) gives to the listener the sense of the key of a piece. Substituting the tonic chord with a different degree of the scale (or with a chord of another key ), you get an interrupted cadence.Modulations and interrupted cadences always more frequent and daring historically have progressively weakened the sense of tonality. Also because in a piece of five minutes the repetition, in the same key, of the initial theme can be perceived as a “return to home”; but in a much longer one it does not produce the same effect. Paradoxically, the maximum development of the tonal system (late nineteenth century) is also the beginning of its crisis.
Around 1920 Arnold Schönberg invented the twelve-tone system, that, if on the one hand is the son of the crisis of the tonal system (from which, in a sense, descends), on the other hand it is opposed to it, with the aim to give to all notes of the chromatic scale equally importance (the tonal system, instead, is hierarchical, in the sense that each note has a different weight depending on whether it is the tonic, the dominant, etc.).
Please note that the terms atonal and twelve-tone are not synonymous: the first refers to any music with no tonal reference, the second to a particular atonal system based on the development of a tone row: ie a succession of twelve notes in which each notes of the chromatic scale must appear once and only once. For example: C-F#-C#-D#-D-E-A#-B-F-A-G-G#
. From this tone row, called original and denoted by O1, you can obtain the following combinations:- retrograde tone row (denoted by R1), exposing the notes of the tone row from the last to the first (in our example, G#-G-A-F-B-A#-E-D-D#-C#-F#-C );
- inverse tone row (I1), transforming the descending intervals in ascending ones and vice versa: for example, since the fragment C-F#-C#-B# is obtained coming down of 6 semitones (C-F#), up of 7 (C#) and again of 2 (D#), in the inverse tone row you must, starting from A, coming up of 6 semitones (F#), down of 7 (B) and again of 2 (A). The complete tone row is transformed therefore in C-F#-B-A-A#-G#-D-C#-G-D#-F-E ;
- inverse retrograde tone row (RI1), ie the retrograde tone row of the reverse one (just take the notes of the tone row I1 last to first: E-F-D#-G-C#-D-G#-A#-A-B-F#-C );
- transposed tone rows, obtained by raising all the notes of a tone row of the same number of semitones. The procedure is similar to that used in the tonal system for the modulation
(at least when the mode does not change): transposition does not affect the intervals between the notes, exactly as in the passage, for example, from C major scale to A major scale. Each of the four base tone row (O1, R1, I1, RI1) generates other twelve transposed tone rows (including itself): one for each note of the chromatic scale, for a total of forty-eight. For example, raising the notes of O1 of a semitone you obtain O2: C#-G-D-E-D#-F-B-C-F#-A#-G#-A
All this may seem a very cerebral system, more mathematical than musical; but the real problem is not the system that a musician uses (even the tonal system has its own rules), but how he uses it, what it communicates by means of if: as Schönberg said, “A Chinese do not speak only Chinese, but it says something. This is what matters, not the language they use (from the interview with the daughter Nuria on the newspaper “Il Messaggero” of July 12 2001).
Fractal
and Imperfect canon use, although with some licenses, the twelve-tone method.| Index | Previous | Process a tone row | Return to my compositions |