Pitch class set theory pdf download

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. Pdf set theory based analysis of atonal music researchgate. The concept of set serves as a fundamental part of the present day mathematics. A concept like pitch, for example, is very concrete, while pitch class is somewhat more abstract. Download pdf class theory and history book full free. Get all rotations for pitch class set 0578 for all instruments download today. However, strauss book has become the standard instructional textbook on this subject for a very simple reason.

Determine the normal order of the following tetrachords using letter names. More exactly, a pitchclass set is a numerical representation consisting of distinct integers i. T4i invert and then transpose up 4 half steps examples of. Class theory and history available for download and read online in other formats.

Today this concept is being used in almost every branch of mathematics. An example of this is that the notes e sharp, f, and g double flat are in all octaves. Composing with sets university of minnesota duluth. Bain musc 525 posttonal theory straus chapter 2 pitchclass sets joseph n. Pitch class sets, normal order, and transformations open. 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. Inversions are marked b sets not marked a or b are symmetrical. Enables better formatting of chord symbols, figured notation, time signatures, pitch class set theory, simple macro music analysis in web pages.

Mar 17, 2012 by simple selecting the desired pitches, the app will generate the pitchclass sets properties. Notate the following tetrachords using integer notation. Transposition is by ordered pitch class interval, which means that we always count the transposition distance in a positive direction and the distance will be 11 or less. Determine the normal order of the following tetrachords using letter. Music notation and theory for intelligent beginners. Every pitch that can be called an f, say, is collected together into the pitch class that we just call f. A pitch class is a set of all pitches with the same note name or its enharmonic equivalent. The rotational order of a pitch class set is not affected by transposition. The study of geometry, sequences, probability, etc. 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. The theory of sets was developed by german mathematician georg cantor 18451918. This is app is full of bugs, and doesnt always provide the correct information.

Within the key of c major, bnatural is attracted to the tonic c, other members of the dominant triad are attracted to the tonic triad, and other scale degrees have functions as well. This note is an introduction to the zermelofraenkel set theory with choice zfc. Since there are no negative numbers in pitch class, you are essentially counting back the same amount of numbers as the first set. Normal order is the most compressed way to write a given collection of pitch classes, in ascending order. For example, the pitch class set consisting of the notes c, e, and g would be written as 0,4,7. Nov 04, 2009 a very particular concatenation of circumstances in america led to the emergence of pitch class pc set theory. These notations and methods can describe and manipulate any type of chord that can be created within a 12tone equally tempered scale. What, then, is the point of pitch class set analysis. 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. Pitchclass theory is treated here as part of the musical and cultural landscape of the united states.

However far the axis is from 0, the inversionallypaired pitch class will always be the. Pitchclass set theory and helix model accademia musicale. The pitch class c stands for all possible cs, in whatever octave position. For example, 418 and 818 are abstract complements of each other.

In arithmetical terms, add ing or subtracting 12 or a multiple of 12 does not change pitch class identity. Setcalc for mobile devices simple set of tools for pitch class set analysis, designed specifically for ios. Complex issues arise in set theory more than any other area of pure mathematics. This intersection turns out to be an expansion of the concept of pitch class set, so that it can express additional information concerning the.

Cardinal number refers to the number of elements in a set. It is, essentially, a histogram of all of the interval classes which can be found in a pc set. Equivalent pitch class sets belong to the same set class. Pdf class theory and history download full pdf book download.

Mathematical and computational approaches to music theory, analysis. Pdf class theory and history download full pdf book. Lower lower on the staff higher higher on the staff another way to understand the idea of pitches being lower or higher is to compare it to bears and birds. The most commonly referenced set classes are trichords. Pitch class theory is treated here as part of the musical and cultural landscape of the united states.

The paper suggests a possible intersection between pitch class set theory theorized by a. Our normal form example 1,2,4 would be 0,1,3 in prime form. Set classes john paul ito general overview pitch class set theory. More exactly, a pitch class set is a numerical representation consisting of distinct integers i. Composers treat sets with varying amounts of freedom when applying the set class method to their atonal music. Two octave displacements for 025 for all instruments. 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. A pitch class is the set of all pitches that can have the same name, for example, all the cs. Musical set theory provides concepts for categorizing musical objects and describing their.

Any group of pitch classes can be a pitch class set. Music theory formusicians normal people and by toby w. We can perform a pitch, but we cant really perform a pitch class. Modern composers will use pitch class sets like chemistry, to mix and create. Pdf slides of lessons, 2629 october 2009 lemmensinstituut, leuven belgium. Pitch class tonality is highly charged system where scale degrees are endowed with a magnetic or gravitational pull towards other tones. Pitchclass set theory practice quiz paul dell aquila. In set theory, a class is a group whose members are all equivalent in some sense. The paper suggests a possible intersection between pitchclass set theory theorized by a. Because pitchclass settheory was developed to provide.

Because music employs a set of pitches ranging from low to high, the staff acts like a map for the notesallowing us to hear, read or write them as. 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 ba. Pitchclass set theory and its contexts combines thorough discussions of musical concepts with an engaging historical narrative. Straus chapter 2 pitchclass sets university of south. Theory of musicbasic atonal theory jonathan dimond. From pitch class set theory to musical composition. It is designed for a onesemester course in set theory at the advanced undergraduate or beginning. Chapter 7 pitch class set complements composer tools. It is an extremely useful technique for composers to help understand and control the harmonies. Pitch class set theory in music and mathematics, authormichael james mcneilis, year2017.

A free visual crossplatform pitch class 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. Free set theory books download ebooks online textbooks. Music theory pitch class set test what students are saying as a current student on this bumpy collegiate pathway, i stumbled upon course hero, where i can find study resources for nearly all my courses, get online help from tutors 247, and even share. The axioms of set theory, ordinal and cardinal arithmetic, the axiom of foundation, relativisation, absoluteness, and reflection, ordinal definable sets and inner models of set theory, the constructible universe l cohens method of forcing, independence. 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. A pitch class set in normal form but transposed so that 0 zero is its first member is said to be in prime form. Usually it isa motive that occurs melodically, harmonically, or both. I wrote it in the rm belief that set theory is good not just for set theorists, but for many mathematicians, and that the earlier a student sees the particular point of view that we call modern set theory, the better. When we talk about a group of pitch classes as a unit, we call that group a pitch class set, often abbreviated pc set. An interval vector is a summary of all of the intervals between all pairs of pitches in a pitch class set. Pitch class sets can be used as scales, chords, melodies, and combinations of chords and melodies. Sets expressed in prime form use square brackets around the set of pitch classes. We have already seen in the notes on set classes that while in tonal theory, to invert a. Yes, theorists since forte have revised pc set theory somewhat in the time since the structure of atonal music was published.

Sets are used to define the concepts of relations and functions. The history of pitchclass set pcset theory as a modern and distinctly. This post the second in our series on pitch class set theory looks at three different ways to number pitch classes. This thesis presents an analysis of coplands first major serial work, the quartet for piano and strings 1950, using pitch class set theory and tonal analytical techniques. Rush this file is a collection of individual sheets covering a bunch of lessons on music theory.

Pitchclass set multiplication in theory and practice music. Circular permutation rotating the order of a pitch class set so that the second ordering permutation of the set begins with the second member. As you can imagine from the name of the theory, pitch class set theory is a theory about pitch classes. An engaging study the first ever of the principles used by noted scholars to unravel the masterpieces of schoenberg, stravinsky, and other modernists. Music theory circle of notes, pitch classes, and symmetry. There are other conceptions of set, but although they have genuine mathematical interest they are not our concern here.

Determine the normal order of the following trichords using letter names. Thus, the set a contains a finite number of elements. Pc set theory connects with serial procedures, but it is fanciful to suggest that composers from the first part of the century composed by consciously making connections and distinctions between precompositionally unordered pc sets. The fundamental concept of musical set theory is the musical set, which is an unordered collection of pitch classes rahn 1980, 27. The elements of a set may be manifested in music as simultaneous chords, successive tones as in a melody, or both. Although elementary set theory is wellknown and straightforward, the modern subject, axiomatic set theory, is both conceptually more di. In chapters 2 through 6 of analyzing atonal music, schuijer focuses on pitch class set theory s conceptualization of musical structure 27.

A pitch class set is an unordered collection of pitch classesa motive from which many of the identifying characteristicsregister, rhythm, orderhave been. This intersection turns out to be an expansion of the concept of pitchclass set, so that it can express additional information concerning the frequencies under consideration. Harmonic organization in aaron coplands piano quartet. Pitch class sets are the basic building blocks of much posttonal music. To transpose a set up by n half steps, add n to each pitch class in the set. The axioms of set theory of my title are the axioms of zermelofraenkel set theory, usually thought ofas arisingfromthe endeavourtoaxiomatise the cumulative hierarchy concept of set. In themselves, pitch classes do not favor one enharmonic spelling or another, although they can take on particular spellings in various scalar or chordal contexts. Pitch class a pitch without regard to its octave position. Organized by the pitchclass sets normal form, prime form, forte name, zmate, interval class, and interval class vector. Pitch class set theory is just an analytical tool that gives you a different way to look at sets of notes.

When applying set ideas to more than two pitches, we need to group them into what is referred to as normal form the most compressed version possible, either ascending or descending. Given a pitch class set in normal form, the transposition number is the pitch class interval that must be added to all the pitch classes to obtain the second set. Set class 0,1,6 was so popular with schoenberg and his disciples that it has been nicknamed the viennese trichord. Lets begin with a pitch class set an unordered group of notes. Set classes john paul ito general overview pitchclass set theory. Pdf from pitchclass set theory to musical composition. Note that the forte designation for a pc set and its complement will always have the same pc set id number after the dash. The rotational order of a pitchclass set is not affected by transposition. T is conventionally used in sets to notate 10 as a single character.

This article examines pitch class set multiplication in its various manifestations, formalized as simple, compound, and complex multiplication. 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. A pitch class pc is the class or set of pitches with the same letter or solfege name that are octave duplications of one another. Pitch class sets 1 1202007 pitch class sets paul nelson revised. The reason this definition seems more confusing is that it involves two kinds of groups. So if you had the set 0,1,2,3, and assuming your axis point is 0, the inversion would be 0,11,10,9. No matter what orderform they take in the music, they will retain their pitch class and interval class identity. Should examples from manuals and textbooks of music analysis or the. With existing literature primarily focussing on pitchclass set theory as an. To transpose a set down by n half steps, subtract n from each pitch class in the set. If you get a number larger than 11 or smaller than 0, add or subtract 12 to get a valid pitch class number. As was made clear in examples 5 and 6 from the diagrams on set. Pitch class set theory and its contexts combines thorough discussions of musical concepts with an engaging historical narrative.