If more than one row seems equally prominent at the beginning, then simply choose one (flip a coin!). If that is not the case, we generally choose the most salient row at the beginning of the work and label it P (for “prime”). In some pieces, one form of the row will clearly dominate the texture. The prime form of the row (top left in Example 1 above) is the main form to which all other forms are related. Serial fake by openmusictheory Prime form Row forms also don’t usually commit to placing pitches in a specific octave, but we’ll set it out in musical notation and with treble and bass clefs to show the inversions nice and clearly. Composers tend to prefer more interesting tone rows, but we’ll start with this simple case for illustration. To get a sense of the basic operations the composers perform on tone rows, let’s start with a fake example: an ascending chromatic scale starting on C ( Example 1). As such, a row produces a collection of 48 forms in what is called a row class. Unless a row has certain properties that allow it to map onto itself when transposed, inverted, or retrograded, there will be 48 forms of the row: the four types-prime (P), inversion (I), retrograde (R), and retrograde inversion (RI)-each transposed to begin on all of the twelve pitch classes. Twelve-tone rows that can be related to each other by transposition, inversion, and/or retrograde operations are considered to be forms of the same row. The order in which you do those operations does matter, but we’ll return to that later on. As the name suggests, this really involves combining two of the operations described above: the retograde and the inversion. “crab” or “cancrizans”) canon, for instance, though it’s a lot rarer in tonal music than transposition and inversion. This, too, has a precedent in tonal music with the “retrograde” (a.k.a. Reverse the order of pitches so the last comes first and vice versa. Again, this is just like melodic inversion in other contexts, and once again, we’re only dealing with exact inversion, preserving the interval size in terms of semitones (not using diatonic inversion or generic intervals here). Reverse the direction of the intervals: rising intervals becoming falling, and vice versa. This will be familiar enough from other, tonal contexts, but note that we’re always working in transposition by semi-tones here and never diatonic steps. Take all the pitches and move them up or down by a specified number of semitones. We call these “operations” (taking that term from the mathematical, rather than medical, sense!). There are four main ways in which composers move a row around without fundamentally changing it. In any case, many other row forms have never been used at all! Operations More precisely, it’s fairer to say that some properties of rows are favored and several composers favor rows with those properties, without necessarily going for exactly the same one. In fact, there are 479,001,600 distinct options to choose from! Some of these row forms are popular and we end up with several pieces based on the same row. There is no one series used for all twelve-tone music. Twelve-tone music is based on a series (sometimes called a row ) that contains all twelve pitch classes in a particular order.
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