Music is a product of both biological and cultural evolution. Cultural transmission is the engine of cultural evolution and may play a role in the establishment of musical universals. Here, we examined how transmission dynamics can shape melodic features in music. Specifically, we tested whether random melodic seeds, in their transformation, take on properties known to characterise music within or even across cultures. Using an iterated learning paradigm, we investigated the transmission of random melodic seeds through a chain of non-musician participants (N = 64). We found that melodies reproduced vocally between “generations” became more similar to known musical scales, exhibited a predominance of consonant intervals, and reduced the number of scale degrees used. Additionally, we observed the previously documented tendency for large intervals to be followed by a change in direction, as well as features common to both music and speech including phrase-final lengthening and the Zipfian distribution of signalling units. As participants' vocalisations converged towards greater memorability, they exhibited decreased entropy, and their contours became smoother and more consistent. Finally, certain short melodic patterns became prominent motifs within the incipient musical “traditions” simulated by the chains. These emerging features may reflect a process shaped by (i) cognitive bottlenecks such as learnability; (ii) statistical properties of the processes and structures involved in inter-generational vocal transmission; but also by (iii) idiosyncratic cultural artefacts specific to the lab samples employed. Overall, our results demonstrate that fundamental aspects of melodic structure emerge naturally through the process of cultural transmission, as simulated in the lab.