In music, especially in musical set theory, a trichord is a collection of three pitch classes, often one of the four ordered trichords in a tone row or set form. Trichords may be used to create derived rows and invariance. ... Musical set theory is a atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... In common usage, a collection is any group of items that has one or more properties in common. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... In music, a tone row or note row is a permutation, an arrangement or ordering, of the twelve notes of the chromatic scale. ... In music using the twelve tone technique a derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the generator. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the...
Rows may derived from a sub-set of any number of pitch classes that is a divisor of 12, the most common being the first three pitches or a trichord.
For example, since a segment may be equivalent to the generating segment inverted and transposed, say, 6 semitones, when the entire row is inverted and transposed six semitones the generating segment will now consist of the pitch classes of the derived segment.
O represents the original trichord, RI, retrograde and inversion, R retrograde, and I inversion.
Trichords are sets of 3 notes, tetrachords are sets of 4 notes, and pentachords are sets of 5 notes.
A set is a defined as a trichord when the next (4th) note is impossible to predict out of multiple choices, as in the Sikah and Mustaar trichords for example.
It a variant of the Sikah trichord, with the 2nd note raised by a 1/2 tone.
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