Upon opening the score of Improvisation for Piano No. 2, one finds melodic fragments labeled A1, A2, A3, A4, B1, B2, B3, B4. The A series and B series each consist of four fragments, and their order of arrangement is left to the performer. The composer's instructions are to perform each of A and B once in any desired order, to omit one performance of A in the middle section and instead play the B series twice consecutively at that point, and to set the beginning and end to the A series. An example of a combination of A and B is as follows:

• A1 → B1 → A2 → B3 → A3 → B2 → B4 → A4

In the score, quarter notes, whole notes, and other note values are notated at slightly varying intervals. Each note represents an approximate proportion of "duration," and the intervals between notes represent an approximate proportion of "tempo." The A series begins with repeated G-sharp notes, while the B series is generally pointillistic. The A series, interspersed regularly, brings a sense of formal unity to the whole. On the other hand, performers are granted freedom in combining the melodic patterns. In other words, this piece exhibits a coexistence of determinacy and indeterminacy. Improvisation for Piano No. 2 was written in 1968 for the 2nd Japan-Germany Festival of Contemporary Music. It is one of the works that clearly reflects Shibata's creative philosophy. The composer stated during his lifetime that the sounds in this work are "strictly arranged in a certain way," and "whoever deciphers the method of their arrangement will be granted anything they desire." While it is no longer possible to question Shibata about Improvisation for Piano No. 2, it might be worthwhile to attempt to unravel the challenge presented by Shibata when performing this work.