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Compositional Language(s) Instructor: Prof. SIGMAN Tuesday 13:00-15:00 Lecture II Announcements • Syllabus and other materials on Keimyung Online Course System 0. Review: Typical Musical Parameters • • • • • • • • • Pitch (고 저) Rhythm (Pulse/Meter) Melody Harmony Dynamic Register Timbre (음 색) Texture (결) Orchestration I. Pitch, Intervals, and Tuning: Pythagoras (582-500 BC) A. Pythagoras’ Monochord Interval Ratios (비 율) Chromatic Intervals Harmonic Series Pythagorean Tuning (or Just Intonation) • • • • Tuning of intervals is relative Reference fundamental = C Reference interval = P5 (3:2) Key signatures with many #’s or b’s rare in Baroque music • http://www.youtube.com/watch?v=Au2QFQ2 ppyg II. Other Tuning Systems A. Meantone Temperament Meantone temperament, cont’d • Used during Baroque (by Zarlino and other Italian composers of the early 17th century) • Keyboard instruments (harpsichord family) tuned according to various meantone temperaments • Pitches tuned in perfect fifth stacks B. Well temperament Well-temperament properties • Nearly equal tempered • Used by Bach and his contemporaries in the 18th century • Permits in-tune triads in all 24 keys • …but each key has a different characteristic/mood • C. Equal Temperament (ET) • • • • • Minor second (m2) = 12√2 (ca. 1.05) ALL m2 the same ALL octaves the same Octaves are stretched (잡아 당기는) Used since 19th century—standard piano tuning • Piano “out of tune with nature” Well Tempered vs. Equal Tempered Tuning • http://www.youtube.com/watch?v=f8MJzIwbog III. Note Names and Solmisation A. US/UK/Dutch etc. System B. German System C. French/Italian/Spanish System D. Pitch vs. Pitch Class • Pitch = Pitch (chroma) + Octave (height) • Pitch class = pitch (chroma), independent of octave (height) IV. Modes/Scales/Tetrachords A. Authentic and Plagal Modes B. Authentic Mode Tetrachords C. Ionian and Aeolian Modes • Theoretical modes, added by Glareanus in 1500’s D. Major and Minor Scale Tetrachords Minor/Major Tetrachord Properties • 2 tetrachords of scale are asymmetrical (비대칭) • Therefore: weight given to tonic E. Other Common Scales 1. Pentatonic 2. Whole Tone (2) Symmetrical 3. Octatonic • • • • • (3) 1) whole-half; 2) half-whole; 3) half-whole Symmetrical Used frequently by Olivier Messiaen (1908-92) “mode of limited transposition” 4. Chromatic • Chroma = colour (색) 5. Harry Partch 43-tone scale V. Microtonality Microtonal Increments • • • • Half-step (minor second) = semi-tone /2 = quarter-tone /2 = eighth-tone /2 = sixteenth-tone Etc… Applications of Microtonality • Tuning systems (e.g., Just Intonation) • Synthetic (invented) scales • Physical phenomena (e.g., beating and difference tones) • “Natural state” of instruments • Spectral harmony (overtones) • Deviations from semi-tones [Microtonal Scale] For next week: • (나는 오늘 나중에 할당을 이메일로 보내드립니다)… • 피타고라스와 플라톤의 텍스트를 읽어