Overview

From the comments to the first part,
there are doubts about the authenticity of the supposed Greek music
sung at the beginning here.
But other than that, this certainly provides a fast overview of
the whole magnificent panorama of Western music!
Note that it continues up to Part XX!



History of music - Part I (From ancient Greece to renaissance) 7:31
Seikilos epitaph
Gregorian chant
Organum
Neidhardt von Reuental: Winter wie ist nu dein Kraft (minnesang)
Guillaume de Machaut: Missa Notre Dame
Guillaume Dufay: Deus tuorum militum
Jean Ockeghem: Missa Ecce ancilla Domini
Josquin Desprez: Missa Pange lingua
Adrian Willaert: Qual dolcezza giamai
Giovanni Pierluigi da Palestrina: Missa Papae Marcelli
Orlando di Lasso: Mattona mia cara, Osculetur me
John Dowland: Time stands still

Part II (Baroque) 9:23
Claudio Monteverdi: Ariadne´s complaint, Madrigals of War and Love
Girolamo Frescobaldi: Fiori musicali
Jean Baptiste Lully: Acis and Galatea
Arcangelo Corelli: La Folia, Concerto grosso in G minor
Johann Pachelbel: Canon
Henry Purcell: Three parts upon a ground
François Couperin: Pièces de clavecin
Antonio Vivaldi: The Four Seasons, Guitar concerto in D major, Violin concerto in A minor, Concerto grosso in C major, Gloria
Georg Philipp Telemann: Suite in B flat major
Jean Philippe Rameau: Pièces de clavecin en concert

History of music - Part III (Baroque) 10:22
Georg Friedrich Händel: Music for the Royal Fireworks, Water music, Serse (Xerxes), Concerto grosso op. 6, Messiah
Johann Sebastian Bach: Toccata and Fugue in D minor, Brandenburg concertos, Preludium in C major, Badinerie, Air, Chaconne, Cantate BWV 147, Double violin concerto, St. Matthew Passion
Domenico Scarlatti: Harpsichord sonata in D major
Giuseppe Tartini: Devil´s Trill sonata
Giovanni Battista Pergolesi: Stabat Mater

History of music - Part IV (Classical) 8:15
Carl Philipp Emanuel Bach: Quartet in A minor
Christoph Willibald Gluck: Melody for violin and piano (from Orpheus and Eurydice), Dance of the blessed spirits (from Orpheus and Eurydice)
Jan Václav Stamic: Symphony in A major
Jiří Antonín Benda: Symphony in B flat major
Joseph Haydn: Trumpet concerto, Symphony nr. 94 "Surprise", Cello concerto in C major, Quartet in C major "Emperor", Quartet in D minor "Quinten", Symphony nr. 104 "London"
Josef Mysliveček: Il Bellerofonte
Carl Ditters von Dittersdorf: Violin concerto in G major
Luigi Boccherini: Minuet
Antonio Salieri: Sinfonia Veneziana
Muzio Clementi: Sonata op. 25 nr. 5

History of music - Part V (W. A. Mozart) 10:36
Wolfgang Amadeus Mozart: The Marriage of Figaro (Le nozze di Figaro), Eine kleine Nachtmusik (A Little Night Music), Rondo alla Turca, Don Giovanni, Clarinet concerto, Violin concerto in G, Symphony nr. 39, 40 and 41, Divertimento in D, Sonata facile, Piano concerto in A, The Magic Flute (Die Zauberflöte), Quintet for clarinet and strings, Requiem

History of music - Part VI (L. van Beethoven) 9:35
Ludwig van Beethoven: Symphony nr. 5 in C minor, Für Elise, Symphony nr. 3 in E flat major "Eroica", Symphony nr. 6 in F major "Pastoral", Violin sonata nr. 5 in F major "Spring", Piano concerto nr. 5 in E flat major "Emperor", Piano sonata nr. 8 in C minor "Pathétique", Triple concerto for piano, violin and violoncello in C major, Romance for violin and orchestra in F major, Piano sonata nr. 14 in C sharp minor "Moonlight", String quartet nr. 16 in F major, Violin concerto in D major, Symphony nr. 7 in A major, Symphony nr. 9 in D minor (with Ode to Joy)

History of music - Part VII (From classical to romanticism) 10:27
Niccolò Paganini: Caprice nr. 24 for violin solo, Violin concerto nr. 2 in B minor "La Campanella"
Carl Maria von Weber: Der Freischütz, Invitation to the Dance
Giacomo Meyerbeer: Robert le diable
Gioachino Rossini: The Barber of Seville, William Tell, La gazza ladra
Franz Schubert: Symphony nr. 8 in B minor "Unfinished", Die schöne Müllerin (Ungeduld - Impatience), Piano Quintet in A major "The Trout Quintet" (Forellenquintett), Ave Maria
Gaetano Donizetti: L´elisir d´amore
Hector Berlioz: Harold in Italy, Fantastic symphony
Johann Strauss I: Radetzky March

Part VIII (Romanticism) 10:34
Mikhail Ivanovich Glinka: Ruslan and Lyudmila, Ivan Susanin
Felix Mendelssohn-Bartholdy: A Midsummer Night´s Dream, Violin concerto in E minor, Symphony nr. 4 in A major "Italian"
Fryderyk Chopin: Fantaisie-Impromptu in C sharp minor, Ballade in F major, Étude in G flat major "Black Key Étude", Nocturne in E flat major, Waltz in D flat major, Étude in C minor "The Revolutionary Étude"
Robert Schumann: Symphony nr. 1 in B flat major "Spring", Scenes from Childhood (Dreaming - Träumerei), Piano concerto in A minor

Part IX (Romanticism) 10:12
Ferenc Liszt: Les Préludes, Dream of Love (Liebestraum)nr. 3, Mephisto waltz nr. 1
Richard Wagner: Tannhäuser, Lohengrin, Valkyrie (Die Walküre)
Giuseppe Verdi: Aida, Rigoletto, The Troubadour (Il trovatore), La traviata, Nabucco
Charles Gounod: Ave Maria
Jacques Offenbach: Orpheus in the Underworld
César Franck: Violin sonata in A major, Symphony in D minor

Part X (Romanticism) 10:40
Bedřich Smetana: Vltava (Die Moldau), Prodaná nevěsta (The Bartered Bride)
Anton Bruckner: Symphony nr. 4 in E flat major "Romantic", Te Deum
Johann Strauss II: The Blue Danube (An der schönen blauen Donau)
Johannes Brahms: Symphony nr. 1 in C minor, Hungarian dance nr. 5, Waltz in A major, Symphony nr. 4 in E minor
Alexander Borodin: Polovetsian dances (from Prince Igor)
Camille Saint-Saëns: The Carnival of the Animals (The Swan), Cello concerto nr. 1 in A minor
Max Bruch: Violin concerto nr. 1 in G minor

This continues up to Part XX!
I will leave you to find your own way as far as you desire.
If you click, not on the triangle, but on the title,
it will come up in its own window
with some side links to some of the other entries.

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Also of interest:

2011-01-09-Tommasini-Choosing-the-greatest-composers

Choosing the Ten Greatest Composers
By ANTHONY TOMMASINI
New York Times, 2011-01-09

2011-01-23-Tommasini-The-greatest-composers

The Ten Greatest Composers
By ANTHONY TOMMASINI
New York Times, 2011-01-23

Tommasini’s list:
1. Bach
2. Beethoven
3. Mozart
4. Schubert
5. Debussy
6. Stravinsky
7. Brahms
8. Verdi
9. Wagner
10. Bartok

KHarbaugh would include Monteverdi, Handel, and Papa Haydn
and ditch Schubert, Debussy, Stravinsky, Brahms, and Bartok.
In particular, how on earth could Tommasini omit Handel?