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 ( 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 ppyg ppyg

II. Other Tuning Systems

A. Meantone Temperament

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

B. Well temperament

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

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”

Well Tempered vs. Equal Tempered Tuning JzIwbog JzIwbog

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 ( ) “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