*Of course, there are tons of women composers. This is something I did as an intro for non-music major type folks. If you want to use women composed pieces for examples in a theory class, I’ve been using this resource: http://musictheoryexamplesbywomen.com/ and there’s also this: https://adaptistration.com/2018/01/02/an-operational-women-composers-database/
There are more, but to keep this brief, I’m going to stick to one composer per time period or so. And this is of course the “classical” western “art” music genre time periods.
Middle Ages: Hildegard of Bingen was a nun in Germany and wrote lots of interesting choral music for her monasteries. She was also a prominent scientist.
O Frondens Virga: https://www.youtube.com/watch?v=QGXXrUvNzec
further reading: https://en.wikipedia.org/wiki/Hildegard_of_Bingen and http://musictheoryexamplesbywomen.com/composers/hildegard-von-bingen-c-1098-1179/
Renaissance: Francesca Caccini worked for Queen Maria de Medici of France at one point, and became the highest-paid musician at the Medici court in the 1620s. She is believed to be the first woman to write an opera.
Ch’amor sia nudo: https://www.youtube.com/watch?v=Rn129DOrmyQ
further reading: http://musictheoryexamplesbywomen.com/composers/francesca-caccini-1587-1641/ and https://en.wikipedia.org/wiki/Francesca_Caccini
Baroque: Elisabeth-Claude Jacquet de la Guerre was accepted as a musician for the French court while still a teenager. While most of her works are for chamber ensembles, she did compose two remarkable stage works: a lost ballet (Les jeux à l’honneur de la victoire, 1691) and an opera (Céphale de Procris, 1694), believed to be the first opera by a woman in France.
Sonata for Violin and Continuo: https://www.youtube.com/watch?v=ZTwsJN3z_iI
further reading: http://musictheoryexamplesbywomen.com/composers/elisabeth-claude-jacquet-de-la-guerre/ and https://en.wikipedia.org/wiki/%C3%89lisabeth_Jacquet_de_La_Guerre
Classical: Louise Reichardt was middle class, receiving some informal education from her father and family friends but primarily self-taught. Many prominent figures in the German Romanticism movement, such as the Grimm brothers, Joseph von Eichendorff, and Ludwig von Arnim, were frequent guests at the Reichardt home and were known to have admired Louise’s song settings and singing ability.
Unruhiger Schlaf: https://www.youtube.com/watch?v=3SCSyQgj4CI
further reading: http://musictheoryexamplesbywomen.com/composers/louise-reichardt-1779-1826/ and https://en.wikipedia.org/wiki/Louise_Reichardt
The Romantic era is hard, partially because it’s pretty long. Seriously go listen to every composer on this list: http://musictheoryexamplesbywomen.com/composers-romantic/ but my favorites are Fanny Hensel, Clara Schumann, Amy Beech, and Rebecca Clarke. I’m choosing to highlight Florence Price here. She studied composition at the New England Conservatory, privately with George Chadwick, and later in Chicago as well. She taught at a number of colleges and universities throughout the American south. Price became the first black American woman to have a work performed by a major American orchestra.
Symphony in E minor: https://www.youtube.com/watch?v=9s4yY_A2A2k
further reading: http://musictheoryexamplesbywomen.com/composers/florence-price-1887-1953/ and https://en.wikipedia.org/wiki/Florence_Price
With the expansion of opportunities for women (as well as better/more recent information storage), the 20th Century has lots of women composers. Here’s a selected list, but there are definitely more. http://musictheoryexamplesbywomen.com/composers-modern/ Some of the most famous from that list are both Nadia and Lili Boulanger, Germaine Tailleferre, Ruth Crawford Seeger, Ursula Mamlok, Kaija Saariaho, and Joan Tower. One that is on that list is Sofia Gubaidulina. She is a Russian composer who has experimented with different tunings, refused to give up modernism when asked by the USSR, and has also worked on film scores.
further reading: https://en.wikipedia.org/wiki/Sofia_Gubaidulina
That doesn’t even get into jazz, rock, and other pop styles in the last century. I’m not well read enough to do justice to those genres. You could start here for jazz: https://en.wikipedia.org/wiki/Women_in_jazz but I’m not even sure where to start for rock and other later styles.
Suggest your favorite women composed pieces in the comments!