About a primary series of his Piano Sonata No.2. This appears clearly in the first two measures of the 1st movement.
The primary series.
What the tone row means, it can be presented as the following propositions.
(6,7) has the element of (1,2) and (11,12).
Because of (3,4,5), and (8,9,10).
It is an interval that this proposition matters. The explanation : as follows.
Perfect fourth added to perfect fourth makes minor seventh.
when inverting it,
Perfect fifth added to perfect fifth makes major ninth which is a compound interval of major second.
Minor second added to minor second makes major second
So we can say,
Minor second *2 = perfect fifth *2 = major second (included it's compound interval)
- Major second is related to two conflicting elements, consonance and dissonance. It is because major second can be reduced to two intervals of minor second (dissonance) or to two intervals of perfect fifth (consonance) respectively -.
That is what the previous proposition ,the tone row says.
Another side of this tone row's structure.
See the divided tone row again.
When (1,2) (6,7) (11,12) was especially noted in the sections divided into five, I thought that (6,7) and (11,12) were completely installed in the frame of perfect fifth of (1,2). And then I noticed following relation.
Twelve tone is filled with a combination of the scale which consists of six tones. The whole of this scale is installed on the frame of perfect fifth. The array of the interval is symmetrical(whole half half half whole). The tone row of P.Boulez's second piano sonata is also based on this feature of twelve tone.