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They are taken from Tchaikovsky's Piano Concerto No.1 in B flat major.
Piano: Prelude in G minor. A perfect "snapshot" of Rachmaninoff's style. The done-to-death "Prelude in C# Minor" is OK, but the G minor is much better, in my opinion. Orchestra with piano: The Concerto #2 in C minor - all three movements, and the "Rhapsody on a Theme of Paganini". Those are the best introductory works.
Rhapsody works with the performing rights societies to ensure songwriters and artists are appropriately compensated for use of their intellectual property.
Of themselves, countries national anthems are not really classical music. However some have been incorporated into classical musical works. For instance Tchaikovsky's 1812 work incorporates the Russian and French national anthems (of the day).
It's difficult to choose, because Tchaikovsky wrote some brilliant works. It depends on what type of work you're thinking of - there's orchestral, concertos, solo works, chamber works, operas, ballet, etc. You should listen to Tchaikovsky's music for yourself and decide which piece you prefer as everyone has their own preferences. He has many compositions to choose from. See the related link for a full list.
Afshin Mofid has produced many famous musical works. One can find more information about these famous musical works by visiting the Scarlet Stone website.
The Fantasy-Overture after Shakespeare, Romeo and Juliet has no opus number. It is one of the very few works by Tchaikovsky which he didn't assign an opus number. It was written in 1870.
Tchaikovsky, usually referred to by his last name only, was a famous Russian music composer of the 19th century. Wikipedia has an extensive article about him.
The works themselves are in the public domain, but certain editions, performances, and recordings would have their own copyrights. Peter Tchaivosky is the owner of his music and receives the money, profits, and awards from it. It is by his permission. Correcting to "Tchaikovsky".
Sergei Rachmaninoff has written: '14 preludes for piano solo' -- subject(s): Piano music 'Four songs, for medium voice and piano' -- subject(s): Songs (Medium voice) with piano 'Rachmaninoff Piano Concerto #2' 'Concerto No. 2 in C Minor, Op. 18' 'Color by Note / Christmas (Color by Note)' 'The Bells, Op. 35 for Orchestra' 'Third symphony, A minor, op. 44' -- subject(s): Scores, Symphonies 'Code by Note (Color by Note)' 'Six Moments Musicaux, Op. 16' 'Rachmaninoff / Preludes Opus 3 No. 2, Opus 23, Opus 32 Complete(Vol.1))' 'Rhapsody on a Theme by Paganini, Opus 43\\' 'Rachmaninoff Works for 1P4H' 'Variations on a Theme by Corelli' 'Rachmaninoff's recollections' -- subject(s): Biography, Musicians, Soviet Union 'Concerto no.4,op.40, for piano and orchestra' 'Etudes Tableaux, Op. 33\\' 'Concerto No. 3 in D Minor, Op. 30' '10 Preludes, Op. 23' 'Music Minus One Piano' 'Etudes Tableaux, Op. 39\\' 'The American premiere performance of the Liturgy of St. John Chrysostom' -- subject(s): Choruses, Sacred (Mixed voices, 4 parts), Unaccompanied, Communion service music, Liturgy, Orthodox Eastern Church, Texts 'Code by Note, Book 2 (Color by Note)' 'Rachmaninoff / Miscellaneous Pieces' 'Rhapsodie, Op. 43' 'Rachmaninoff / Piano Concerto #3' 'A commemorative collection' 'Piano Concerto No. 1 and Piano Concerto No. 2' 'Songs with piano accompaniment' -- subject(s): Songs with piano 'Romans = Romance' 'Rachmaninoff / Transcriptions vol. 12'
Musical works written for an orchestra!
Tchaikovsky is a famous composer from the romantic era and he is rather famous for composing the music from the Nutcracker, which is also not copyrighted. This is why you hear alot of music from the Nutcracker in shopping centres and on advertisements around Christmas time.