A pub quiz question for you, dear reader: with which work did 20th century music begin? The rest is noise, Alex Ross's history of 20th century music, opens with Richard Strauss's 1905 opera Salome, focusing particularly on its final bars. As Princess Salome is crushed under the shields of King Herod's guard, the music turns to what Ross describes as "...a tumult... a howl... a shriek... In effect, the opera ends with eight bars of noise". Last night's all-Strauss concert, which closed with the Dance of the Seven Veils and the last scene from Salome marked the start of a year-long programme of events dedicated to telling the story of 20th century music, inspired by and named after Ross's book.

Salome was sung by Finnish soprano Karita Mattila, introduced by Thomas Hampson as "one of the great Salomes of this or any age". Mattila lived up to such star billing. The last scene of Salome is all about mental extremes, as the crazed princess swings from vengeful fury to terror to dreaminess to necrophiliac lust. The piece still shocks, and Mattila has a flexibility of voice and an understanding of the music which lets her reach every one of those extremes, bringing her character to life in front of your eyes. She brought the house down.

It's always a difficult task to balance a giant orchestra like Strauss's with a single singer's voice, a task made even harder when playing in concert without the protection of an orchestra pit. The LPO's conductor Vladimir Jurowski explained that he had attempted to alleviate the problem by going to the archives in Dresden to find a reduced orchestration written by Strauss himself (but never printed) for performances when the soprano who created the role, Marie Wittich, was replaced by a more Mozartian singer with a lighter voice. The ploy was effective in making it possible to hear Mattila, who is no longer at quite the power levels of a decade ago.

At the mid point of each half of the concert, Jurowski exchanged his baton for a microphone to tell us about the music. He proved an excellent presenter: immensely knowledgeable, affable and able to pick points of real interest and explain them with crystal clarity. It added greatly to my enjoyment of the evening, and I wish that conductors would do this more often. In particular, Jurowski placed each work in context in the development of both Strauss and the composers who followed him.

If Salome marks the start of 20th century music, the 1899 Notturno and the 1897 Four Songs, Op. 33 mark the close of the 19th, prefiguring the changes to come. The Notturno is a dark, reflective song based on a poem by the influential Richard Dehmel and featuring an achingly beautiful part for solo violin. It's a tonal work, but one whose key is constantly changing, and Thomas Hampson proved adept at navigating these shifting sands. His voice was full, expressive and clear, eloquently transporting us into Dehmel's snowscape filled with dreams both nightmarish and sweet. Hampson's low register notes were occasionally lost, and he sometimes overemphasised closing consonants, but he is marvellous at following a vocal line and taking you wherever it leads.

In contrast to Strauss's Four Last Songs, the Op. 33 set is rarely performed. Listening to it in this concert, I wondered why – this is music of great beauty and, as Jurowski explained, classical symmetry: two each for baritone and soprano voices, two each Apollonian and Dionysian. Mattila gave us elegance of phrasing and beautiful timbre, but struggled to make herself heard above Strauss's lush orchestration. Hampson brought out the poetry to the full.

The LPO's performance was decidedly mixed. In the concert's opening piece, the tone poem Also sprach Zarathustra, the orchestra lacked urgency and coherence. Both strings and woodwind lacked richness and clarity of phrasing, and my attention wandered on several occasions. But the LPO improved considerably when accompanying the songs, and they were quite splendid in the Notturno and the Dance of the Seven Veils, giving us a vivid account of Strauss's extraordinary blend of orientalism, Viennese waltz and psychodrama.

Although not without its imperfections, this concert did a wonderful job of showcasing Strauss's music. Whether you view Strauss as the end of a glorious era, the start of an exciting one or both, it made fascinating listening, and it's a privilege to have heard Mattila performing this role.