Dmitri Tymoczko is a composer and music theorist. His music, which draws on rock, jazz, and romanticism, has been performed by ensembles such as the Amernet String Quartet, the Brentano Quartet, Janus, Newspeak, the San Francisco Contemporary Players, the Pacifica Quartet, and the pianist Ursula Oppens. [1] [ failed verification ] As a theorist, he has published more than two dozen articles dealing with topics related to contemporary tonality, including scales, voice leading, and functional harmonic norms. His article "The Geometry of Musical Chords", was the first music-theory article ever published by the journal Science . [2]
Tymoczko was born 1969, in Northampton, Massachusetts. [3] His father Thomas Tymoczko was a philosopher of mathematics at Smith College, while his mother Maria Tymoczko is a professor of comparative literature at the University of Massachusetts Amherst; his sister, Julianna Tymoczko, later herself became a mathematics professor at Smith. [4] He attended Harvard University, studying composition, music theory, and philosophy, and did graduate work in Philosophy at Oxford University as a Rhodes scholar. After being asked to leave the philosophy D. Phil. program, he eventually returned to music, acquiring a Ph.D. in composition from The University of California, Berkeley. Since 2002, he has been a professor at Princeton University. He is the recipient of fellowships from the Guggenheim foundation and the Radcliffe Institute of Advanced Study. He is married to the philosopher Elisabeth Camp, with whom he has a son Lukas and a daughter Katarina.
Tymoczko's album Beat Therapy (Bridge 9353), combines jazz instrumentation with classical ideas of development. The critic Frank Oteri describes it as "far reaching and utterly entertaining." [5]
In Crackpot Hymnal (Bridge 9383), he presents expressly composed chamber pieces inspired and mixed from a number of traditional styles. Jazz, popular, blues and rock styles interact with folk and contemporary classical music. [6]
A third CD, Rube Goldberg Variations was released in 2018. Joshua Kosman, writing at SFGate, called it "whimsical", "ingenious", and with a "rich emotional arc" produced by a "warmth of personality that is distinctive". [7]
In A Geometry of Music, [8] Tymoczko proposes a general framework for thinking about tonality, arguing that there are five basic features that jointly contribute to the sense of tonality:
The first part of the book explores theoretical questions about how these properties can be combined. In particular, Tymoczko uses orbifolds to develop "maps" of musical chords, showing that the first two properties (e.g. conjunct melodic motion and harmonic consistency) can be combined only in special circumstances. The second part of the book uses these tools to analyze pieces from the Middle Ages to the present. Tymoczko argues that there is an "extended common practice" linking superficially distinct styles, with jazz being much closer to classical music than many have thought.
Tymoczko showed that nearly even chords (such as those prevalent in Western tonal music) are represented by three main families of lattices. Two of these :
are particularly useful in analysis. What results is a systematic perspective on the full family of chord-based graphs. [9]
Tymoczko has also written a free software program, "ChordGeometries", allowing users to visualize the orbifolds representing musical chords.
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The major scale is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double its frequency so that it is called a higher octave of the same note.
Polytonality is the musical use of more than one key simultaneously. Bitonality is the use of only two different keys at the same time. Polyvalence or polyvalency is the use of more than one harmonic function, from the same key, at the same time.
In jazz and blues, a blue note is a note that—for expressive purposes—is sung or played at a slightly different pitch from standard. Typically the alteration is between a quartertone and a semitone, but this varies depending on the musical context.
An octatonic scale is any eight-note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory, this symmetrical scale is commonly called the octatonic scale, although there are a total of 42 enharmonically non-equivalent, transpositionally non-equivalent eight-note sets.
In the mathematical disciplines of topology and geometry, an orbifold is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space.
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is called the tonic. The root of the tonic chord forms the name given to the key, so in the key of C major, the note C can be both the tonic of the scale and the root of the tonic chord. The tonic can be a different note in the same scale, when the work is said to be in one of the modes of the scale.
Pandiatonicism is a musical technique of using the diatonic scale without the limitations of functional tonality. Music using this technique is pandiatonic.
In music, quartal harmony is the building of harmonic structures built from the intervals of the perfect fourth, the augmented fourth and the diminished fourth. For instance, a three-note quartal chord on C can be built by stacking perfect fourths, C–F–B♭.
Voice leading is the linear progression of individual melodic lines and their interaction with one another to create harmonies, typically in accordance with the principles of common-practice harmony and counterpoint.
A level, also "tonality level", Gerhard Kubik's "tonal step," "tonal block," and John Blacking's "root progression," is an important melodic and harmonic progression where melodic material shifts between a whole tone above and a whole tone below the tonal center. This shift can occur to both neighboring notes, in either direction, and from any point of departure. The steps above and below the tonic are often called contrasting steps. A new harmonic segment is created which then changes the tonality but not necessarily the key.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale. It corresponds to the Raga Sarasangi in Indian Carnatic music.
Transformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his 1987 work, Generalized Musical Intervals and Transformations. The theory—which models musical transformations as elements of a mathematical group—can be used to analyze both tonal and atonal music.
"All the Things You Are" is a song composed by Jerome Kern with lyrics written by Oscar Hammerstein II.
Fratres is a musical work by the Estonian composer Arvo Pärt exemplifying his tintinnabuli style of composition. It is three-part music, written in 1977, without fixed instrumentation and has been described as a “mesmerizing set of variations on a six-bar theme combining frantic activity and sublime stillness that encapsulates Pärt's observation that "the instant and eternity are struggling within us".
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.
Neo-Riemannian theory is a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry Klumpenhouwer. What binds these ideas is a central commitment to relating harmonies directly to each other, without necessary reference to a tonic. Initially, those harmonies were major and minor triads; subsequently, neo-Riemannian theory was extended to standard dissonant sonorities as well. Harmonic proximity is characteristically gauged by efficiency of voice leading. Thus, C major and E minor triads are close by virtue of requiring only a single semitonal shift to move from one to the other. Motion between proximate harmonies is described by simple transformations. For example, motion between a C major and E minor triad, in either direction, is executed by an "L" transformation. Extended progressions of harmonies are characteristically displayed on a geometric plane, or map, which portrays the entire system of harmonic relations. Where consensus is lacking is on the question of what is most central to the theory: smooth voice leading, transformations, or the system of relations that is mapped by the geometries. The theory is often invoked when analyzing harmonic practices within the Late Romantic period characterized by a high degree of chromaticism, including work of Schubert, Liszt, Wagner and Bruckner.
Third stream is a music genre that is a fusion of jazz and classical music. The term was coined in 1957 by composer Gunther Schuller in a lecture at Brandeis University. Improvisation is generally seen as a vital component of third stream.
"Bernie's Tune" is a 1952 jazz standard. The music was written by Bernie Miller, with lyrics added later by Jerry Leiber and Mike Stoller. It was popularised with a recording by the quartet of the American saxophonist and composer Gerry Mulligan, on the 1952 album of the same name, which also featured Chet Baker on trumpet. Despite this association, the piece was actually composed, as aforementioned, by a slightly unsung composer Bernie Miller, who also wrote the tune "Loaded" which was also covered by Chet Baker and saxophonist Stan Getz. The tune was a popular choice for musicians jamming at the time, though information about the composer himself is scarce, all that people really know of him is that he was a piano player from Washington DC. Mulligan speculated that by the time he had discovered any of Bernie's tunes, Bernie was dead. Later on in Mulligan's life, he took the same changes but invented a new melody to fit over the piece, entitling it 'Idle Gossip'.
Vogel's Tonnetz is a graphical and mathematical representation of the scale range of just intonation, introduced by German music theorist Martin Vogel 1976 in his book Die Lehre von den Tonbeziehungen. The graphical representation is based on Euler's Tonnetz, adding a third dimension for just sevenths to the two dimensions for just fifths and just thirds. It serves to illustrate and analyze chords and their relations. The four-dimensional mathematical representation including octaves allows the Evaluation of the congruency of harmonics of chords depending on the tonal material. It can thus also serve to determine the optimal tonal material for a certain chord.
