This could end up being an extremely long answer, so I'll limit myself to the Romantic period and to certain composers who achieved huge levels of fame during their time. Which only narrows it down to a very long answer.

By the time the classical style went out of fashion, around the end of the 18C, a radical shift in paradigm was starting to become apparent in the sphere of what we now call "art" or "academic" music. See, for centuries, large scale music had been composed primarily at the behest of monarchs and nobles, and therefore tended to be incredibly out of reach for most of the population. That didn't necessarily mean the emerging bourgeoisie couldn’t occasionally get to enjoy performances by renowned composers during the classical period, but it wasn’t the norm, folk music would be what we now understand to be “pop” music. But I’m not an expert in European folk, so I’ll leave that bit to my betters.

What exactly is the Romantic period?

Very broadly speaking, it’s an artistic movement. No shit, Sherlock. But seriously though, that’s what it is. In terms that interest us, it’s part of the never ending evolution of art music. Most musicologists agree in determining that it gradually emerged in what is now Germany, largely due to the work of several composers who lived around the same period, and who initially subscribed to a movement known as the Sturm und Drang, which is German for Storm and Drive, although it’s also referred to as Storm and Stress.

The core principle was based on opposing the traditional ideals of the enlightenment: while the enlightenment principle of reason as the basis for all creation had influenced artists to compose music based in grand, emotionless structures, reflecting techniques and virtuosity above all else, this movement, proposed by several writers such as Johann Wolfgang von Goethe and by composers like Johann Baptist Vanhal and Carl Ditters von Dittersdorf, implied abandoning reason as the basis for art, focusing instead in the freedom and expressivity that emotions allow. And so, new composition styles arose, which favor change instead of rigid structures; melody takes preeminence, which can, like a storm, change drastically in just one set of notes, one single measure. The result gives us unpredictable pieces, with sudden shifts in tempo, and the incorporation of mechanisms like the tremolo, a technique consisting in adding gravitass and emphasis to the melody through strong vibrations in the strings. Oftentimes, compositions written following this style are in a minor key, which typically serves to demonstrate deep and often dark emotions and feelings.

This style was instrumental in the development of Beethoven’s new wave of pieces that, starting with his Third Symphony, the Eroica, drifted away from the classical structures imparted to him by Joseph Haydn, one of the most influential classical composers and his teacher, focusing instead on emotional elements. Other contemporaries of his who became more and more interested in leaving the overly rigid structures of classicism behind, such as Louis Spohr, also German, renowned as one of the greatest violinists of his time. Most of his compositions are for violin as soloist, and many of them include the harp. Why is this relevant for this emotional component? Well, ever since he was a child, Spohr had felt a deep fascination for this instrument, which he could not play without feeling incredibly frustrated, due to his deeply rooted perfectionism. When he moved to Gotha in 1805 to take the position of kapellmeister, he met a young harpist called Dorette Scheidler, who was 18 at the time; young Louis fell in love immediately, according to his autobiography. After spending time conducting the orchestra in which Dorette would often play harp, piano and violin solos, Spohr decided to confess his love when, after a private concert from which they departed together alone in a carriage, he held her hands in his own and asked her “shall we thus play together for life?”

They got married and of their marriage two daughters were born, as well as a series of compositions specifically designed either for the violin and the harp, or for the harp as soloist. The motivation and inspiration for these pieces came, according to his own words, from his deep love and devotion to his wife. Fascinated by Dorette's prodigious technical skills, and still an admirer of the instrument itself, Spohr decided, working together with Dorette, that they should design a technique that would allow them to play together, since both instruments are, typically, incompatible. The result was a technique that introduced modifications to the tuning in both instruments, to avoid, when it came to producing sounds at the same time, that the necessary tension ended up breaking the extremely fragile strings of the harp.

But aquatermain, why is emotion relevant if we’re talking about fame?

Because emotionality and nationalism go hand in hand. The 19C is a century that sees the full emergence of capitalism, nationalism, and imperialism. Nation states are showing up everywhere on the European map. Capitalism is starting to delete the aristocracy as the only real big and powerful social class. Wanna know what capitalism and imperialism need to exist in this period? Nationalism. Patriotic sentiment is something rather new to most European nations, since most of them hadn’t even considered themselves to be nations up to this point, at least not in the traditional sense we now understand a nation to be.

Many composers from the romantic period felt a deep connection to their own nations. You mentioned Franz Liszt, and, well, he was definitely one of the precursors of the introduction of nationalistic themes, borrowed from folk tunes and styles, into art music. And my oh my was Liszt famous. By the time he turned 30, he embarked on a set of tours through Europe that lasted, on and off, almost the entire 1840s, mainly because he was one of the greatest pianists of his time, but also because he created deeply emotionally charged music, often rooted in nationalistic Hungarian themes and sounds. Although Liszt spent most of his later years composing and teaching instead of performing in public, he remained a legend, a legend that survives to this day.

A good friend of Liszt's also became exceedingly famous in his time: Camille Saint-Saëns, one of my favorite composers of all time. Born in Paris in 1835, he showed signs of having perfect pitch by the time he was three, learning the basic elements of the piano from his great aunt.

Saint-Saëns received formal piano lessons from Camille-Marie Stamaty, a composer renowned for composing pedagogically friendly pieces, as well as piano interpretation techniques. In spite of Clarence’s initial doubts, his prowess was so great, that he gave his first public performance aged 10, playing pieces by Mozart and Beethoven, marvelling the audience. 3 years later, he was admitted at the Paris Conservatoire, one of the most prestigious musical instruction institutions in the world, remaining to this day one of its most distinguished alumni. There, aged 13, he began composing the first of his almost three hundred works.

After leaving the Conservatoire, between 1861 and 1865, a very much still young Camille started working as a teacher at the Niedermeyer School in Paris. During this period, his teaching post demanded most of his time, and so he ended up resigning in 1865 in order to go back to composing and performing in public, since he barely composed anything during his tenure (with the notable exception of his Introduction and Rondo Capriccioso, dedicated to virtuoso violinist and composer Pablo de Sarasate).

The final decades of the 19C meant a huge uptake on his popularity, rapidly becoming one of France’s most popular composers and performers. By this point, Saint-Saëns, who had been considered to be some sort of reincarnation of Mozart in his youth, had also gained the approval and admiration of many of his peers by this point, including his friend Liszt, and other big names like Hector Berlioz and Giachino Rossini. By the time the 1880s showed up, his fame had crossed the channel, and he became a favorite of the London music scene, travelling with some regularity to England to perform his own works, as well as to conduct other composer’s pieces, where he premiered his Third Symphony in 1886, commissioned by the Royal Philharmonic Society, and eventually dedicated to the memory of his friend Liszt after his death that same year. I particularly recommend listening to this recording of his Third Symphony performed by Letonian organist Iveta Apkalna.

The Red-Headed League

I could go on forever. As an honorable mention, let’s talk briefly about Pablo de Sarasate. He was a Spanish composer who is considered to be, together with Niccolo Paganini, one of the greatest violinists in history. He composed only 54 pieces, because unlike most of his contemporaries, he prefered to spend his days performing in public rather than actually composing.

Sarasate was so incredibly gifted with the violin that he spent most of his adult life touring Europe, North América AND South América, and his fame was so great, that Arthur Conan Doyle included him as an important element in his short Sherlock Holmes story The Red-Headed League. In the story, Holmes interrupts his investigations to go and see Sarasate performing live.

Wanna see something cool? We have a few recordings of Sarasate playing, done at the very beginning of the 20C. Here he is playing the second movement of one his most famous pieces, arguably one of the hardest pieces ever composed for the violin, Zigeunerweisen.