadence" is a melodic formula that proceeds as 8-7-7-6-8 (scale degrees).

cambiata. [1,2] also known as changing-tones; a pair of nonharmonic-tones separated by the interval of a third, approached stepwise and resolved to the note in between the third.

canon. [2] a contrapuntal form defined by continuous imitation.

cantus-firmus. [1] ("firm song") an unchanging melody that is used as the basis for a composition -- originally was Plainchant.

cardinality. [4] (set-theory, nonlinear) the number of pcs in a pc-set, e.g. C,E,G,C,G is a set of cardinality 3, since there are only three different pitch-classes in this set.

cell. [4] (set-theory) a small set used as a structural building block. e.g. a,c,c# in Scriabin's op. 74, no.4. Most often this is a pc-set used vertically (harmonically) or horizontally (melodically).

chance-music. [4] music composition in which chance or random operations play some role (through composition or performance). Chance is sometimes confused with aleatory (see aleatory), a European term that uses controls. It is also often confused with indeterminacy, which refers primarily to a performance outcome rather than to composition. However, compositions are called indeterminate when they allow strongly divergent performances.

changing-tones. see cambiata.

chorale. [1] a German protestant hymn.

chord-progression. [1] a series of chords that strengthens a key. The opposite is called a retrogression.

chord. [0,1] three or more pitch-classes considered simultaneously. A chord must have at least three pcs in it, but these may or may not sound simultaneously; e.g., in a "broken chord" or arpeggio. A broken-chord is, nonetheless, a chord because its content is considered together as a group. Memory plays a part in the perception of arpeggiated chords.

-chord. suffix used with an appropriate prefix to designate a specific number of pitch classes considered to be a structural unit, e.g. dichord, trichord, tetrachord, hexachord, etc..

chord-structure. [4,5] (Solomon) a cyclically ordered DIC set contained in a chord that cycles to the octave; the proto-structure of a chord may be determined by first placing it in prime-form; e.g. a major chord, C E G, contains the DIC set 4,3,5 (semitones) as a triad, cycling back to the octave (C<4>E<3>G<5>C). In first inversion it is 3,5,4 (E G C E), and in second inversion it is 5,4,3 (G C E G). Notice that the complete chord structure fills an octave.

chord-tone. see: harmonic-tone.

chromatic. [0,1] 1. pitches outside the prevailing key. 2. different notes with the same letter names, e.g. F and F#. Most scales contain all seven different letter names; thus, chromatic-notes are those outside of the key. See also: chromatic-semitone and chromatic-scale.

chromatic-chord. [1] a chord whose notes have been changed from diatonic to chromatic, i.e., chords containing notes outside of the key. E.g., a iv6 can be altered to an "Italian" augmented-sixth chord by raising the root. Chromatic chords usually evolve from the contrapuntal, linear structure of music.

chromatic scale. [0] a scale containing twelve equal divisions of the octave. Such a scale must contain notes of the same letter name, and, thus is chromatic.

chromatic-semitone. [0] a half-step notated with the same letter name; e.g. C, C#.

clef. [0] a sign that normally occurs at the beginning of each staff to refer a particular staff line to a specific pitch; e.g. a G clef, or treble clef, indicates middle G (G4) as the second line. A bass clef, or F clef, indicates F-below-middle-C (F3) as the fourth line. See also International Pitch Notation.

close position. [1] voicing of a chord where there is less than an octave between the soprano and tenor voices in a four-part setting.

closure-property. [5] (Forte) (set-theory, nonlinear) a property in which every member of a complex is a subset or a superset of every other member.

color. see tone-color.

combination tone. [4] (syn. difference tones) a frequency that is heard as the difference in two frequencies.

combinatorial/combinatoriality. [4,5] (Babbitt) (set-theory, linear) the special capability of combining various row transformations, simultaneously, without duplications of pcs before all 12 pcs have occurred -- that one nonlinear segment of a row can be mapped into another by operations of transposition, R, I, or RI. The primary type of combinatoriality is hexachordal; e.g. the first six notes of P0 of any 12 tone row are the same as the last six notes of R0, therefore, they are combinatorial; i.e., if the two transformations are combined in a note-against-note (first species) contrapuntal texture, all 12 pcs will sound before any are duplicated. This is one of four types of combinatoriality, called retrograde-combinatoriality (Babbitt originally excluded this type, because it wasn't special). The other types are prime-combinatoriality, inversional-combinatoriality, and retrograde-inversional-combinatoriality. Special hexachords have all four types of combinatoriality, and are therefore called all-combinatorial.

common-chord. [1] a chord that is diatonic in two or more different keys; see also pivot-chord.

complement. 1. [0,1] (interval) the interval that when added to a given interval will form an octave ; e.g. minor 3rd + major 6th; also known as interval inversion; 2. [4,5] (set-theory) in set theory, the elements not in a given set. e.g. c#,d#,f#,g#,a# is the complement c,d,e,f,g,a,b and vice versa.

complex-tone. [1] a tone containing inharmonic overtones.

composite-chord-symbol. [0,1] a symbol that consists of a Roman-numeral, indicating the chord's position in the scale, and the figured-bass, indicating its inversion. For example, V6, meaning first inversion dominant.

compound-interval. [0] an interval greater than an octave.

compound-meter. [0] a meter in which each beat is divided into three pulses; for example, 6/8 contains two beats, each of which is divided into three pulses; e.g. 6/8 is a duple meter containing two groups of three eighth notes.

consecutive-octaves and fifths. [1] similar to parallel octaves and parallel fifths, except that the voices are moving in contrary motion.

consonance. [0,1] any sound that carries little or no specific expectation for its continuance, and is perceived as logical.

contour-inversion. [2] 1. (exact) reversal of interval direction. 2. (tonal) diatonic reversal of interval direction. syn. melodic inversion. E.g., c up to g may be inverted as c down to g.

contrapuntal. adjective for counterpoint.

contrary-motion. [1] part-writing where one voice moves opposite to another.

counterexposition. [4] in a fugue, a recurrence of the exposition, but with different keys and order of entrances.

counterpoint. [0,1] (adj: contrapuntal) two or more simultaneous, independent lines or voices. Counterpoint is a matter of degree. Lines or voices may move in contrary-motion for maximum pitch independence, but they may also be rhythmically different.

countersubject. [2] a line in counterpoint with the subject of a fugue which recurs when then subject returns.

coupling. [5] (Schenker: Koppelung) an octave transfer permitting a line to extend its register and prolong motion towards a goal. Hoherlegung and Tieferlegung are similar transfers, higher and lower respectively, at an interval other than an octave. However, due to their similar functions, it is here suggested that these also be classified as couplings.

crab-canon . [2] a retrograde canon. A crab canon, or canon cancrizans, has an axis of reflection at its midpoint of time, about which every event is reversed. It is, therefore, a temporal palindrome.

cross-relation. [1] a part-writing problem where two voices encounter a contradictory chromaticism, either simultaneously or in succession.

crossed-voices. [1] voicing in which the normal relative position of voices is violated, e.g., if the soprano goes below the alto, or the bass goes above the tenor.

cyclic permutation. [4] (set-theory) rotation of the order of a set by circling back to its beginning; e.g., the ordered set f#,g,a,d,e can be cycled to g,a,d,e,f# and to a,d,e,f#,g, etc. Rhythms and other parameters may be cycled; see also rotation.

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decay. [1] the aspect of the end of a sound in which the sound diminishes in loudness and into apparent silence.

deceptive-cadence. 1.[1] a cadence formula that moves from dominant to submediant, V, vi, or sometimes V, IV6. 2. any cadence in which the normal expectation is not fulfilled.

Decktone. [5] (Schenker: overlay-tones) any tones moving above the basic tones of the Urlinie, or structural-upper-line.

Delay. [5] (Schenker: Aufhaltung) a prolongation before scale step #2 (in the dominant) of the Urlinie that delays that scale step.

density. [0,1] 1. the number of different sounds at a time within a given time and spatial interval, inversely proportional to frequency and time. The triad c,e,g is relatively thin in a high register compared to the same triad in a low register, i.e., as the frequency of pitch lowers the density increases. 2. the number of different sounds within a given time.

derived-set. [4,5] (set-theory, linear) a tone-row that is constructed by symmetry operations upon a subset; e.g. the trichord G A# B can be used to create F E C# by retrograde transposition (R6), and C A G# by inversion (I4), and D D# F# by retrograde-inversion (RI7) to form the complete derived-set: G A# B F E C# C A G# D D# F#.

developing-variation. [3,4] (Schoenberg) the generation of music from a single idea, or "basic shape" (Grundgestalt), especially in tonal music after the Baroque. Previously, musical development was achieved not so much by reworking ideas but by repeating them and placing them in different contexts. After 1750, however, composers focused more on the transformation of an idea, e.g. by changing its rhythm, interval expansion, contraction, interpolation, etc. Schoenberg cites Brahms's music as the prime example of using this type of variation.

development section. a section in which subjects or themes are varied and played in counterpoint; it is also characterized by modulation.

DI. [4,5] (set-theory, linear) abbreviation for directed-interval.

diabolus in musica. (the devil in music) a melodic tritone.

diatonic-semitone. [0] a half-step with different letter names.

diatonic. [0] 1. part of the key, 2. having different letter names, e.g., C#,D.

DIC. (Solomon) [4,5] abbreviation for directed-interval-class.

difference tone. [4] (syn. combination tones) a frequency that is heard as the difference in two frequencies, also called combination-tones or beat-frequencies. Two frequencies that are very close to a unison contain beats, which are pulse-like variations. The rate of beating is determined by subtracting the two frequencies; e.g., 440 and 442 Hz will have a beat-frequency of 2 Hz. These are difference tones that are heard as beats, rather than as "tones". When the frequencies differ by 20Hz or more, the beats fuse into a tone. Thus, 440 and 330 Hz combine to create a difference tone of 100Hz.

diminution. 1. [1,2] a thematic variant which is played faster than the original theme. 2. [5] (Schenker) variation achieved by an elaboration of a basic shape, or prolongation, especially in the Foreground.

diminished-seventh chord. [0,1] a diminished chord with the added interval of the diminished-seventh.

diminished-chord. [0] a chord whose triad is diminished (consists of a minor-third and diminished-fifth).

directed-interval. [4,5] abbrev. DI (set-theory, linear); sometimes, unfortunately, shortened to simply "interval" by some contemporary theorists; the shortest distance between two linear pcs (see "linear-set") always measured in an upward direction; e.g. A to G is 10 semitones, even if the G is below the A.

directed-interval-class. [4,5] abbrev. DIC (Solomon) (set-theory, linear); the distance between two ordered pitch-classes (in semitones from 0 to 6, positive or negative); the interval-class designated by a sign for direction, e.g., the DIC from C to B is -1 and not 11 as in the DI; DIC is particularly useful for describing relationships of ordered-sets since these would appear as the same numbers with different signs, e.g., 1 and -1 rather than 1 and 11 as in the DI.

direct-octaves and -fifths. [1] motion to a perfect fifth or perfect octave in similar motion.

dissonance. [0,1] any sound that carries a special expectation for its continuance, or which is perceived to be illogical; thus, a rule or law of continuance is constructed.

Divider. [5] (Schenker: Teiler). the dominant used as a boundary before a returning tonic section.

domain. (Solomon) a harmonic function that dominates a section of music; e.g., in many works the dominant (V) is prolonged. The section where this happens would be called the dominant domain. See also Schoenberg's region.

dominant. [0] 1. the fifth degree of a scale, a perfect fifth above the tonic. 2. a chord built on the fifth scale degree.

dominant-seventh chord. [1] a seventh chord that is normally built on the fifth degree of a scale. Its structure always consists of a root, major third, perfect fifth, and minor seventh, and any chord having this structure is called a dominant seventh, whether or not it is built on the fifth scale degree.

dominant-function. [0,1] any chord or sound that implies motion to the tonic; e.g., vii6.

dominant-preparation. [1] any chord or sonority that acts as a link between the two poles of a harmonic axis and implying motion toward the pole of instability. A traditional example is the IV between I and V. See: harmonic-function.

doppler-effect. [4,5] a change in frequency due to the relative motion of the sound source and listener.

Dorian. [1,2] a mode consisting of T-S-T-T-T-S-T. (T=tone or whole-step; S=semitone or half-step).

double-counterpoint. see invertible-counterpoint.

doubling. [0,1] two or more pitches of the same pc sounding in one chord.

duple. [0] a meter consisting of alternating strong and weak beats.

duration-series. [4,5] (set-theory) an ordering of time lengths. syn., rhythmic series.

Durchgang. [5] (Schenker) a passing sonority, a chord or tone of lesser importance that acts as a bridge between two structural chords; e.g., a dominant-preparation.

dyad. [4] (set-theory) a group (set) of two pitch-classes.

dynamics. [0] 1.signs that indicate the loudness or softness of music; e.g. f = loud, p = soft, mf = medium loud. 2. the actual loudnesses and softnesses themselves.

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elision. [3,4] 1. the omission of pitches from a melodic line, thereby truncating it. 2. (Riemann) the superposition of the end of one phrase with the beginning of another, or by omission of a weak rhythmic element.

empty-set. see null-set.

enharmonic. [0] different notations of the same sound; e.g. F# and Gb.

envelope. [0,1] the shape of a loudness curve in time; normally this includes an attack, a sustain, and a decay time.

episode. in a fugue, a section in which a complete subject is absent.

equal-temperament. [1,2] the most pervasive contemporary tuning system, in which the octave is divided into twelve equal intervals, called semitones; each semitone is mathematically tuned to the twelfth root of 2.

ergodic. [5] (Tenney) a form that is static or statistically homogeneous, as in minimalism.

escape-tone. [1,2] a nonharmonic-tone that is approached by step-motion and resolved to a harmonic-tone by a leap.

etude. an instrumental exercise. Etudes are used to build up techniques on an instrument.

exposition. [1] 1. the first section of a sonata-form, in which two contrasting themes are introduced, the first in the tonic key and the second in the dominant (or relative major key if the first theme is in a minor key), 2. [4] the first section of a fugue where a subject is stated and followed by an answer on the dominant.

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Fibonacci series. [4,5] a series of integers in which each is the sum of the previous two integers, e.g., 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.

fifth-species. [2] counterpoint that uses a mix of 1:1, 2:1, 3:1, and 4:1 counterpoints.

figured-bass. [1] a notation for the intervals above the bass. They also indicate the inversion of a chord. For example, the figured bass symbol 6 indicates that there is a sixth and a third above the bass, i.e., the chord is in first inversion.

filter. [4,5] a device or process in which a band or bands of frequency are passed while other bands are blocked.

first-inversion. [1] a tertian chord whose third is in the bass.

first-species. [2] 1:1 counterpoint, i.e., note against note.

Foreground. [3,5] (Schenker: Vordergrund) the most immediate levels of musical structure, e.g. phrase , motives and all other surface detail.

Foreground-keys. [3,5] (Schenker: Scheintonarten) apparent keys of modulation taking place in Foreground layers.

form. [1] the overall structural organization of music; e.g., a piece of music that demonstrates a temporal symmetry and climaxes in the middle is usually said to be in arch form. Other standard forms include strophic, binary, ternary, sonata, rondo, and theme and variations. Contrapuntal forms include the canon and fugue.

formant. [4] a frequency band that is emphasized by the resonance of an instrument.

forms. [1] existing structural frameworks that are used to compose music; e.g. binary (AB), ternary (ABA), sonata, rondo, fugue, canon, etc.

fragmentation. [1-4] the use of a part of a melodic line instead of its entirety. It is a common technique of thematic variation.

frequency. [0] the rate of vibration, normally measured as the number of vibrations per second, a unit called Hertz, abbrev. Hz.

French-sixth. [3] an augmented-sixth chord which is a dominant-seventh with a flat-5th; i.e., D F# A-flat C in C-Major. It customarily occurs in second inversion as A-flat C D F# forming an augmented-sixth which resolves to an octave on the dominant.

fugato. [2] a fugue that is contained within a larger composition; e.g., the orchestral fugato in the final movement of Beethoven's Symphony No. 9 that follows the tenor aria.

fugue. [2] a contrapuntal form that is built from a single subject and has an exposition where all voices state the subject in turn, alternating tonic and dominant entrances. The fugue continues with various contrapuntal artifices which may include restatement of the subject, stretto, subject manipulations (fragmentation, inversion, retrograde, augmentation, etc). The fugue usually has several sections that are a combination of subject-sections, episodes, counterexpositions, stretti, etc.

fundamental. [0] 1. the lowest frequency of a tone, 2. the lowest frequency in a sound.

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genre. [1] classification of music by some combination of function, medium, form, or idiom; examples are: opera (voices, orchestra, dramatic action, staging), etude (an exercise composed for developing skills on an instrument), lullaby (song used to put one to sleep), dirge (a funeral music).

German-sixth. [3] an augmented-sixth chord that is built on the raised fourth in the key and normally occurs in first-inversion. Thus, F# A-flat C E-flat in C-Major becomes A-flat C E-flat F#, forming the augmented-sixth that resolves to an octave on the dominant. This chord is enharmonically equivalent to a dominant-seventh chord built on the minor-sixth degree of the key.

Golden-mean or -section or -ratio. [4] a mathematical proportion in which the smaller number is to the larger as the larger is to their sum. This works out to be approximately .618 :1 in practice. A number of composers and artists have used this proportion, whether consciously or not, throughout history. It is well known in architecture. Recently, the proportion has been used consciously by Stockhausen, Xenakis, Le Corbusier and others; see also Fibonacci series.

grace-note. [0,1] an auxiliary note normally written smaller than the main note that follows it. It is played just before the main note and normally subtracts from the value of the previous note or from the main note.

ground or ground-bass. [1,2] syn. basso ostinato; a series of notes that is repeated over and over again in the bass, usually a part of a theme-and-variations.

Grundgestalt. [5] (Schoenberg: basic shape) a basic structural shape that is used as a building block for a composition; similar to a motive, but which abstracts the qualities of a motive, such as rhythm, contour, intervals, harmony, etc. The basic shape is usually formed in the first two or three measures of the work.

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half-step. [0] the smallest distance between notes in a chromatic scale; syn., semitone.

half-cadence. [0,1] a cadence on the dominant.

half-diminished-seventh. [3] a chord made of a diminished triad with an added minor-seventh; e.g., B D F A.

harmonic-axis. in tonal music it is believed that tonic and dominant form the structural foundation for a key. This pair forms the harmonic axis.

harmonic-cluster. [4] a tone cluster produced by sympathetic vibration.

harmonic-function. [1] traditional harmonic theory holds that chords have "functions". These functions are believed to spring from the idea of a harmonic axis consisting of I and V. The other sonorities, or chords are considered to be substitutes for I or V, or for the IV, called the dominant preparation. The function of I is that of resolution and stability, whereas V represents instability, tension and drive.

harmonic. [0] an overtone whose frequency is equal to the fundamental frequency multiplied by an integer. A harmonic series consists of a number of harmonics ascending from the fundamental. Although all harmonics are overtones, the converse is not so.

harmonic-minor. [0] a mode consisting of T-S-T-T-S-T+S-S. See also minor.

harmonic-rhythm. [0,1] the rate of chord change. A fast harmonic rhythm occurs in the Bach chorales, usually a different chord on every beat. A slow harmonic rhythm occurs in minimal music, where a single chord can continue indefinitely. Usually, the harmonic rhythm is inversely proportional to the tempo.

harmonic-sequence. [3] a repeating pattern of root-movements manifested as a chord progression. A series of root movements down by third, for instance, is a harmonic sequence.

harmonic-series. [0] a series of partials whose frequencies are integer (whole number) multiples of the fundamental frequency. In a harmonic series the second partial is two times the frequency of the fundamental, the third partial is three times the fundamental frequency, etc.

harmonic-tone. [0,1] a pitch or note that is a part of the chord that is sounding; syn. chord-tone.

harmonization. [0,1] the choice of chords to accompany a melodic line, chosen so that the melody notes are contained in the chords.

harmony. [0,1] the sound of tones in combination. The study of harmony makes up a large part of theory courses due to its importance and complexity in our traditional music. It is sometimes considered synonymous with the study of chords and homophony.

Hauptstimme. [5] (Schoenberg) the principal or leading voice, abbreviated H in Schoenberg's scores.

hemiola. [1] a metric pattern of triple in a normally duple meter or, vice versa, a pattern of duple in a normally triple meter. Hemiola need not be confined to duple and triple meters, however. It is used applied to any type of metrical anomaly.

Hertz. [0] (abbrev. Hz) the unit of frequency, the number of vibrations per second.

heterophony. [2] a special type of monophonic texture where the voices move essentially in parallel octaves, unisons, fifths, or fourths, but one or more of the voices may be ornamented or played slightly out of time with the other voice/s.

hexachord. [0,4] (set-theory) a unit consisting of six pitch-classes, often used as segments of a twelve-tone row.

Hoherlegung. [5] (Schenker) see Coupling.

homo-. [1] (prefix) moving together.

homophony. [0,1] a type of polyphony with a predominate melody accompanied by chords.

homorhythm. [1] all voice parts moving together in the same rhythm.

Hz. Abbreviation for Hertz

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I. [2] (set-theory, linear) abbreviation for melodic-inversion (complement in set theory).

ic. [4] (set-theory) abbreviation for interval-class.

idiom. [1] any aspect of a composition that is especially adapted to, or explores, an instrument's capabilities.

idiomatic. [1] the degree of use of an instrument's special capabilities.

imitation. [1,2] one or more voices answering an initial statement by repeating a line; often occurs in imitative-counterpoint.

imitative-counterpoint. [1,2] imitation in which voices are in counterpoint with one another.

improvisation. [4] (Solomon) the spontaneous invention of music while performing it, without preconceived formulation, scoring, or content.

inclusion. (Forte) (set-theory, nonlinear). see subset.

indeterminacy. [4] any musical performance or composition where the outcome is unforeseen by the composer. Sometimes this is confused with chance or improvisation.

infra-diatonic scale. [5] (Yasser) a pentatonic scale, such as C D F G A, plus two additional degrees, e.g., E B, the latter used as embellishments of the basic scale.

inharmonic. [0,1] an overtone that does not correspond with an integer multiple of the fundamental frequency.

intensity. [0] the perceived loudness and tension (subjective).

International-Pitch-Notation (IPN). [0,1] A system of pitch designation agreed upon internationally under the auspices of the Acoustical Society of America. In this system the international standard A=440 Hz is designated A4 and middle C is C4. All pitches are designated with capital letters and their octave placement by an accompanying Arabic number changing with each octave C. Thus, the lowest C on the piano is C1 (the A below that is A0). The first F# below middle C is F#3, etc.

interpolation. [3,4] the insertion of new pitches between pitches of a given theme; inserting new elements between those of any given linear-set.

interruption. [5] (Schenker: Unterbrechung) The principle means of prolongation of the Ursatz achieved by pausing on the dominant before it continues with the fundamental line, the Urlinie. This pause is usually on the second scale degree and requires a return to the Kopfton. Most often the interruption occurs with a 3-2-1 Urlinie with a pause on the 2. The return to the Kopfton in sonata-form and in rounded-binary occurs at the beginning of the recapitulation.

intersection. [4] (set-theory) element/s (usually pitch-classes) in common.

interval. [0] the distance between two pitches or notes. Intervals may be measured in a number of ways; e.g., by counting the number of semitones, subtracting frequencies, etc. Counting semitones is used in set theory. However, the most common method is by counting letter names; e.g. C,D,E,F includes 4 letters--thus, C to F is called a fourth and is always a fourth, no matter how the notes may be altered by sharps or flats. This is called the "general size" of the interval. However, each general interval may have several "specific sizes"; e.g. a third could be major, minor, diminished, augmented, etc. The specific size is determined by 1. the general size, and 2. the number of semitones it contains.

interval-class. [0,1,4] abbrev. ic (set-theory); the distance between two pitch-classes, measured as the shortest distance between them; G to D appears to be a fifth, but G down to D is a fourth; the ic of G to D is always a fourth since direction is irrelevant to ic and the fourth is smaller than the fifth. There are six interval-classes designated by the numbers 1 to 6 (semitones); e.g. a semitone = ic1 (also a major-seventh = ic1), a whole-step = ic2 (also the minor-seventh), and E C = ic4. There are no interval-classes larger than a tritone (ic6); see also: directed-interval-class and directed-interval.

interval-vector. [4] (Forte) abbrev. IV (set-theory, nonlinear). an array of six digits representing the interval-class (ic) content of a chord, where the first digit indicates the quantity of ic1, the second digit = the quantity of ic2, the third digit = the quantity of ic3, the fourth digit = the quantity of ic4, the fifth digit= the quantity of ic5, and the sixth digit = the quantity of ic6. E.g., 001110 is the IV for a major chord, showing that it contains zero semitones (ic1), no ic2 (wholetones), one ic3 (minor 3rd), one ic4 (major 3rd), one ic5 (perfect 4th) and no tritones (ic6).

invariant. [4,5] (Babbitt-2) (set-theory, linear) anything remaining unchanged after a transformation, e.g., in transposition the interval series may be invariant although the pitches change.

invariant-subset. [4,5] (set-theory) the elements of a pc-set that remain unchanged after an operation of transposition, R, I, or RI (or a quadrate tranformation).

inverse. [4,5] (set-theory, nonlinear) a set whose intervals are turned upside down (not to be confused with traditional chord inversion), e.g., D E G would become D F G; these are sets 3-5 and 3-5B. Many nonlinear sets have the property that, upon inversion, they become the same PCs, e.g., C D G inverted becomes G C D, set 3-9*. Therefore, these sets have no distinct nonlinear inverse. These sets have the property that if they are inverted they map into themselves (usually after a transposition), and this property is called a mirror.

inversion. [0,1] 1. (harmonic) in tertian harmony, a chord whose bass note is not the root. 2. [2] (contour or melodic) a reversal of direction in an interval series or chord (mirroring); e.g., intervals in an upward direction are changed to the same intervals downward. 3. [0,4] (complement) an interval that when added to a given interval will complete the octave. See also inverse.

invertible-counterpoint. [2] counterpoint where the upper and lower parts have been interchanged.

Ionian. [0,1] an ancient mode consisting of T-T-S-T-T-T-S, equivalent to the modern major mode.

IPN (abbrev). [0] see International-Pitch-Notation.

iso-. [2] (prefix) the same in succession.

isomelos. [4] a repeating pitch series or pitch-class series (or any of their transpositions) as a distinctive overall compositional feature, i.e., a repetition of an interval or directed-interval series. Isomelos is the principle feature of serial composition and of passacaglias.

isorhythm. [4] (literally, same rhythm) a rhythmic pattern that is repeated successively.

isotrophy. [5] (Xenakis) regions or planes of sound balanced in contrary motion. This may take the form of two sound masses moving in opposite directions.

IT. [5] inversion and transposition of a pc-set.

Italian-sixth. [3] an augmented-sixth chord built on the raised fourth degree of the key; e.g. F# A-flat C in C-Major. Normally it occurs in first inversion as A-flat C F# forming the augmented-sixth that resolves to an octave on the dominant.

IV. abbrev for interval vector.

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just-intonation or pure-intonation. [0,1] a tuning system that corresponds to the natural harmonic-series.

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key. [0] a combination of a tonic and a mode. E.g. a piece that is in the key of G major has G as tonic and major as the mode.

key-signature. [0] sharps or flats that are placed at the beginning of a staff to indicate the pitch-classes that are to be so altered on that staff. Notice that, contrary to common thought, a key signature (sic) does not specify key.

klang. [5] (Schenker: primordial sonority) a chord that functions as a generating cell, usually the lower part of an overtone series coinciding with the major tonic triad, the fundamental sonority.

klangfarbenmelodie. [4] a melody whose tone color is changing, i.e., distributing successive notes of a melody among different instruments; e.g. Webern's orchestration of a Ricercar from Bach's A Musical Offering.

Kopfton. [5] (Schenker: initiating tone) a tone of the tonic (3,5, or 8) that initiates a descent in the Urlinie.

Koppelung. [5] (Schenker: coupling) an octave transfer, or coupling, permitting a line to expand its register and prolong motion towards a goal.

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layer. [3] (Schenker: Schicht) a level of compositional structure other than the Ursatz.

layering. [4] the process of superposing heterogeneous lines or "streams" on one another, e.g. in Charles Ives's Central Park in the Dark.

leading-tone or leading-note. [0] the note that is a diatonic half-step below the tonic.

leitmotif. [3] a brief idea, such as a melodic line, that is used by a composer to symbolize a character, feeling, or thought, most often in a vocal genre, such as opera.

linear-set. [4] A set ordered in time, as a temporal array, e.g. a tone row.

linear pitch set. [4] A group of pitches arranged in a temporal order.

linear pitch-class set. [4] A group of pcs arranged in a temporal order.

location modulation. [4] changing the apparent position of a sound source. normally this change is periodic.

Locrian. [4] a seldom used mode consisting of S-T-T-S-T-T-T.

Lydian. [0,1] a mode consisting of T-T-T-S-T-T-S.

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macrotonal scale. [4] a scale having intervals larger than a semitone and not a sum of semitones.

major. [0] a mode consisting of T-T-S-T-T-T-S.

major-chord. [0] a chord whose triad is major; see major-triad.

major-seventh chord. [0,1] a chord consisting of a major triad with an added major seventh; e.g. C E G B.

major-triad. [0] a triad consisting of a root, major-third, and perfect-fifth.

mediant. [0,1] the third degree of a scale or a chord built on that degree.

medium. [0] the instrument/s that are intended to perform a piece of music.

melodic-inversion. [1,2] see contour inversion.

melodic minor. [0] see minor.

melody. [0] a combination of a pitch series and a rhythm having a clearly defined shape.

metamorphic. [5] a type of form in which each new section is a transformation of a previous section.

meter. [0] a grouping of pulses. Meter actually sounds and is not the same as a time signature, which is written. A time signature is actually a meter signature, and tells us something about the meter, but a signature is not the meter itself.

meter-signature, or time-signature. [0] a symbol normally consisting of two vertically placed numbers occurring at the beginning of a score, the upper indicating the metric organization of the music, i.e., the number of pulses in a group in a compound meter or the number of beats in a group in a simple meter; the lower number is a notational reference for the pulse, e.g., 3/4 indicates three beats per metric group, and a quarter note gets a beat.

metrical-modulation.[4,5] (Carter/Goldman) a change from one meter to another by using common note values or pulses as intersections.

microtone. [0,1] an interval smaller than a semitone.

Middleground. [3,5] (Schenker) a layer of compositional structure between the Foreground and Background. a broad level of structure which is shown by the elimination of selected detail.

minimalism. [4] a style of music that uses a very small amount of material, repeats it and gradually varies it; e.g. Steve Reich's Come Out.

minor. [0] A group of three modes, the most basic of which is the natural minor, or Aeolian, consisting of T-S-T-T-S-T-T. The harmonic minor consists of T-S-T-T-S-T+S-S. It may be derived from the natural minor by raising the subtonic by a semitone. The melodic minor mode differs as its direction changes. Ascending, it is T-S-T-T-T-T-S, but descending it is the same as the natural mode. The ascending form of the melodic minor scale may be derived from a natural minor scale by raising each of the sixth and seventh degrees by a semitone.

minor-chord. [0] a chord whose triad is minor (see minor-triad).

minor-seventh chord. [0,1] a chord consisting of a minor-triad with an added minor-seventh; e.g. D F A C.

minor-triad. [0] a triad consisting of a root, minor-third, and perfect-fifth.

mirror. [4] (set-theory) 1. an exact contour-inversion. An interval or interval series whose direction is reversed, e.g. D up to F is mirrored by D down to B; 2. a mirror-chord.

mirror-chord. [4] (set-theory, nonlinear) a chord that is reflectively symmetric, e.g., B, D, F when mirrored is B, D, F.

mirror-set. [4,5] (set-theory, nonlinear) a pc-set whose intervals are symmetric by reflection around a pitch-axis. See also mirror-chord.

Mixolydian. [0,1] a mode consisting of T-T-S-T-T-S-T.

mod-12. [4] (set-theory) modulo 12 arithmetic, i.e., that with a cyclic base 12 as in a clock. particularly useful for describing and analyzing music in the equal tempered twelve-tone scale. each 12=0 as on a clock.

modal-rhythm . [1,2] a fixed, pre-established, repeating rhythmic pattern that is used for the rhythmic organization of a composition; e.g. long-short-short-long-long from the second movement of Beethoven's Symphony No. 7.

modal-modulation. [3] changing from one mode to another; e.g. changing from C Mixolydian to C major.

mode. [0] an interval or ic series used to construct a scale. Examples of the traditional modes include: major, minor, Dorian, Phrygian, Lydian, etc. These are all interval series; e.g. major is T-T-S-T-T-T-S, where T=whole-tone or whole-step and S=semitone or half-step. Notice that a mode is actually a series of gaps, or holes, between pitches and not the pitches themselves.

modulation. [1] 1. a change of key. 2. a smooth, gradual change from one state to another, e.g., tempo, key, meter, timbre, etc.

Moment-form. [5] (Stockhausen) a form in which short time segments are controlled by some process or constant, e.g., the repetition of a pitches of a chord, or the subtraction of elements until reaching silence; used in Stockhausen's Momente.

mono-. [0] (prefix) one at a time.

monophony. [0] a single line; also: one pitch-class at a time.

motet. [1] Originally (Medieval), a vocal genre with words, a song, but the prototype is the late Renaissance motet, a contrapuntal work for voices without essential instrumental parts, i.e., a cappella, and normally based on a sacred topic.

motif. [0] see motive.

motive. [0] a brief melodic or rhythmic idea used to organize a composition.

Mounting. [5] (Schenker: see Anstiegascent).

multi-. [4] (prefix) more than one in succession, e.g., multimetric or multimodal.

multimeter. [4] two or more meters in succession.

multimodal. [4] two or more modes in succession.

multiphonic. [4] (Bartolozzi) simultaneous pitches produced on a wind instrument.

musique concrete . [4] tape or other electronic alteration of non-electronic sounds.

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natural-minor. [0] a mode consisting of T-S-T-T-S-T-T, equivalent to the ancient Aeolian.

Neapolitan chord. [3] A major chord built on the minor second degree of the key. It is a chromatic chord that normally occurs in first inversion and functions as a dominant-preparation.

neighboring-tone. [0,1] a nonharmonic-tone that is approached by step from a harmonic-tone and moves by step back to the same harmonic-tone.

Nebenstimme. [5] (Schoenberg) a line of secondary importance, abbreviated N in Schoenberg's scores.

nexus-set. [5](Forte) (set-theory, nonlinear) a referent set for a set-complex.

nonlinear set. [4] (set-theory, nonlinear) A set in which linear order is irrelevant (syn. unordered-set).

nonharmonic-tone. [0] a tone or note that is not a part of the sounding chord; syn. nonchord-tone.

normal-order. [4,5] (adapted from Howe) (set-theory, nonlinear) the most compact rotation of the pitch-numbers of a pc-set. E.g. G B D F has pitch-numbers 7,11,2,5. Rotations of these are: (a) 7,11,2,5, (b) 11,2,5,7 (c) 2,5,7,11, and (d) 5,7,11,2. The most compact of these is (b) since the distance from the first to last numbers is the smallest mod-12. If two or more rotations have the same distance from first to last numbers, the rotation with the greatest compaction at the beginning is the normal-order. Compare with prime-form.

note. [0] a written symbol for a pitch. A note does not sound.

nucleus. [4] (set-theory) a set of elements used as a central focus, similar to a tonic.

null-set. [5] (set-theory, nonlinear) a pc-set with nothing in it.

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oblique-motion. [1] a type of voice-leading in which one voice moves against another that is stationary, or repeats.

octatonic scale. [4] a scale having eight pcs. The most commonly known octatonic scale is the alternating-octatonic, or diminished-octatonic. This scale alternates semitones and tones, as in F#, G, A, A#, B#, C#, D#, E#, F#. There are two alternating-octatonic modes. One begins with a semitone, the other with a whole-tone. All the triads built in this scale are diminished.

octave. [0] two frequencies, or pitches, in the ratio of 2:1.

octave-displacement. [4] the displacement of tones into octave registers that are not their referent position.

open-position. [1] voicing where there is at least an octave between the soprano and tenor voices.

order-inversion. [4] (set-theory, linear) a property of two given sets such that both contain the elements A and B; in one set A occurs before B (not necessarily consecutively), but in the other set, B comes before A.

order-number. [4] (set-theory, linear) a number assigned to a pc in a linear-set to indicate its temporal position in the series; e.g. in D,F,G, the pc D is order-number 0, the pc F is order-number 1 and G is order-number 2.

order-number-pitch-number-couple. [5] (set-theory, linear) two numbers that identify a pitch class in a series. the first indicates the order, starting with zero, and the second indicates the directed-interval above the first pc of the prime set, e.g. c,d#,b,g would be (0,0) (1,3) (2,11) (3,7). in c,d#,b,g: (0,0)=c ((1,3)=d# (2,11)=b (3,7)=g.

ordered-set. [4,5] 1. (set-theory, linear) a pc-set arranged in a linear order. 2. [4] a set, normally a pc-set, that is arranged in an array. Note that an ordered-set by definition #2 may be arranged in a non-temporal dimension, e.g. an alphabetical pitch order (e.g. A#,B,C#,D), and, therefore, it is not the same as a linear-set (see ordering), although it is sometimes used this way by modern scholars. Also, an ordered-set is not necessarily a pitch-class set, e.g. it may be a set of durational values, hence rhythm. Because of the confusion of the meanings, it is here recommended that the term linear pitch-class set be used for pcs placed in a temporal order.

ordering. [4] (set-theory) a set placed into some logical order; e.g., the set played as D,B,G,F may be placed into different logical orderings: 1. alphabetically as B,D,F,G, 2. temporally as it is played, D,B,G,F, 3. tertially as G,B,D,F, or in normal-order as 0,3,6,8.

ostinato. [1,2] see ground-bass.

overlapping-voices. [1] two adjacent voices move to a position in which the lower voice is higher than the previous note in the higher voice, or they move to a position where the higher voice is lower than the previous note in the lower voice.

overtone. [0] any frequency sounding above the fundamental.

overtone-series. [0] the order of overtones ascending from the fundamental.

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P. [4] abbreviation for prime-set.

panchromatic. [4] a free use of the twelve-tone equal tempered scale. i.e., without a tonal hierarchy. syn. atonal.

pandiatonic. [4] the use of the tones of a diatonic scale without a tonality or hierarchy.

pantonality. [4] see atonality. Schoenberg's preferred term over atonality.

parallel-harmony. [4] chords whose voices (may be implied) are in parallel motion.

parallel-fifths and -octaves. [1] a part-writing problem where two voices move in parallel perfect-fifths, octaves or unisons (see parallel-motion). When they occur in polyphonic music, one voice sounds as if it has dropped out, and the voices are no longer independent. Additionally, the notes that are parallel sound accented. Students often don't understand the restriction on the use of these intervals in part-writing. Parallel-octaves and fifths are only wrong if the student doesn't perceive that they are there. Since traditional part-writing exercises deal exclusively with developing the perception and writing of independent voices (parallel-fifths and octaves are the opposite of independence), they are avoided.

parallel-keys. [0] keys having the same tonic; e.g., C major and c minor.

parallel-motion. [1] partwriting in which two voices move in the same direction by the same amount or interval.

parameter. [4] an aspect with variable characteristics, e.g., harmony is a parameter maintaining its identity even though it may be constantly changing.

parent set. [4] a set that contains all others. An example is a scale that contains all the diatonic chords in a key.

part-writing. [1] the motion of voices with respect to one another. Traditional part-writing deals exclusively with independent voices and, therefore, outlaws parallel-octaves and fifths. See also voice leading and voicing.

partials. [0] all the frequencies comprising a tone or sound; a fundamental and its overtones.

partition. [4] (set-theory, linear) a division or section delineating a structure, e.g., subsets of a tone row, exposition of a fugue, etc.

passacaglia. [1] (syn. chaconne). a slow theme-and-variations in triple meter with the theme recurring in the bass.

passing-tone. [0] a nonharmonic-tone that proceeds by step from one harmonic-tone to a different harmonic-tone.

pc. [1,4] (set-theory) abbreviation for pitch-class.

pc-set. [4] Abbrev. for pitch-class-set (set-theory); a group of pitch-classes.

pedal-tone. [1] a nonharmonic-tone that is stationary through a chord change, usually occurring in the bass.

pentachord. [0] a chord or pc-set with five pitch-classes.

pentatonic. [0] a common scale type consisting of five pitch-classes. There are many types of pentatonic scales, but the so-called "black-key pentatonic" is actually a a set of modes.

period. [1] a pair of balanced phrases, antecedent and consequent, or question and answer, that occur consecutively, are united by motivic similarities, and make up a complete statement.

permutation. [4] (set-theory) any possible ordering of a set; e.g., the set G,E,C has 3 factorial (6) different permutations: 1.C,E,G , 2.E,G,C, 3.G,C,E, 4. G,E,C, 5. C,G,E, or 6.E,C,G.

phase. [4] a small time difference (usually less than 1/16 of a second) between overlapping sound events of the same content. If this is zero the sounds are said to be 'in phase'; if not, they are out of phase. Most often the sounds are cyclic or rotational.

phrase. [0] a musical sentence that lasts a single "breath", with a beginning, end, and a clear shape, usually melodic. Phrases in music are most often four or two measures in length.

Phrygian. [0,1] a mode consisting of S-T-T-T-S-T-T. (S=semitone, T=tone)

Phrygian-cadence. [1] a half-cadence in a minor key with contrary step motion to the dominant between the soprano and bass. Either the soprano or bass moves by a semitone to the dominant.

picardy-third. [1] the use of a major third in a cadence on the tonic in a minor key. Thus, the tonic ends with a major chord.

pitch. [0] the predominant frequency in a sound. Note the difference from tonic.

pitch-axis. [4] (set-theory) a pitch or pc that is used as a pivot for turning a set around to create inversions. See also: axis.

pitch-class. [0] (set-theory) all pitches having the same name and their enharmonic equivalents. The pitch-class C consists of all Cs, high and low, as well as all B#s, whereas middle-C is a specific pitch.

pitch-class-number. [4] (set-theory) see pitch-number.

pitch-class-set. (set-theory) a group of pitch-classes.

pitch-number. [4] (set-theory) a number assigned to a pitch-class in a set, in one of two ways: 1. (absolute system) the number of semitones the pc is above C (C=0, C#=1, D=2, etc.), or 2. (relative system) the number of semitones the pc is above a reference pc, the latter of which is normally taken to be the first pc of a prime-set or a prime-form.

pitch-structure. [4] (Howe) (set-theory) the intervallic organization of a pc-set.

pivot-chord. [1] (syn. common-chord) a chord that functions in two different keys and is used to modulate from one key to another.

plagal-cadence. [1] the cadence formula IV I.

planing. [4] chords moving in parallel-motion.

pointillism. [4] short bursts of instrumental tone color.

polarization. [1] opposites forming the most important structural pillars in the texture; e.g., soprano and bass or solo and tutti.

poly-. [0,1] (prefix) more than one simultaneously.

polychord. [4] more than one triadic-chord sounding at once.

polymeter. [4] more than one meter at once.

polymodality. [4] more than one modality at once.

polyphony. [0] 1. two or more melodic lines simultaneously, 2. two or more pcs simultaneously.

polytonality. [4] more than one tonality or key at once.

prepared-piano. [4] a piano in which the sound has been altered by the placement of various objects in or on the strings or action.

primary-chords. [0] the most important chords in a key: I, IV, V.

prime. [4] (abbrev. P) (set-theory, linear) an ordered-set taken as a reference.

prime-form. [4] (set-theory) 1. (linear) a prime-set or the presumed original order of a tone row, 2. (nonlinear, Forte) the best-normal-order of a set, where the pitch-numbers are transposed so that the first number is set to zero, and the most compact form is chosen from that set and its inverse. 3. (Solomon) the normal-order of a set transposed so that the first pitch-number is set to zero. Note the conflict with Forte's meaning. 9,0,5 has a normal-order of 5,9,0 and its prime-form would be 047. However, in Forte's system, the prime-form is 037, because 037 is the inverse of 047 and it is more compact. Thus, in Forte's The Structure of Atonal Music there is no distinction made between major and minor chords. This distinction is retained in Solomon's system. See Solomon, "The List of Chords, Their Properties and Uses", in Interface, Journal of New Music Research, Vol. 11, no. 2 (1982).

prime-set. [4] (set-theory, linear) a row taken as a reference, abbrev. P; compare to prime-form.

process-music. [4] a compositional procedure in which there is no traditional score but rather, the composer describes the process that the performers are to use to "create" the music.

prolongation. [3,5] (Schenker) a repetition or sustaining of a sonority before it moves on to the next sonority on the same level of structure; the sustaining or contiguous structure ultimately exemplified as the Ursatz. Prolongation normally consists of an elaboration of a fundamental structure, such as the Ursatz, to generate the substance of a tonal work.

pythagorean-intonation. [5] a tuning system based on simple mathematical ratios.

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quadrate. [5] (Solomon) (set-theory, linear) an operation of 90-degree rotation in a time/pitch matrix. (See Solomon, "New Symmetric Transformations" in Perspectives of New Music (1973).

quadrate-form. [5] (Solomon) a 90-degree rotation of an ordered-set in a time/pitch matrix. It was once thought that the only transformations of a linear-set were the forms P, R, I, or RI. It is now known that there are four more transformations: QP, QR, QI, and QRI. (See Solomon, "New Symmetric Transformations" in Perspectives of New Music (1973).

quartal. [0,1] Anything that can be spelled, or arranged, in fourths.

quintal. a misnomer for chords constructed in fifths. All "quintal" chords are inverted quartal chords just as "sextal chords" are really inverted tertian chords.

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R. [2,4] (set-theory, linear) abbreviation for retrograde.

R-relation. [5] (Solomon) (set-theory, nonlinear) a maximal similarity-relation in which two sets are equal excepting one pc pair that are a semitone from a match, and their interval-vectors have a minimum of interval correspondence, T, where T equals the Total number of ic common to both sets. In order to satisfy R, A must be less than T, where A= xy/8, and x=sum of all ic in either set, and y=cardinality.

As an example, take the sets: 1. 6-Z50* (014679) and 2. 6-30 (013679). Notice that the sets would be equivalent, except that the third pc pair is off by a semitone, satisfying the first condition for R. Set#1 has an interval vector of 224232, while #2 has an IV=224223. There are two ics in common in the first position (ic1). There are two in the second position (ic2), and there are four in the third position (ic3). There are two in the fourth position (ic4), and there are two in the fifth position (ic5). Finally, there are two that are common to the sixth position (ic6). (These results are deduced mathematically by subtracting the two numbers in each position as an absolute value.) Adding these together, 2+2+4+2+2+2, we get T=14. When we compute x, the sum of all the ics in either set we get 2+2+4+2+3+2 from the first set; i.e., x=15. This number will be the same for all sets in the same cardinality. The cardinality is 6; i.e., y=6. Now we can test if A<T with the formula A=xy/8. So substituting, we compute A=(15x6)/8, which gives a result of 11.25. Since T is greater than 11.25 the two sets are R related. The R relation is computed within a few nanoseconds with a modern desktop computer.

real-imitation. [2] imitation where the intervals are exactly the same as in the statement.

recapitulation. [1] a return of a section of music, especially in the sonata-form.

reduction. (Schoenberg) a distillation of a Grundgestalt (basic-shape) to a smaller, more concentrated figure. See also fragmentation.

reflection. [4] (Solomon) the result of turning a figure about an axis. e.g. to invert a theme, it is reflected about a pitch-axis; to retrograde, it is reflected about a time axis.

reflective-chord . [4] a mirror-chord.

region. [5] (Schoenberg) a tonal area in music as it relates to the initial key; thus, modulation is superfluous. Everything is considered as related to the initial key.

register-transfer. [2] the transfer of a melodic line from one register to another within the midst of its statement. See also coupling.

relative-keys . [0] keys having the same key-signature (but not the same tonic).

retardation. [1,2] a nonharmonic tone that is repeated or held from a harmonic-tone and then resolves up by step to a harmonic-tone.

Retrograde. [2,4] (set-theory, linear) the reverse order of a tone-row or melody.

Retrograde-Inversion. [2,4] (set-theory, linear) the retrograde of the inversion (abbrev. RI) is a retrograde of the interval series of the Prime.

retrogression. [1] a series of chords that weakens a tonality.

reverberation. [4] the continuing sound after the sound source has ceased to vibrate. Reverberation is caused by the bouncing of sound waves in a finite space.

rhythm. [0] any aspect of music having to do with time. Notice that since music must exist in time, all music is rhythmic.

RI. [2,4] (set-theory, linear) abbreviation for retrograde-inversion.

rondo. [1] a sectional form whose sections follow the pattern: A B A C A D A....(B) A.

root. [0,1] 1. lowest (or first) pitch-class in a Itertian spelling. Root is not the same as bass, tonic, key, or fundamental. Note the differences. In the chord B D F G, B may be the bass but it is not the root. Spelled in thirds, the root is revealed to be G. 2. the pitch in an interval which is emphasized by combination tones (Hindemith). The root of odd numbered scalar intervals is the lower pitch and the upper pitch for even numbered (scalar) intervals.

root-movement . [1] the change of roots indicated by a directional-interval-class.

root-position . [0] in tertian harmony, a chord with the root in the bass.

rotation. [4] (Solomon) (set-theory) the revolution of a figure; a cyclic translation or repetition; e.g., a repeating Alberti-bass. Another example: C E G rotates to E G C and to G C E.

round. [1,2] a circular or perpetual canon.

rounded-binary. see: binary.

row. [4] (set-theory, linear) syn. series.

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scale. [0] a group of pitch-classes arranged in ascending or descending order. E.g., take the pc-set G, C#, A, F#, D, B, E and arrange it as E, F#, G, A, B, C#, D, E (with E as tonic) and you have an E Dorian scale.

Scheintonarten. [5] (Schenker: see foregound-keys)

Schicht. [5] (Schenker: layer or level) a level of compositional structure other than the Ursatz.

secondary-dominant. [1] a dominant of a diatonic chord other than tonic.

secondary leading-tone. [1,3] the leading-tone of a note in the key other than tonic.

secondary-set. [5] (Babbitt) (set-theory, linear) a twelve tone row formed from the first hexachord of one set-form(1) combined with the second hexachord of another set-form where the two are combinatorial.

second-inversion. [1] a tertian chord whose fifth is in the bass.

second species. [4,5] counterpoint in which the rhythm is 2:1, e.g., eighth notes against quarters.

secundal. [1] anything that can be arranged in seconds (interval-class).

segment. [1,4] (set-theory, linear) a contiguous part of a series.

segmental-invariance. [4] (set-theory, linear) a contiguous part of an ordered-set that remains constant after a transformation.

segmentation. [4] (set-theory, linear) the division of a twelve-tone-row into 2, 3, or 4, etc. segments, normally of equal length.

semi-combinatorial set. [4,5] (Babbitt) (set-theory, linear) "a set so constructed that one of its transformations other than that of the retrograde can be transposed so that its first six notes are equivalent with regard to content, to the last six notes of the original set."

semitone. [0] the smallest interval in the chromatic-scale. In equal-temperament it is mathematically tuned to the twelfth root of 2.

serial. [4] (set-theory, linear) a compositional type consisting of a fixed order of elements.

series. [4] (set-theory, linear) syn: row, ordered-set. a linear order, usually an ordering of the twelve tones of the chromatic scale.

set. [4] 1. a collection of things; 2. (Babbitt) (set-theory, linear) an ordering of the twelve tones; 3. (set-theory, nonlinear) a group of pcs.

set-aspect. [4] (Perle) (set-theory, linear) one of the four transformations: P,R,I,RI.

set-complex. [5] 1. (Babbitt) (set-theory, linear) the 48 forms, including transpositions, of a twelve tone row. 2. (set-theory, nonlinear) see set-complex-k.

set-complex-K. [5] (Forte) (set-theory, nonlinear) a set of sets associated by virtue of the inclusion (subset) relation with a nexus-set or to its complement.

set-complex-Kh. [5] (Forte) (set-theory, nonlinear) a special subcomplex of the set-complex-K in which each set bears the inclusion (subset) relation with the nexus-set and its complement.

set-list. [4] (set-theory, nonlinear) The list of all possible unordered-sets in the twelve tone system. Allen Forte's original list contains 208 sets in The Structure of Atonal Music (Yale, 1973), Appendix I. Larry Solomon's revised list contains all 352 possible sets, in Interface (V11/2, 1982) and his Music Analysis System software (Softstuff, 1976), including the 0-,1-,2-,10-, 11-, and 12-note sets omitted by Forte.

set-name. 1. [4] (Forte) (set-theory, nonlinear) two numbers adjoined but separated by a dash, the first representing cardinality, and the second representing their order of compactness (prime-form) in a numerical array containing all possible sets within that cardinality; e.g., 3-11 is a three-note set that is number 11 in compactness in the list of all three-note sets. Solomon adds the inverse sets to Forte's list with an appended B to each set-name that is distinct. 2. (proposed by Solomon) a number that is the prime-form of the set in hexadecimal notation with the beginning zero omitted; e.g. Forte's 7-33 whose prime form is 0 1 2 4 6 8 10 would have a set-name of 12468A. See also, Solomon, "The List of Chords, Their Properties and Uses", in Interface, Journal of New Music Research, Vol. 11, no. 2 (1982).

set-theory. [4] (Forte, Babbitt, et al) theory dealing with the relations existing between pitch-class sets. Set-theory divides into two categories: 1. nonlinear set-theory is that which deals with pc-sets where temporal order is not relevant, such as in chords. Allen Forte is the primary authority in the field, especially in his The Structure of Atonal Music (Yale: 1973). It is essentially a generalization of the principles of traditional harmony to include post tonal harmony; 2. linear-set theory deals with those sets whose temporal order is essential. Milton Babbitt is the primary authority in this field. It is concerned with tone-rows, their properties, and compositional treatment.

seventh chord. [0,1] a tertian chord consisting of a root, third, fifth and seventh. It is an extension of the basic triad by adding the seventh.

similar-motion. [1] part-writing in which two voices move in the same direction.

similarity-relations. [4] (Forte) (set-theory, nonlinear) ways in which two non-equivalent sets of the same cardinality may be compared. Forte describes three basic types of maximum similarity relations, when two sets have all but one pc in common (after transposition). However, he regards this first type, Rp, to be less significant than two other relationships that are more particular in regard to ic. Both have the same interval content (IV) in four out of six IV positions. The remaining two numbers may be interchanged (R1) or they may not be interchanged (R2). In Larry Solomon's Music Analysis System (1976) R1=is symbolized X and R2=is symbolized O; see also Solomon's R-relation.

simple-interval. [0] an interval of an octave or less.

simple-meter. [0] a meter that is not subdivided into units of three.

simultaneity. [4] all pitches sounding at the same time.

sine-tone. [1,4] a pitch having a fundamental but no overtones; the simplest sound.

smooth-voice-leading . [1] A traditional type of voice-leading where there is no leap greater than a perfect-fourth in the soprano, alto, or tenor voices, and no leap greater than a perfect-fifth in the bass (the octave excepted in the bass). Certain other intervals are also avoided melodically, namely the tritone and augmented-second.

sonata. [2,3] a three or four contrasting movement, classical form in which the first movement is in sonata-form and, in the three movement sonata, any of the other movements may also be in sonata-form. The first movement is fast, in the tonic key; the second movement is slow, in a different but related key, and the last movement is very fast. In the four-movement sonata, the extra movement is inserted before the last. It is a minuet or scherzo, A B A, triple time, in the home key.

sonata-form. [1] a complex musical-form that is essentially a large rounded binary. It has a first section, called an exposition, with two contrasting themes in tonic and dominant (or relative) keys, a development section containing theme fragments, modulations and counterpoint, and a recapitulation that recalls the first section with both themes in the tonic key.

sonority. [0] a sound complex, consisting of a combination of sounds.

sound mass. [4] a large block of sounds and/or pitches in which no individual pitch predominates.

sound. [0] audible vibration, i.e., any vibration that is capable of being heard, whether or not it actually is.

source-set. [4] a subset of a tone-row that is used to generate the entire row through symmetric transformation, e.g., a 4 note figure may be transposed, inverted, etc., to form two more four-note figures to comprise a whole row; see also the G,A#,B example under derived-set.

step-progression. [3,5] 1. (Schenker) a line moving by scale steps, often summarizing a structural movment from one significant point in time to another. Hindemith also uses the term in this manner

stratification. [4] see layering.

stretto. [2] imitative-counterpoint where the voice-parts overlap.

strophic. [1] a form in which the same music is repeated with different verses (or words).

Stufe. [5] (Schenker: scale degree) the fundamental root or harmonic degree; normally this is a root of the tonic, dominant, or subdominant.

Stufengang. [5] (Schenker) root relationships in the Middleground and Background levels of structure.

subdominant. [0] the fourth degree of the scale or the chord built on it.

subdominant-function. [1] see dominant-preparation.

subharmonic. [4] a frequency sounding as an integral division of (below) the fundamental frequency.

subject. [2] similar to a motive, but longer, normally applied to contrapuntal music.

submediant. [1] the sixth degree of a scale or the chord built on it.

subset. [4] (set-theory) a set that is contained within a larger set.

subset-relation. [4] (set-theory) the property that two sets have when one is contained in the other.

Substitution. [5] (Schenker: Vertretung) the replacement of a note for one otherwise missing (usually in the Urlinie).

subtonic. [1] the seventh degree of a scale or the chord built on it. Normally, the subtonic is a whole-tone below the tonic, but in its original meaning it was simply the seventh scale degree. Today, the term leading-tone is reserved to mean the seventh degree that is a semitone below the tonic.

superset. [4] (set-theory) A set that contains other set/s and whose cardinality is larger than the other/s.

supertonic. [1] the second degree of a scale or the chord built on it.

suspension. [1] a nonharmonic-tone that is held over or repeated from a chord where it was a harmonic-tone. It then resolves downward by step to a harmonic-tone.

symmetrical meter. a meter that is evenly divided; e.g., 9 is a symmetrical group of three 3s.

symmetry. [4] (Solomon) a congruence resulting from an operation of translation, reflection, or rotation. e.g., an Alberti bass pattern may be translated in time and thereby be superimposed on itself. P and I may be reflected together around a pitch-axis to yield a congruence.-- see Larry Solomon's Symmetry as a Determinant of Musical Composition (Univ. Microfilms, 1973).

synaesthesia. [5] a mental abberation confusing a mixture of sensory phenomena as one; e.g., the confusion of sight and sound.

syncopation. [0] any unexpected rhythm.

synthesis. [4] 1. additive: the creation of complex sounds by mixing sounds of a simpler nature; usually electronic. 2. subtractive: selective elimination of elements of a complex sound to create a simpler one.

synthetic-scale. [4] any scale not having a common name.

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Teiler. [5] (Schenker: see Divider)

tempo. [0] the speed of music. Tempo marks are normally indicated in one of two ways: 1. as an Italian word, e.g. allegro=fast, lento=slow, or, 2. as a metronome mark, e.g. quarter note=144, meaning there are to be 144 quarter notes per minute.

ternary. [0,1] A three-part form, A B A. Each section is normally self sufficient, i.e., ends with a cadence on the key of the section. This form is also variously called Da Capo form, song form, and Minuet form. It is used extensively for short works, such as marches, waltzes and songs.

terraced-dynamics . [1] a compositional use of sudden changes from one dynamic level to another, normally to the exclusion of gradual changes.

tertian. [0] anything that can be spelled (or arranged) in thirds. Notice that tertian structures may or may not occur arranged in thirds; i.e., D G F B is tertian since the letters can be rearranged into thirds as G B D F.

tessitura. [1] the comfortable range of a voice or instrument.

tetrachord. [0] a chord consisting of four pitch-classes or four different pitches.

texture. [0] the way that lines and tones are woven together in music. Some common terms used to describe musical texture are: monophony, polyphony, homophony, heterophony, counterpoint, thin, thick.

theme. [1] a compositional idea that recurs, normally melodic, that is of some length, i.e., is a complete musical statement in itself.

theme-group. [3](Tovey) a group of themes within a section of form that are united by virtue of being in the same key.

theme-and-variations. [1] a musical form based on a theme and a series of sections that are variations of this theme. Normally each section is of the same length as the theme and carries the same formal scheme.

Tieferlegung. [5] (Schenker: see coupling)

third. [0] an interval whose pitches encompass three consecutive letter names in the alphabet; e.g. C up to E encompasses C-D-E; A-flat to F is a third going down (A-G-F) but is a 6th going up (A-B-C-D-E-F).

timbre. [0] the tone color of an instrument as determined by its overtone-series or spectrum. It is timbre that makes possible the distinguishing of one instrument from another. syn., tone color, color.

time signature. [0] (also: meter-signature) two vertically aligned numbers normally appearing at the beginning of a score that give the number of rhythmic units (normally beats) per measure (top number), and the value of note in a rhythmic unit (bottom number).

time-point set (Babbitt). [5] a set of initiated durational values translated from pitch-numbers of a tone-row. Each measure is divided into twelve equal time segments corresponding to the twelve-tone scale, and each pitch-number translates to a corresponding time segment within a measure whence the next event is initiated.

tonal. [0] 1. having tonality, 2. music in major or minor keys.

tonal-center. [0] the most prominent pitch-class; syn., tonic.

tonal-imitation. [2] the imitation of a subject where some intervals are altered to retain the key.

tonality. [0,1] a hierarchy (ranking) of pitch-class. Tonal is the adjective. If only one pc is stressed more than others in a piece of music, the music is said to be tonal. If all pcs are treated as equally important, the music is said to be atonal, or pantonal.

tone. [0] 1. a pitch and all of its overtones. 2. a whole-step, or whole-tone.

tone-cluster. [4] a simultaneity of several pitches that are a second apart.

tone-color. [0] see timbre.

tone-row. [4] (set-theory, linear) a fixed, linear order of pitch-classes normally used as the organizational structure of a serial composition by means of repetition, transposition or other transformation; see also series.

tonic. [0] the predominant pitch-class. Tonic is not necessarily the first pc of a scale; i.e., a C major scale does not have to start or end on tonic in a musical context, yet it is a C major scale. The convention in writing scales out of context, however, is to begin and end on the tonic. A tonic is determined by its prominence in the music (by means of repetition, accents, and other means of emphasis). Thus, a tonic can only be determined in a musical context, which is why a key signature cannot tell us what the key is. Syn., tonal center.

-tonic. [0] suffix used with appropriate prefix to indicate a specific number of pitch-classes in a scale, e.g., ditonic, tritonic, tetratonic, pentatonic, etc.).

tonic-function. [1] a chord that can substitute for the tonic, e.g., the submediant.

tonicization. [1,3] (Sessions) transient tonics normally created by a secondary-dominant emphasis; a transitory modulation.

transducer. [4] a device that changes one form of energy into another; e.g., a loudspeaker changes electrical energy into mechanical energy and sound. A microphone changes sound into electrical energy. A tape recorder changes an electrical signal into magnetic energy.

transformation. [4] 1. (Babbitt) (set-theory, linear) in a row, P, R, I or RI and/or any of their transpositions. A transformation of a row is normally indicated with the transposition-number, e.g. "R7" indicates the Retrograde transposed up seven semitones. 2. [4, 5] (Solomon) (set-theory, linear) an operation of R, I, RI or a quadrate used to generate a new variation.

transform. [4, 5] (Solomon) (set theory, linear) any of the transpositions of a prime-set, or its retrograde, inversion, or retrograde-inversion, or QP, QI, QR, or QRI. There are 48 different transforms without the quadrate forms and 96 including the them.

translation. [1,4] moving a figure through a dimension of time, pitch, space; e.g., a recurring theme is a translation through time, while one major chord is a translation of another in pitch, as in transposition.

transpose. verb for transposition.

transposition. [0,1] a translation in pitch.

transposition-number. [4] (set-theory, linear) the measure of transposition indicated as the directed-interval from a reference, usually P0. If a melody is transposed up three semitones, its transposition-number is 3, but if it is transposed down three semitones its transposition-number is 9 (see directed-interval).

triad. [0] three pitch-classes spelled, or arranged, in thirds. A triad is three pcs already arranged in thirds. E G C is not a triad, but C E G is.

triadic-chord. [1] a trichord that can be spelled in thirds.

trichord. [0] a chord containing three pitch-classes; triads are a special class of trichords.

triple. [0] a simple meter consisting of a strong beat followed by two weak beats.

tritone. [0] any interval consisting of three whole-steps.

twelve-tone-composition. [4] (set-theory, linear) serial composition based on repetition and transformations of an ordered-set of the twelve equal tempered pitch-classes; a tone-row that may form melodies or chords. Octave duplication is avoided.

twelve-tone-row. [4] (set-theory, linear) a specific ordering of the twelve equal-tempered pcs that are used to generate a musical composition.

two-voice framework. [3,4] (Hindemith) a structural outline of the bass line and the most important upper voice, similar to Schenker's Ursatz.

U

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Underlap. [5] (Schenker: Untergriefen) a line rising from a voice below the Urlinie whose goal is a tone in the Urlinie already being approached from above.

undertone-series. [5] (Cowell) a fictitious inversion of the interval of the overtone-series.

unordered-set. [4] (Forte) (set-theory, nonlinear) a pitch-class set in which the linear order is irrelevant. syn.: nonlinear-set.

Unravelling. [5] (Schenker: Auswicklung) the spinning out of intervals or chords in the Middleground layers of structure.

Unterbrechung. [5] (Schenker: interruption) a return to scale degree #3 (mi) or #5 (sol) following scale-degree #2 of the dominant (la) in the Middleground layers.

Untergreifen. [5] (Schenker: see Underlap).

Urlinie. [3,5] (Schenker: fundamental line) the fundamental upper line in a tonal structure. This ordinarily takes one of three forms: 3-2-1 or 5-4-3-2-1 or 8-7-6-5-4-3-2-1 (scale degrees).

Ursatz. [3,5] (Schenker: Background). the fundamental structure of a composition normally shown as a horizontalized tonic chord. This frequently takes the form of two voices: the Urlinie, or basic melodic line, a stepwise progression above the bass with passing tones (normally between tones of the tonic) and the bass arpeggiation (Grundbrechung) (usually the roots of I and V). this is called the background or simplest sketch of the overall motion.

V

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Vertretung. (Schenker/Slatkin: see substitution).

voice. [0,1] refers to virtual voices, which are even simulated in a single chord. The highest voice is called the soprano, the lowest is called the bass. If there are more than two voices, a second treble voice that lies below the soprano is called the alto, and a third voice, lying above the bass, is called the tenor.

voice-leading. [1] the motion of a single voice. Traditional voice-leading consists of a restricted type called smooth voice-leading.

voicing. [1] the registrational positioning, spacing, and doubling of notes in a chord and/or their placement in conventional vocal or instrumental ranges. Two types are common in four-part settings: (1) close voicing, the distance from soprano to tenor voices is less than an octave, and (2) open voicing, where the distance from soprano to tenor is an octave or greater. See also crossed-voices and doubling.

W

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white noise. [4] a combination of all frequencies of sound of equal intensity, similar to the sound of wind or a waterfall.

whole-step. [0] a distance or interval equal to two semitones.

whole-tone scale. [0,1] a scale consisting of all whole-steps.

X-Z

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Z-related pair. [4] (Forte) (set-theory, nonlinear) a pair of sets with the same interval-vector, but are not reducible to the same prime-form. Note that inversely related sets always have the same interval-vector. In Forte's The Structure of Atonal Music, Yale, 1973) inverse sets are reduced to the same prime-form; i.e., are not Z-related. However, in Solomon (Interface, 1982) inverse sets are not reduced to the same prime-form; i.e., are Z-related. Z hexachords have special properties; e.g. one is always the complement of the other. Thus, Z hexachord pair set-complexes are unified.

Z-symmetric set. [4,5] (Solomon) (set-theory, nonlinear) a set whose prime-form is equivalent to its inverse. Note that all mirror-sets are Z-symmetric but not vice versa. In Solomon's Musical Analysis System (1984) all mirror-sets are indicated with an "*" in their set-names.

Zug. [5] (Schenker: directed motion) a linear, directed stepwise motion towards a goal in the structure.

©Copyright 2000 Howard Richards