In 1928 he went to Leipzig to study composition (H. Grabner and L. Wenninger) and piano (O. Weinreich). After only two years of studies, his Two-Part Inventions were published by Breitkopf and Härtel and soon after his Piano Concerto No. 1 was performed by the Leipzig Symphony Orchestra. He left Leipzig after four years. In 1932, 1933 and 1935 he studied for periods of time in Paris where he was taught composition and orchestration by Honegger and Villa-Lobos, among others. In Vienna, he received musical training under the guidance of Egon Wellesz. He then settled in Oslo and the years up to the outbreak of the Second World War were to become a prosperous period for him as a composer. The performance of the ballet Baldur’s Dreams in Oslo in 1938 was a climax. This massive work is built on an old Norse legend. The piece was later performed in Paris and was also supposed to be staged in Covent Garden, but the score was lost in the bombing of London during the Second World War.

In 1942 Tveitt moved back to Hardanger where he began to systematize the collecting and the arranging of folk-tunes. Numerous trips around the fjord resulted in the transcription of more than a thousand folk-tunes (according to Tveitt himself). He arranged a hundred of the tunes, both for piano and orchestra. Luckily, copies of the first fifty piano versions as well as four suites, each including fifteen folk-tunes for orchestra, existed at the time of the tragic fire that destroyed his farm house in 1970. These tunes have since been considered Geirr Tveitt’s main work, and especially the orchestral versions have received acclaim.

In the years to come, Geirr Tveitt toured extensively in Europe as a pianist in addition to his composing. Among the most significant events was a concert in Paris in 1947 with first performances of Sonata No. 1, some Hardanger Tunes, as well as the more modernist works, Sonata No. 29 and Piano Concerto No. 4. This was a unanimous success. Seven years later he returned to Paris to a first performance of his own Piano Concerto No. 5 Op. 156, an event that was equally successful. A number of piano recitals where the composer played his own music, often together with works by Grieg, Chopin and Liszt, gained him fame as a virtuoso pianist. As a composer, however, he faced greater opposition than before in his own country. The national style represented by Tveitt was increasingly criticized in the Norwegian press.

Geirr Tveitt was a prolific composer. He worked quickly and seldom used drafts. Instead he transcribed complicated scores from memory. He was clearly impulsive; his compositions were frequently altered, often a change was made in the music only just before the musicians were going on stage. Tveitt wrote music in all different kinds of formats, from snatches of songs to concertos, ballets and operas. He was a strong supporter of the national idiom and especially his early compositions show signs of this. Several works are also programme oriented. The inspiration from Hardanger nature was important to the composer and often a walk in the mountains was what led to a new composition. Themes of folk-music were, however, seldom integrated in his works the way Grieg did. Tveitt was careful to credit different sources. In fact, he was so eager to inform the general public about other sources than himself, that there have been speculations as to whether some of the Hardanger Tunes really are his own compositions, either partly or fully. There is, however, no doubt that the majority of the Tveitt works are folk-music inspired.

A considerable number of Geirr Tveitt’s works are written in modal keys. In 1937 the composer published a theoretical thesis (Tonalitätstheorie des parallelen Leittonsystems) in which he stated that the modal scales dorian, phrygian and lydian really are old Norse keys. He did not find support for his ideas in central musical circles in Norway where he was often looked upon as a reactionary, but in France his thesis was given credit by Florent Schmitt, among others. Later Tveitt considered his thesis "a bit youthful in its form", but he did not give up these theories in his composing.

From the 1960s onwards, the composer spent a lot of time in Oslo working partly as a radio producer. In this period a number of songs were added to his body of works, often written on a moment’s inspiration. Many of these songs were made for radio programmes, produced by Tveitt, about Norwegian authors such as Hamsun and Wildenvey. Nonetheless, the 1970 fire which led to the loss of possibly 80% of his musical production, took away a lot of his will to live. Geirr Tveitt, once described as "an unstoppable waterfall" in Norwegian musical life, died a reduced man, after a period of illness, on 1 February, 1981.

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