Suppose F1 and F2 are distinct reflections in a dihedral group Dn such that F1F2 = F2F1. Prove that F1F2 = R180.
The Classical Era (1750-1800) Age of Enlightenment Rejection of traditional authority principles for human reason, analysis, and individualism. Human control over a rational universe Galileo Galilei, Sir Francis Bacon, Sir Isaac Newton, Jean-Jacques Rousseau Denis Diderot- French philosopher, art critic, and author of the first encyclopedia Challenged aristocracy’s responsibility to common man Submitted to detention, house searches, and ostracization for authorship Sonata Form- the structuring of an entire movement into three ordered sections, each based on how it treats the thematic materials, majority of classical movements in sonata form 1. Exposition- introduction of two contrasting themes, the first generally being more energetic and the second more lyrical a bridge section occurs between each theme 2. Development – exploration of the themes in various keys, rhythms, dynamics, and timbres often contains a “strum und drang” (storm and drive) quality 3. Recapitulation- restatement of the exposition in the tonic/ home key may contain coda- an extended conclusion, at the end of the movement (rests in music can help distinguish sections) absolute music vs. program music – (in general the classical era = absolute music) music for its own sake vs. music for physical/ storytelling representations Ludwig Van Beethoven (1770-1827) recognized as a leader of the Romantic movement in music career divided into 3 sections early career as Classicist mid-years as transitionary late career as Romantic eventually went deaf, blaming God and fate for the ultimate irony of a genius composer being denied his hearing Beethoven’s opera depicting true love, symphonies proclaiming man’s ultimate truth in nature and fraternity, and piano sonatas/late string quartets bearing his isolation and solitude become the fundamental qualities of Romanticism Romanticism (1810-1880) Romanticism A cultural movement emphasizing solitary emotions in relation to nature and the exotic/supernatural Reactionary to the logic and reason behind Enlightenment/ French Revolution Nationalism as important to style Characteristic of Romantic Music Melodies are expressive, lyrical, emotional Rhythm uses more rubato for ambiguity, dance rhythms indicating nationalistic styles Exploration of instrumental colors Wide range of dynamics, frequent fluctuations in levels Art song- musical setting of poem for solo voice and piano Lied- a German art song Song cycle- a series of art songs that relate or tell a story Art songs often performed in Salon setting- gathering in an upper- class home for informal literary/ musical performance by those in attendance Art Song Form Strophic- each verse of a poem is set to exactly the same music Modified strophic- some verses of the poem are set to the same music, while others are set to different music Through composed- each verse of a poem set to different music, contains sections of narration and dialog Also the form of Ballard Franz Schubert