The concerto's first theme, which follows the famous introduction, is based on a melody that Tchaikovsky heard performed by blind beggar-musicians at a market in Kamenka (near Kiev), is notable for its apparent formal independence from the rest of the movement and from the concerto as a whole, especially given its setting not in the work’s nominal key of B-flat minor but rather in D-flat major, that key's relative major. Despite its very substantial nature, this first theme is only heard twice, and it never reappears at any later point in the concerto.
Russian music historian Francis Maes writes that because of its independence from the rest of the work, "[f]or a long time, the introduction posed an enigma to analysts and critics alike.…The key to the link between the introduction and what follows is…Tchaikovsky’s gift of hiding motivic connections behind what appears to be a flash of melodic inspiration. The opening melody comprises the most important motivic core elements for the entire work, something that is not immediately obvious, owing to its lyric quality. However, a closer analysis shows that the themes of the three movements are subtly linked. Tchaikovsky presents his structural material in a spontaneous, lyrical manner, yet with a high degree of planning and calculation."
Maes continues by mentioning that all the themes are tied together by a strong motivic link. These themes include the Ukrainian folk song "Oy, kryatshe, kryatshe…" as the first theme of the first movement proper, the French chansonette, "Il faut s'amuser, danser et rire." (Translated as: One must have fun, dance and laugh) in the middle section of the second movement and a Ukrainian vsnyanka or greeting to spring which appears as the first theme of the finale; the second theme of the finale is motivically derived from the Russian folk song "Podoydi, podoydi vo Tsar-Gorod" and also shares this motivic bond. The relationship between them has often been ascribed to chance because they were all well-known songs at the time Tchaikovsky composed the concerto. It seems likely, though, that he used these songs precisely because of their motivic connection and used them where he felt necessary. "Selecting folkloristic material," Maes writes, "went hand in hand with planning the large-scale structure of the work."
All this is in line with the earlier analysis of the Concerto published by Tchaikovsky authority Professor David Brown, who further suggests that Alexander Borodin's First Symphony may have given the composer both the idea to write such an introduction and to link the work motivically as he does. Brown also identifies a four-note musical phrase ciphered from Tchaikovsky's own name and a three-note phrase likewise taken from the name of soprano Désirée Artôt, to whom the composer had been engaged some years before.