Pitch class set theory
http://www.foreversound.com/setcalculator/main.asp Webb音高集合（英語：pitch class）是一個集合，其中所有的音高都剛好差整數倍的八度音，舉例來說，音高集合C包含了所有八度音中的C。 {Cn : n 為整數} = {..., C-2, C-1, C0, C1, C2, C3...}; 其中，C2比C1高八度音，頻率為後者兩倍，數字每多一，就高一個八度，頻率變兩倍。 雖然n沒有正式的範圍，但人耳只聽得到部分的音高(約20赫茲到20000赫茲)，故n大 …
Pitch class set theory
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WebbThe term “pitch class” (abbreviated “pc”) employs the notion of octave equivalence and refers to any member of the set of pitches of the same “name” (i.e. C-sharp). When looking at the non-diatonic relationships among the twelve chromatic pitches, it can be useful to look at the chromatic scale as a mathematical group (the Z-12 additive group). One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Visa mer Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Visa mer Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition Visa mer "For a relation in set S to be an equivalence relation [in algebra], it has to satisfy three conditions: it has to be reflexive ..., symmetrical ..., and transitive ...". "Indeed, an informal notion of equivalence has always been part of music theory and analysis. PC set theory, however, … Visa mer The number of distinct operations in a system that map a set into itself is the set's degree of symmetry. The degree of symmetry, "specifies the number of operations that preserve the unordered pcsets of a partition; it tells the extent to which that partition's … Visa mer The fundamental concept of musical set theory is the (musical) set, which is an unordered collection of pitch classes. More exactly, a pitch … Visa mer The basic operations that may be performed on a set are transposition and inversion. Sets related by transposition or inversion are said to be transpositionally related or inversionally related, and to belong to the same set class. Since transposition and … Visa mer Two transpositionally related sets are said to belong to the same transpositional set class (Tn). Two sets related by transposition or … Visa mer
Webbpitch-class set is a group of pitches that the analyst decides to put together for some reason. The pitch-class set class —a term that is very unwieldy, so theorists have agreed … Webbpitch-class set – An unordered collection of pitch classes, usually grouped into curly brackets: {C, E, G}, {D, E-flat, G}, or {4, 5, 9}. pitch-class set class or simply set class – A category of pitch-class sets that are all related by transposition or inversion.
Webb2 This table corresponds to that of “Appendix 1, ‘Prime forms and Vectors of Pitch-Class Sets,’” in Forte (1973:179-81) and “Table II, ‘T n/T nI-Types of Sets,’” in Rahn (1980:140- ... 1987 Composition with Pitch-Classes: A theory of Compositional Design. New Haven: Yale University Press. Rahn, John 1980 Basic Atonal Theory. WebbPitch-class set theory takes over once the more challenging and creative work has already been done – choosing which pitch classes to include in the set. This is called …
Webbピッチクラス・セット理論（英語: Musical set theory ）は、西洋音楽における12の音高（ピッチクラス）の組み合わせに関する理論。 セット理論とも呼ばれるが、日本においては専らこの名称で呼ばれることが多い 。
Webb27 okt. 2009 · Pitch-class set analysis had a more chequered history in Europe, with little uptake and much hostility on mainland Europe even if it has been of more consequence in the United Kingdom. One reason is well known—the Europeans favour interpretation and analysis that enhances understanding of the canon of European works. ararat kebab audierneWebb19 juli 2024 · 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. These groups of pitch classes are called pitch-class sets. We’ve already seen sets of pitch-classes, though we haven’t really been calling them that. bake companyWebb18 nov. 2014 · SET THEORY, Part 1 The pattern EFG also resides in the key of one flat, BCD in the key of one sharp. Because they can appear in more than one pitch set, these two patterns form an intersection between two diatonic pitch sets. Example 3: Set intersection The pitches of a trichord need not be adjacent notes of a scale. ararat kebab menuWebbExpanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the pitch classes in an equally tempered octave form an abelian group with 12 elements. It is possible to describe just intonation in terms of a free abelian group. Serial composition and set theory bake cmWebbTake all the pitches and move them up or down by a specified number of semitones. Transposition is a familiar process from tonal music, but note that (as in set theory) … ararat kebab gossauWebbThis is a book about the mathematics of musical set theory. Musical set theory applies some key ideas from set theory and other fields of mathematics to the analysis of (mostly) atonal music in twelve tone equal temperament. Its goal is to achieve an understanding of the structure of music by first reducing it to fundamental musical objects ... bake corner kaniyapuramWebbList of set classes. Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form. This is a list of set classes by Forte … ararat kebab pizzeria