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Any list of revolutionary women in music can't help but fall spectacularly short, so take this one - published to celebrate - as just a suggestion, or an argument, and please tell us who you think we've missed. Nina Simone and Dolly Parton, perhaps? Taylor Swift? We'd love to hear your choices, and your reasons why.

Our criteria was not to collate a list of the most successful female musicians in history, although many here were/are extremely successful, but to think of women who have had a profound effect on the history of music - even if, in the case of the top two on this list, it's taken musicologists hundreds of years to realise it.

Correctly or not, Kassia - born around 805 - is often called "the first female composer of the Occident" (the Western world) and her place in Byzantine folkore was sealed even before we knew of her music. She was from a wealthy family and dissed Emperor Theophilos at a "bride show" after he used the story of Eve from the Book of Genesis to suggest that women were responsible for much evil.

"And through a woman [came forth] the better [things]," she replied, annoyed. The Emperor decided to marry Theodora, who became empress, and Kassia adopted the monastic life. About 50 of her magical hymns survive, although authorship of some has been debated, as well as hundreds of her non-liturgical verses, including this zinging epigram: "I hate the rich man moaning as if he were poor."

In his book The Story of Music, Howard Goodall credits Kassia with "mixing the parallel organum style with the drone style", adding that her music "gracefully refutes the assumption that the development of early music is exclusively the handiwork of men".

In 2014, Howard Goodall and Suzy Klein made a case for Hildegard of Bingen's Ave, generosa being one of 50 pieces that changed the course of music history. In an In Our Time episode broadcast in the same year, Melvyn Bragg said: "Little known until 30 years ago, the music of Hildegard is now regarded among the best of the Middle Ages, but remarkably her music is only a small aspect of her overall achievement. Hildegard was a 12th century nun and a scholar of impressive breadth. Sometimes known as the Sibyl of the Rhine, she wrote a series of works documenting prophetic visions she had experienced, she was an accomplished theologian and also wrote about science, medicine and the natural world."

Hildegard has become a feminist icon with champions in the non-classical world, too, including Canadian art-pop artist Grimes, American singer-songwriter Julia Holter, and Cerys Matthews, who said she felt that "she could hear the tumble weed rolling through the listeners' houses" when she played Hildegard's music on her 6 Music show. Listen to Cerys discussing Hildegard of Bingen on Radio 4's Great Lives:

We're now moving on 700 years to the great German pianist and composer Clara Schumann - a jump that says much about the pressures on women not to compose music throughout history, as Schumann knew all too well. "I once believed that I had creative talent, but I have given up this idea; a woman must not wish to compose - there never was one able to do it," she said later in her life. "Am I to be the one? It would be arrogant to believe that."

But her achievements were huge. She had a distinguished 61-year career as a concert pianist, during which time she normalised playing from memory, rewrote the rule book on what kinds of pieces could and should be played at recitals (thereby changing the public's tastes) and was an influential teacher. She was also instrumental in drawing attention to the equally huge talents of her husband, Robert, as well as their friend Brahms, whose music she was the first to play. And her own compositions are finally getting the recognition they deserve too, particularly her 1846 Piano Trio in G minor, different recordings of which are discussed above.

We have in Sister Rosetta Tharpe a singer, songwriter and guitarist who had a considerable influence on spiritual and popular music in her hey-days of the 1930s and 1940s, and also left a lasting legacy. Often called 'The Godmother of Rock 'n' Roll', she inspired Elvis, Jerry Lee Lewis, Johnny Cash, Little Richard and Chuck Berry and is perhaps more revered now, 44 years after her death, than she was in her lifetime.

"Nobody - not Chuck Berry, not Scotty Moore, not James Burton, not Keith Richards - played wilder or more primal rock 'n' roll guitar than this woman who gave her life to God and would have celebrated her 100th birthday on 20 March," . "With a Gibson SG in her hands, Sister Rosetta could raise the dead. And that was before she started to sing."

Here's her 1948 self-penned hit, Up Above My Head:

Above, former 麻豆社 Radiophonic Workshop employee Brian Hodgson explains how the bare bones of the Doctor Who theme were written by Australian composer Ron Grainer and taken to the Workshop to be reimagined in a structures sonore ('sonorous sculptures') style. The job was handed to Delia Derbyshire, who worked with sound engineer Dick Mills. Grainer was so surprised by the final track he said, "Jeez Delia, did I write that!?"

The 1963 song is one of the most recognisable pieces of music ever written: a legendary TV signature tune, but also an historically significant recording - perhaps the most influential electronic music track ever composed. But there was far more to Derbyshire's work than the Doctor Who theme. Two years after it was completed, Tomorrow's World visited her at the Workshop (below) to discover how she made such seemingly alien music. She demonstrated a process that was surprisingly human and organic, but also revolutionary. Did Derbyshire inadvertently invent British techno music in the course of her work at the 麻豆社? Some of her certainly sound astonishingly modern.

The 1960s and 70s witnessed a boom in female singer-songwriters, from Joni Mitchell, to Dolly Parton and Carly Simon, and they all owe much to Carole King, the most successful female songwriter of the second half of the 20th century in both the US and UK.

King started out in the very late 1950s as a performer and writer and made her name with Will You Love Me Tomorrow in 1960, which she wrote for The Shirelles with lyricist Gerry Goffin, her first husband. It became the first No. 1 in history for an African-American girl group and kick-started King's extraordinary career. By the 70s, she broke out as a recording and performing star in her own right, particularly with her smash 1971 album Tapestry, and in 2013 became the first ever female recipient of the Library of Congress Gershwin Prize for Popular Song.

In this clip from 麻豆社 Radio Scotland's The Jazz House, which starts with Aretha singing (You Make Me Feel Like) A Natural Woman - a Carole King/Gerry Goffin song - presenter Stephen Duffy says: "Aretha Franklin has one of the most individual voices in all of music and I don't mean that in a purely vocal sense; she is a complete musician."

And she didn't budge an inch on her journey to become perhaps the most fêted soul singer of all time - female or male. She had a string of crossover hits on Atlantic Records between 1967 and 1980 without ever diluting her sound or message. She was the spirit of the age and with her reimagining of Otis Redding's Respect, in particular, she laid down an anthem for civil and gender rights that's as potent today as it was 50 years ago.

Aretha's 1985 album Who's Zoomin' Who? was her first to go platinum and two years later she became the first woman to be inducted into the Rock and Roll Hall of Fame. Her soul, sass and mastery of music live on in contemporary superstars like Beyoncé, Alicia Keys, Mary J. Blige and Adele.

With Patti Smith, as with every artist on this list, it helps to think what came before, and what happened after. There were of course female rock stars before Smith - Suzi Quatro, especially - but she was a new kind of artist in music, and in her wake came punk, grunge, riot grrrl, alternative rock and indie. So many of the key figures of those genres - from Siouxsie and the Banshees to Kurt Cobain, Bikini Kill, R.E.M., The Smiths - cite Smith as an influence and, in turn, their music has fed back into hers.

Smith's 1975 debut album Horses, which she once called "three-chord rock merged with the power of the word" was ahead of its time, foreseeing an explosion in DIY music-making and also the targeting of songs to the disenfranchised. Horses, Smith also said, was an attempt "to make a record that would make a certain type of person not feel alone. People who were like me, different…"

As well as being a musician, Smith is a poet, writer, visual artist, photographer and activist. Who else was going to introduce, and sing happy birthday to, the Dalai Lama at Glastonbury in 2015?

Sylvia Robinson was a true pioneer. The first hip hop hit - 1979's Rapper's Delight - was recorded by a group, The Sugarhill Gang, put together by Robinson and released on Sugar Hill Records, the label she founded with her husband, Joe. She went on to sign Grandmaster Flash and the Furious Five, who released The Message in 1982, a legendary track that introduced social commentary to hip hop, paving the way for groups like Public Enemy and N.W.A.

But there was far more to Robinson than just hip hop. Long before Rapper's Delight - in the late 60s - she was one of the few women producing records, and she was a killer songwriter, singer and performer herself. Check out Pillow Talk from 1973, a track Robinson penned for Al Green. He turned it down because it was too steamy, so she recorded it and had a hit - in the US, where it went to No. 3, and here. A Hollywood biopic is coming soon.

It felt like the announcement that Björk had won best International Female Solo Artist at the 2016 Brits was almost met with a shrug, like, "Of course Björk is the best, and she always has been." And we're finishing our list with her and not someone like Madonna or Taylor Swift - revolutionary in their own ways - because Björk is the consummate modern musician; the artist that, more than anyone else working in the pop field, sees the giant changes in technology and commerce over the last 20 or so years as an artistic opportunity, not a hindrance.

People now listen to music through tiny, computer speakers? Great, thought Björk, I'll make an album (2001's Vespertine) that sounds perfect at those sound frequencies. And after Wired magazine claimed in 2010 that (predicting a future of "getting", not "searching" - apps, in short), she rose to the challenge again with her so-called 'app' album Biophilia, but it was far more than a gimmick. Conceived during the Icelandic financial crisis, it was a statement - of music and art, but also politics and economics. Here's an example of how Iceland could be run from now on, she was saying - by investing in small companies based around local cooperation, which is exactly what she did to make Biophilia.

• 麻豆社 Music - Playlist: Celebrating Female Composers
• 麻豆社 Radio 3 - 7 lessons female composers can teach us about life
• 麻豆社 Music - What we've learned from interviews with female musicians on Woman's Hour