1. Compositional Language(s) Instructor: Prof. SIGMAN Tuesday 13:00-15:00 Lecture II

2. Announcements Syllabus and other materials on Keimyung Online Course System

3. 0. Review: Typical Musical Parameters Pitch ( 고 저 ) Rhythm (Pulse/Meter) Melody Harmony Dynamic Register Timbre ( 음 색 ) Texture ( 결 ) Orchestration

4. I. Pitch, Intervals, and Tuning: Pythagoras (582-500 BC)

5. A. Pythagoras’ Monochord

6. Interval Ratios ( 비 율 )

7. Chromatic Intervals

8. Harmonic Series

9. 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 http://www.youtube.com/watch?v=Au2QFQ2 ppyg

10. II. Other Tuning Systems

11. A. Meantone Temperament

12. Meantone temperament, cont’d Used during Baroque (by Zarlino and other Italian composers of the early 17 th century) Keyboard instruments (harpsichord family) tuned according to various meantone temperaments Pitches tuned in perfect fifth stacks

13. B. Well temperament

14. Well-temperament properties Nearly equal tempered Used by Bach and his contemporaries in the 18 th century Permits in-tune triads in all 24 keys …but each key has a different characteristic/mood

15. 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 19 th century—standard piano tuning Piano “out of tune with nature”

16. Well Tempered vs. Equal Tempered Tuning http://www.youtube.com/watch?v=f8M- JzIwbog http://www.youtube.com/watch?v=f8M- JzIwbog

17. III. Note Names and Solmisation

18. A. US/UK/Dutch etc. System

19. B. German System

20. C. French/Italian/Spanish System

21. D. Pitch vs. Pitch Class Pitch = Pitch (chroma) + Octave (height) Pitch class = pitch (chroma), independent of octave (height)

22. IV. Modes/Scales/Tetrachords

23. A. Authentic and Plagal Modes

24. B. Authentic Mode Tetrachords

25. C. Ionian and Aeolian Modes Theoretical modes, added by Glareanus in 1500’s

26. D. Major and Minor Scale Tetrachords

27. Minor/Major Tetrachord Properties 2 tetrachords of scale are asymmetrical ( 비대칭 ) Therefore: weight given to tonic

28. E. Other Common Scales

29. 1. Pentatonic

30. 2. Whole Tone (2) Symmetrical

31. 3. Octatonic (3) 1) whole-half; 2) half-whole; 3) half-whole Symmetrical Used frequently by Olivier Messiaen (1908-92) “mode of limited transposition”

32. 4. Chromatic Chroma = colour ( 색 )

33. 5. Harry Partch 43-tone scale

34. V. Microtonality

35. Microtonal Increments Half-step (minor second) = semi-tone /2 = quarter-tone /2 = eighth-tone /2 = sixteenth-tone Etc…

36. 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

37. [Microtonal Scale]

38. For next week: ( 나는 오늘 나중에 할당을 이메일로 보내드립니다 )… 피타고라스와 플라톤의 텍스트를 읽어