Pitch class
Pitch class is a term from mathematical music theory , which is mainly used in America. There its conceptual equivalent is “pitch class”.
background
Human pitch perception is periodic. Pitches that are a full number of octaves apart are perceived as having a similar "quality" or "color". Psychologists refer to this quality of a pitch as “chroma”. In a mathematically oriented music theory, the term “pitch class” has established itself for “chroma”, but its meaning differs somewhat. While “chroma” is an attribute of pitches like “whiteness” is an attribute of white objects, a pitch class represents a set of pitches with the same chroma, just as a set of all white things represents a collection of all white objects. The musical theoretical use of the term “pitch class” instead of “chroma” is due to the logical positivism of its author, Milton Babbitt . Mathematical music theory uses the terminological tool of set theory for its statements . In translation of the English term "pitch class set analysis" one could call their activity "pitch class set analysis".
Explanation
The pitch class "C" is therefore the infinite set of all pitches with the Chroma "C", irrespective of the Oktavräume (z. B. Contra octave, octave above middle etc.). In scientific notation, this statement reads as follows:
- {C _{n} } = {..., C _{-2} , C _{-1} , C _{0} , C _{1} , C _{2} , C _{3} ...}
Since different tone symbols denote the same frequencies in the equal tuning due to the Enharmonics , z. B. His _{3} , C _{4} and Deses _{4 have} the same frequency and thus belong to the same pitch class. _{}_{}_{}
To avoid the ambiguity of enharmonic notation, theorists use numbers to denote pitches. The following formula can be used to determine the fundamental frequency of a pitch (measured in Hertz ) as a real number :
It creates a pitch space in which octaves are size 12, semitones are size 1 and z. For example, the dashed C is the number 60. The description of pitches in real numbers is also the basis of the midi protocol , which uses numbers from 0 to 127 to represent the pitches from C _{-1} to G _{9} .
In order to display pitch classes , all pitches of a pitch class must be identified or summarized - i.e. H. all the numbers p and p + 12. The result is a quotient space , the musician pitch room call and mathematician R / 12 Z .
Points in this space can be labeled with real numbers in the range 0 ≤ x <12. These numbers represent numerical alternatives to the letter symbols in traditional music theory:
- 0 = C, 1 = C # / Db, 2 = D, 2.5 = "D + quarter tone" etc.
To avoid confusing 10 with 1 and 0, some theorists use the letters "t" (for "ten") and e (for "eleven") or A and B, as in the writings of Allen Forte and Robert Morris .
TK | Tonal equivalent |
---|---|
0 | C (also His, Deses) |
1 | Cis, Des (also Hisis) |
2 | D (also Cisis, Eses) |
3 | Dis, Es (also Feses) |
4th | E (also Disis, Fes) |
5 | F (also ice cream, Geses) |
6th | Fis, Ges (also Eisis) |
7th | G (also Fisis, Ases) |
8th | G sharp, a flat |
9 | A (also Gisis, Heses) |
t or A | Ais, B (also Ceses) |
e or B | H (also Aisis, Ces) |