All of Panufnik's symphonies have titles. In fact, he originally assigned them only titles, not numbers. It was only when he reached his eighth or ninth that he also numbered a symphony. This allows one to count backwards and determine that the First Symphony is his "Sinfonia rustica" and that Panufnik does not count the two earlier symphonies that were lost in the fire associated with the Warsaw uprising against the Nazis during World War II.

All musical composition can be seen as a process of limiting the entire available spectrum of sound into just the notes that are written in the score. For Panufnik, the first step in writing music after determining the general shape and nature of the piece is to impose a preliminary restriction on the choices he might make. As the title of the symphony says, this was to be Panufnik's "Symphony of Hope." Taking the rainbow as the traditional symbol of hope, Panufnik drew a diagram setting a three-note cell (E-B-F) as a "prism" that set up a spectrum of emotions and guided the melodic line through the keys of E, G, B flat, Ff, c, e flat, f#, e flat, c, fF, B flat, G, and E. (In this list of keys the upper case letters denote Major keys, the lower case letters minor keys, and the "Ff" and "fF" stand for the emotional pivots of the work, where the modality switched from F Major to f minor and back.) It will be seen that this rainbow of tonalities has seven different keys (colors), and arcs back on itself like a rainbow. This generates a continuous melodic line. In the meantime, the original three-note cell is also kept present in all its permutations and transpositions.

The formal construction is also in arch patterns. For instance, in the first arc the three-note pattern begins in a lower register, works its way upward, and then falls back to complete the arch. Meanwhile, the melodic line traces a reverse arch.

Panufnik employs analogous procedures in most of his works. It is this that makes his music most controversial, for some listeners find the results arid and "mathematical." Other find that these methods create very moving music. The emotional journey of the symphony begins in "warm colors" representing hope, through "cold colors" representing the opposite emotions, doutbt and fear, and back again. Much of the symphony is in slow tempo, allowing the composer to exploit the singing quality of the orchestral instruments.

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