1. A basic concept in pitch-class set theory is that these levels of concreteness and abstractness encompass not only pitch and interval, but groups of pitch classes as well. Ordered pitch intervals are associated with a very specific sound (e.g., +15); unordered pitch-class intervals (e.g., interval class 1) are less vivid or real. Table of set theory symbols. Motivation When you start reading these notes, the first thing you should be asking yourselves is “What is Set Theory and why is it relevant?” Though Propositional Logic will prove a useful tool to describe certain aspects of meaning, like the reasoning in (1), it is a blunt instrument. Here are some examples that many undergraduate students in computer science will come across. Here is the online musical set theory calculator for you to make the PC set calculations with ease. Compare the results of steps (2) and (4). Invert the results from step 2 (any inversion will work) and put the result in normal order. We can perform a pitch, but we can’t really perform a pitch class. It has been and is likely to continue to be a a source of fundamental ideas in Computer Science from theory to practice; Computer Science, being a science of the arti cial, has had many of its constructs and ideas inspired by Set Theory. The same observation applies in Bartók’s “Subject and Reflection.” The four pitch-class sets in those two passages all have the same intervallic content and that’s why we can label transpositional and inversional relationships between them. For any two sets X and Y, either there is a one-to-one function from X into Y or a one-to-one function from Y into X. 2. Here are three simple statements about sets and functions. Here is the online musical set theory calculator for you to make the PC set calculations with ease. When we extract a group of notes from a passage of music and put them in normal order, that group of notes is a pitch-class set. We’ve already seen sets of pitch-classes, though we haven’t really been calling them that. This set finder tool provides you the options to choose between the algorithms Forte and Rahn. In order for a pitch-class set to be transpositionally or inversionally related to some other pitch class set, they must share the same collection of intervals. Transpose it so that the first pitch class is 0. Major triads are transpositionally related to one another, while major and minor triads are inversionally related to one another. As we’ve seen in class, one very interesting way of looking at a lot of post-tonal music is by studying the transpositional and inversional relationships between pitch-class sets. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Prime form is the most compact version. We follow a simple process to put a pitch-class set in prime form: The example below walks demonstrates using the motive from Bartók’s “Subject and Reflection.”. Set Theory Symbols. A basic concept in pitch-class set theory is that these levels of concreteness and abstractness encompass not only pitch and interval, but groups of pitch classes as well. Basic Set Theory LX 502 - Semantics I September 11, 2008 1. We’ve seen similar examples in the intervallic realm. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. In the short example below (from Bartók’s “Subject and Reflection”) you’ll notice that the right hand of the two passages is T5-related, as is the left-hand. We’ve already seen sets of pitch-classes, though we haven’t really been calling them that. This is most easily grasped by remembering that all major and minor triads have the same interval content (M3, m3, and P5). The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. If you are a dynamic composer then this Composer Tool will be a very efficient one for you to do the PC set calculations to come out with a pleasant composition. Lots of concepts in pitch-class set theory are best viewed along a sliding scale of “concreteness” or “abstractness.” A concept like pitch, for example, is very concrete, while pitch class is somewhat more abstract. These groups of pitch classes are called pitch-class sets. n values for T n invariance:: n values for T n I invariance:: Subsets: Supersets: A branch of music that is concerned about the pitches and pitch classes, which can be either ordered or unordered, and can also be related to operations in music like transposition, inversion, and complementation is called as a musical set theory. These groups of pitch classes are called pitch-class sets. Within each passage, the right and left hands are T8I _and _T6I related, respectively. Naïve set theory (as opposed to axiomatic set theory) is widely used in computer science and is a central part of the underlying mathematical language. List of set symbols of set theory and probability. They look like they could appear on a homework assignment in an undergraduate course. Enter the prime form and choose an algorithm in the set finder, the tool will display the output for forte code, interval vector and prime inversion. A branch of music that is concerned about the pitches and pitch classes, which can be either ordered or unordered, and can also be related to operations in music like transposition, inversion, and complementation is called as a musical set theory. All pitch-class sets that are transpositionally and inversionally related belong to the same set class, and they are represented by the same prime form. Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. Set Theory is indivisible from Logic where Computer Science has its roots.