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The problem raised in this article is: if Stravinsky did indeed start to compose his Symphony of Psalms in what was to be the middle of the work, as he claimed, how did he construct the often changing rhythms, meters and tempi in order to create logic and coherence? Why, in this constantly changing flow of tempi, does the score look so remarkably uniform? It will be proposed that before working out the rhythmical patterns, Stravinsky made a complete design for the entire composition, of measures, groups of measures and tempi. For the composition of this grid, use was made of the numbers 3, 4 and 7.