Pitch class set theory pdf free

The group is a pitch and all other pitches related by. It makes no claims about music itself, but it does make some claims about the basic. Having problems finding the prime form of that hexachord. You have probably encountered both of these concepts before, even if not by name. Pitch class sets, normal order, and transformations open. A concept like pitch, for example, is very concrete, while pitch class is somewhat more abstract. The fundamental concept of musical set theory is the musical set, which is an unordered collection of pitch classes rahn 1980, 27. Normal order is the most compressed way to write a given collection of pitch classes, in ascending order. The paper suggests a possible intersection between pitchclass set theory theorized by a. This neat app for ipod, iphone, and ipad has all the index information that can be found at the back of joseph n.

For example, the pitch class set consisting of the notes c, e, and g would be written as 0,4,7. Pdf a pitchclass set complex is a multidimensional object that spatially represents a collection of pitchclass sets and the intersections between. Transposition is by ordered pitchclass interval, which means that we always count the transposition distance in a positive direction and the distance will be 11 or less. These notes were prepared using notes from the course taught by uri avraham, assaf hasson, and of course, matti rubin. Introduction to modern set theory judith roitman december 6, 2011 1. This intersection turns out to be an expansion of the concept of pitchclass set, so that it can express additional information concerning the. Inversions are marked b sets not marked a or b are symmetrical.

More exactly, a pitchclass set is a numerical representation consisting of distinct integers i. Get all rotations for pitch class set 0568 for all. It has also been the subject of sometimes furious debates between music theorists and historically oriented musicologists, debates that only helped heighten its profile. Set theory is a method of musical analysis in which pitch classes are represented by numbers, and any grouping of these pitch classes is called a set. To transpose a set up by n half steps, add n to each pitch class in the set. Distinction between classes and sets in set theory. Composers treat sets with varying amounts of freedom when applying the setclass method to their atonal music. Pitch class a pitch without regard to its octave position. Chapter 2, objects and entities, provides a rigorous look at the concepts of pitch, pitch class, intervals, pc set, and the interval content of sets. T is conventionally used in sets to notate 10 as a single character. You can search the forum without needing to register. Complex issues arise in set theory more than any other area of pure mathematics. Pitchclass set theory practice quiz paul dell aquila. We can perform a pitch, but we cant really perform a pitch class.

You should be able to connect this concept to the concept of pitch vs. This post the second in our series on pitch class set theory looks at three different ways to number pitch classes. Circular permutation rotating the order of a pitchclass set so that the second ordering permutation of the set begins with the second member. Set class calculator given certain pitch classes in a given modulus, this program calculates the set class, the interval and tics vectors, the complement, the fourier partition, and finds zrelated sets if any.

A primer for atonal set theory college music symposium. Download pdf class theory and history book full free. Determine the normal order of the following trichords using letter names. If you get a number larger than 11 or smaller than 0, add or subtract 12 to get a valid pitch class number. Basic concepts of set theory, functions and relations. Pitchclass set theory and its contexts combines thorough discussions of musical concepts with an engaging historical narrative. A pitch class is a set of all pitches with the same note name or its enharmonic equivalent. Interval class is a useful concept because it relates intervals, their inversions, and any compound versions of those intervals. Introduction to logic and set theory202014 general course notes december 2, 20 these notes were prepared as an aid to the student. Class theory and history available for download and read online in other formats. It is not a theory about music in any common sense that is, it is not some set of ideas about music that may or may not be true. The history of pitchclass set pcset theory as a modern and distinctly modernist methodology for music analysis can be traced back to its origins in the late 1950s and early 1960s, through its codi. Given a pitchclass set in normal form, the transposition number is the pitchclass interval that. Normal order is the most compressed way to write a given.

For the past forty years, pitchclass set theory has served as a frame of reference for the study of atonal music, through the efforts of allen forte, milton babbitt, and others. A free visual crossplatform pitchclass set theoretical application mika kuuskankare sibelius academy cmt marcus castrdn sibelius academy docmus mikael laurson sibelius academy cmt abstract macset 4 is a computer application intended to assist in learning and teaching basic pitch class set theory and analysis of posttonal music. Set classes john paul ito general overview pitchclass set theory is not well named. An acquaintance with various examples and properties of well. Introduction to pitchclass set theory flashcards quizlet. Pdf from pitchclass set theory to musical composition. In any system, a class is a unary predicate a seen as the set of objects where a is true, that is the class of all x such that ax in a set theoretical universe, each set e is synonymous with the class of the x such that x. Like schenkerian analysis in its earlier days, set theory has had an air of the secret society about it, with admission granted only to those who possess the magic password, a forbidding technical vocabulary bristling with expressions like 6z44 and interval vector. Pitchclass theory is treated here as part of the musical and cultural landscape of the united states.

Circular permutation rotating the order of a pitch class set so that the second ordering permutation of the set begins with the second member. A pitch class set is simply an unordered collection of pitches. In chapters 2 through 6 of analyzing atonal music, schuijer focuses on pitch class set theory s conceptualization of musical structure 27. Pitch class set theory is just an analytical tool that gives you a different way to look at sets of notes. Cardinal number refers to the number of elements in a set. The 12 uniqye pitches on the keyboard, or pitch classes, are numbered from 0 to 11, starting with c. When manipulating pitch classes, you will use a special operator, called the modulo operator. Set class and prime form 1 lots of concepts in pitchclass set theory are best viewed along a sliding scale of concreteness or abstractness. Be working on it before then, and feel free to raise questions about it in class. Pitchclass set theory and its contexts eastman studies in music.

They are not guaranteed to be comprehensive of the material covered in the course. Set class 0,1,6 was so popular with schoenberg and his disciples that it has been nicknamed the viennese trichord. 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. Notate the following tetrachords using integer notation. This course has many related books and courses that will increase your understanding of pitch class set theory as well as various ways you can apply these structures both melodically and harmonically.

Pitchclass set theory emerged during the 20th century as a manner of analyzing the atonal compositions of various composers. Chapter 2 simple operations on pitch classes and pitch. Every pitch that can be called an f, say, is collected together into the pitch class that we just call f. A pitchclass set is a subset of the pitches of the chromatic scale, represented by integers 0 through 11. Music theory circle of notes, pitch classes, and symmetry. When we talk about a group of pitch classes as a unit, we call that group a pitch class set, often abbreviated pc set. Chapter 2 simple operations on pitch classes and pitch class sets return to table of contentsreturn to table of contents 2. The elements of a set may be manifested in music as simultaneous chords, successive tones as in a melody, or both. Ling 310, adapted from umass ling 409, partee lecture notes march 1, 2006 p. Any group of pitch classes can be a pitch class set. Pdf class theory and history download full pdf book. Usually it isa motive that occurs melodically, harmonically, or both. An example of this is that the notes e sharp, f, and g double flat are in all octaves. To transpose a set down by n half steps, subtract n from each pitch class in the set.

One of the basic properties of an ordinal is that it is a wellordered set. The spine of the settheoretic universe, and the most essential class of objects in the study of set theory, is the class of ordinals. Survey of music theory ii musi 6397 university of houston. Determine the normal order of the following tetrachords using letter. As you can imagine from the name of the theory, pitch class set theory is a theory about pitch classes. Pitchclass set orders and forms wolfram demonstrations. These notations and methods can describe and manipulate any type of chord that can be created within a 12tone equally tempered scale. Pitchclass set theory and its contexts eastman studies in music schuijer, michiel on. Pitch class sets 1 1202007 pitch class sets paul nelson revised. These numbering systems are alarmingly similar, so they can get confusing, but an understanding of them is essential for what follows, so hold onto your hat. 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.