There are only a few previous EEG studies that were conducted while the audience is listening to live music. However, in laboratory settings using music recordings, EEG frequency bands theta and alpha are connected to music improvisation and creativity. Here, we measured EEG of the audience in a concert-like setting outside the laboratory and compared the theta and alpha power evoked by partly improvised versus regularly performed familiar versus unfamiliar live classical music. To this end, partly improvised and regular versions of pieces by Bach (familiar) and Melartin (unfamiliar) were performed live by a chamber trio. EEG data from left and right frontal and central regions of interest were analysed to define theta and alpha power during each performance. After the performances, the participants rated how improvised and attractive each of the performances were. They also gave their affective ratings before and after each performance. We found that theta power was enhanced during the familiar improvised Bach piece and the unfamiliar improvised Melartin piece when compared with the performance of the same piece performed in a regular manner. Alpha power was not modulated by manner of performance or by familiarity of the piece. Listeners rated partly improvised performances of a familiar Bach and unfamiliar Melartin piece as more improvisatory and innovative than the regular performances. They also indicated more joy and less sadness after listening to the unfamiliar improvised piece of Melartin and less fearful and more enthusiastic after listening to the regular version of Melartin than before listening. Thus, according to our results, it is possible to study listeners' brain functions with EEG during live music performances outside the laboratory, with theta activity reflecting the presence of improvisation in the performances.