Pitch class sets pdf

This set contains three pitch classes, and its what we usually call the c major triad. Pitchclass theory is treated here as part of the musical and cultural landscape of the united states. Pitch class set theory is just an analytical tool that gives you a different way to look at sets of notes. A pitchclass set is an unordered collection of pitch classesa motive from which many. Tonal implication, tonal ambiguity, and tonalness david temperley eastman school of music 26 gibbs st. Pitchclass set multiplication in theory and practice. When two setsaandbconsist of the same elements, they are. The use of acoustic measures of dissonance to characterize.

Composing music with pitchclass sets involves mathematical operations on these sets. It enumerates the notes in the 12 et system and allows certain calculations to be carried out on sets of notes that would you not be able to easily able to do otherwise. Intervalclass content in equally tempered pitchclass. Applying pitch class set chord voicings to traditional. Pitchclass sets and microtonalism hudson lacerda 2010 introduction this text addresses some aspects of pitch class sets, in an attempt to apply the concept to equaltempered scales other than 12edo.

Set theory encompasses the notion of defining sets of pitches and organizing music around those sets and their various manipulations. Recent scholarship in acoustics has provided a mathematical model for the approximation of what has been termed acoustic dissonance, or roughness in the interaction of two or more simultaneously sounded complex tones. Sets may be outwardly different but have identical interval vectors such as 5z12 and 5z36. Straus chapter 2 pitchclass sets university of south. The space odyssey in this article delves into several new issues, such as a methodology for the creation of a comprehensive array of bonded inclusional growth chains, the formation of a diatonic. Any group of pitch classes can be a pitch class set.

If not specified, the elements are denoted by lowercase letters. Transposition is by pitch class, which means that a transposition could contain octave displacements and still be a transposition. Inversions are marked b sets not marked a or b are symmetrical. We can perform a pitch, but we cant really perform a pitch class. Set class analysis refers to the efforts of music theorists to reveal the systems that composers like schoenberg and his followers used. Also, in bars 9 and 10 a method of developing a melodic and harmonic idea. Pitchclass sets an unordered collection of pitchclasses that forms a basis for some kind of compositional activity used to generate harmonies or melodies. Pitch class sets are a method for describing harmonies in 20 th century music. Pitchclass sets and microtonalism hudson lacerda 2010 introduction this text addresses some aspects of pitchclass sets, in an attempt to apply the concept. Citations 0 references 0 this research hasnt been cited in any other publications. Pitch class sets, normal order, and transformations open. Pitch class sets 1 1202007 pitch class sets paul nelson revised. Pitch class a pitch without regard to its octave position.

Youll find youve filled twelve bags, and each of these bags is what we call a pitch class. The frequency of occurrence of various interval classes in a given pitchclass set can be correlated with corresponding measures of perceived consonance for each interval class. Pitchclass sets such as scales can be characterized. Table of pitch class sets forte solomon chord music. Pitchclass sets, serialism and intervallicism, and the integration of systematic and intuitive music making examines the interaction of systematic and intuitive elements in my compositional and improvisational practice, and the outcomes of my sustained investigation of pitchclass sets, serialism and intervallicism as creative tools. The intervalclass vector is an index of the number of common notes under transposition. Transposition transposition of pitchclass sets is by ordered pitchclass interval. Composing with sets university of minnesota duluth. Usually it isa motive that occurs melodically, harmonically, or both. Set class and prime form 1 lots of concepts in pitchclass set theory are best viewed along a sliding scale of concreteness or abstractness. More importantly, though, the basic results of pcset theory. It is an extremely useful technique for composers to help understand and control the harmonies. These notations and methods can describe and manipulate any type of chord that can be created within a 12tone equally tempered scale.

Then the difference between sets and classes takes meaning in an open, dynamical way. Introduction to pitchclass set theory flashcards quizlet. Hey, as part of an assignment ive been instructed to invert some pitch class sets, but im really confused. Thus the idea that the purpose of set theory is to modelize this open hierarchy or flow of time. It is an extremely useful technique for composers to help understand and control the harmonies which. Major and minor chords, dominantseventh and halfdiminished seventh chords. Pitchclass set theory and its contexts combines thorough discussions of musical concepts with an engaging historical narrative. Pitch class sets an unordered collection of pitch classes that forms a basis for some kind of compositional activity used to generate harmonies or melodies.

A concept like pitch, for example, is very concrete, while pitch class is somewhat more abstract. This article examines pitchclass set multiplication in its various manifestations, formalized as simple, compound, and complex multiplication. Pitchclass set pitchclass collection a pitchclass set or pitchclass collection is a group of pitch classes. In this example, all slices have the duration of a eighth note. Pitchclass sets are the basic building blocks of much posttonal music. Setclass similarity, voice leading, and the fourier transform.

Note bar four in which we have employed the technique of dovetailing sets by joining two groups of four notes with a shared tone b. Set class and prime form 1 lots of concepts in pitch class set theory are best viewed along a sliding scale of concreteness or abstractness. It is true that the intervals of pitch class space are isomorphic to z12. No matter what orderform they take in the music, they will retain their pitchclass and intervalclass identity. If a goal of musicmaking is to promote a euphonious. Applying pitch class set chord voicings to traditional harmony provides a student interested in modernizing their chord playing with four pitch class sets that effective create a new and intriguing sound for playing traditional harmony.

Table of pitch class sets forte solomon free download as pdf file. Cardinal number refers to the number of elements in a set. No matter what orderform they take in the music, they will retain their pitch class and interval class identity. A voice leading between pitchclass sets corresponds to a phrase like the c major triad moves to e major by moving c down to b, holding e fixed, and shifting g up by semitone to g we can notate this more efficiently by writing 3 by perfectly even nnote chord i mean the chord that. Several questions arise, since there are limitations of application of certain pitch class sets properties and relations in other scales. Pitchclass sets such as scales can be characterized according to the inventory of possible intervals that can be formed by pairing all pitches in the set.

Pitch class set theory july 7, 2012 elliott carters harmony book is his compilation of the pitch class sets he uses, like a painters color mixing palette, as he composes his music. Pitch class set theory considers sets of several of these bags say, just the bags labelled c, e and g. This is a list of pitch class sets by forte number. Transposition is by ordered pitchclass interval, which means that we always count the transposition. Before going any further, consider the implications of that first statement. The intervalclass vector is a visual tally of the number of interval classes in a set class. Im aware of interger notation, standard form, transcribing pitch class sets etc, but im really stumped when trying to invert them. Pdf from pitchclass set theory to musical composition. Although these measures necessitate certain artificial considerations in their present form i. The table of pitch class sets 1997, rev 2005 by larry solomon.

Pitchclass sets can be used as chords, scales, and motives. Simpl we use cookies to enhance your experience on our website. Table of pitch class sets pitch music music theory. Setclass table page 1 setclass table1 the following pages contain a complete listing of all of the t nt ni setclasses after allen forte and john rahn. The table of pitch class sets of allen forte has been extended by larry solomon through the differentiation of the pairs of pitch set classes of inverse chord i. When we talk about a group of pitch classes as a unit, we call that group a pitch class set, often abbreviated pc set. Normal order is the most compressed way to write a given collection of pitch classes, in ascending order. Intervalclass content in equally tempered pitchclass sets. In pitchclass set theory, too, a set is defined by its elements only, not by a particular arrangement of these elements or by their quantities. Lets begin with a pitch class set an unordered group of notes. For example, g7 is a pitchclass set, gbdf, and so is the cmajor scale, except c in this context has two. Introduction to pitch class set analysis octave equivalence. Pdf intervalclass content in equally tempered pitch.