(an incomplete list)
Here are some noted musicians/composers who also have a significant scientific background. The list is clearly far from complete and additional suggestions are welcomed.
Franklin was an American publisher, writer, polititian, scientist, and amateur musician, among other accomplishments. He is noted for composing at least one "drinking song" and an unusual string quartet is also attributed to him. He is the inventor of the glass harmonica.
Garcia was a Spanish baritone and music instructor. His interest in the mechanics associated with singing led him to invent a device which is considered the first laryngoscope – a medical device to visualize the larynx (vocal folds, glottis, etc). He has a small number of musical compositions and should not be confused with his father, also Manuel Garcia (1775-1832) a tenor and a more prolific composer.
Herschel was a British musician and composer turned Royal Astronomer. While he has many compositions to his credit, mostly unplublished and including over 20 symphonies and a number of violin concertos, he is probably best known for his accomplishments in his second carrer such as discovering that Uranus is a planet and discovering infrared radiation. Holographic (handwritten) manuscripts for many of his compositions can be found within the collections of the British Library.
May is perhaps most well known for his role as the lead guitarist and composer/song writer for the rock band Queen. His compositions include "We Will Rock You," among many others. Though he started the research much earlier, he returned to his work, finished his PhD requirements and was awarded a PhD in Astrophysics by the Imperial College, London, in 2008. He has since co-authored several books about astrophysics.
Saint-Saëns was an avid amateur astronomer who wished he had studied science and math better in school. He became active in his local astronomy society and he regularly contributed at their meetings and to their newsletter. Some of his ideas, such as the assertion that there must be planets about other stars, were spot on. Other ideas were, well, pretty far off even by the standards of the day. Perhaps his biggest contribution to astronomy was through his fame as a composer. His involvement and enthusiasm with the society, and astronomy in general, attracted attention to astronomical issues by way of his celebrity.
Paulo Vanzolini was a leading herpetologist and composer, most notably of sambas. A member of the Brazillian Academy of Sciences and a Guggenheim Foundation Fellow, among other recognitions, and he has roughly 20 different animal species named after him. He is considered one of Sao Paulo's best known samba musicians and there are several recordings available that feature his music.
Wheatstone was a British scientist known as a principle inventor of the telegraph. Those who have made sensitive scientific measurements may have also heard of the "Wheatstone bridge" method for comparing two resistance values. (Wheatstone did not invent the circuit but mearly popularized it.) Wheatstone's early scientific work dealt largely with the propagation of sound, which arose from his early involvement with the family business – a music store. That line of thinking later led him to study the propagation of electrical signals. Work with William F. Cooke led to many early patents for the telegraph. From his youth until old age Wheatstone remained heavily involved his family's music business. One of Wheatstone's surviving inventions is the English concertina, a small accordion. Wheatstone was very shy in front of large crowds and often had others present his results for him. One regular presenter was the very prominent physicist at the time, Michael Faraday.