1816 Beethoven1770 1827 29Hämmerklavier articulation 116
1The Pianoforte 230 165 18 88 60 8000 yxt c T 1 2 y t 2 = c2 2 y x 2 1 1 Anatoli StulovPiano String Motion and Spectra The international Symposium on Musical AcousticsISMA, 2004 117
K Y m A = Kym3 3 A felt 2 8000 5100mm 1 A0 3 C8 7 2 2750cps 4 4186cps 12of 2 Equal Temperament Cristofori16551731 1700 2Tunings 5 Pythagoras BC570BC500 21 21 32 5 12 2 C M van WykNote on the Compressibility of Wool Journal of the Textile Institute 371946285292 3 C4Middle C 2616 4 cps cycle per second 5 pitchclass C B 0 11 118
B C 531441524288 7473 24 6 7 Just Intonation Ptolemaeusc 100 c170 Syntonon 21 32 54 3 2 98Major tone 109Minor tone Aronc1480c1550 Meantone Temperament 3 54 52 9 51 5 4 51 Syntonic 354 38164 1 8180 215 5 4 702546966 100 AristoxenusBC375BC360 Gregorian chant 5 6 cent 100cents 7 comma 1 9 119
4 8 456 3 2 5 5 24key JSBach16851750 The WellTempered Clavier 24 57005702 2 5697 3 100 5 700 2 3 Stevin15481620 9 1596 12 2 10 8 parallel organum vox principalis cantus firmus vox organalis 4 5 9 12 9 Simon Stevinc1600Van de Spiegeling der Singconstedited by DBierens de Haan Amsterdam1884 10 Stevin 1584 2 120
312Dodecaphony 17 20 Schönberg18741951 Subdominant 11 12 7 3 12 12 12 0 12 4096 12 12 13 479001600 11 Subdominant Tonic Dominant 12 Tonic Subtonic 7 121
Babbittb1916 12 14 aggregatecombinatorialitysegmentation partition 15 4Proportions Xenakis19222001 1958 Pavillion Philips Metastasis 1436 Santa Maria del Piere Dufayc14001474 motet Nuper rosarum flores 16 6423 13 set 14 series 12 15 12 12 1995 16 cantus firmus 122
Tictoris 14351511 17 5 25 21 145 ECarterb1908 2 Double Concerto 1 7 353152824521175 3529 2521 6 8 9 19 175 44 18 4 20 2 19 Pithoprakta f(v) = e -v 2 /a 2 a 1148 Gauss 58 Stochastic 17 Johannes TinctorisProportionale Musicestransby Albert SeayColoradoColorado Spring College Music Press1979 18 metric modulation meter tempo duration transition 19 f(v) a v a a 2 123
5 20Hz 20 20000Hz 2750HzA0 4186HzC8 3m 94dB 21 130dB 19 9 Tchaikovsky 18401893 250 20 Hz Herz 1 21 db decibel 124
12 Webern 18831945 4 6Sechs Bagatellen 22 Crumbb1929 Microcosmos Varése 18831965 13 Ionisation 40 Edison 1925 Respighi18791936 The Pines of Rome 23 1949 Schaeffer19101995 Henryb1927 1951 1952 22 am Stegpizzicato harmonics mit Dämpfer 23 musique concréte 125
Déserts 6 Computer Music 20 1960 Mathewsb1926 Fortran 24 5MUSIC5 25 19 21 24 Fortran Formula Translation 25 Max Mathews1969 The Technology of Computer MusicCambridge MA MIT Press1969 126
26 27 Helmholtz18211894 1863 amplitude envelope 28 Fourier17681830 29 30 31 26 algorithm 27 program 28 Hermann von HelmholtzOn the Sensations of Tone as a Physical Bases for the Theory of Music1863translby AEllisLondon1885 29 amplitude 30 phase 1 360 127
32 Fourier Transform X(f) = x(t)e 2ift dt 33 x(t) = x(f)e 2ift df. Discrete Additive Synthesis Rissetb1938 10 11 34 35 11 11 36 Subtractive Synthesis 31 sine wave sinusoidal waveform0zero 32 spectrum 33 x(t) t x(f) x(t) f e 27182818i i 2 = -1 34 oscillator 35 unit generator 36 JeanClaude Risset Introductory Catalogue of Computer Synthesized Sounds Bell Telephone Laboratories Murray HillN J1969 128
FrequencyModulating Synthesis Speech Synthesis 12 12 18 2 18 37 3 Trihexadral Ballads 18 18 38 37 Eugene LeeA Notational System for Third-Tone MusicOrganised Sound Vol2No3 Cambridge University PressUK1997213223 38 Eugene LeeSome Aspects of ThirdTone MusicSonus Vol 20 No 2 CambridgeMAUSA20003756 129
39 5 Fünf Orchesterstücke3 Farben crossfade transformation 3 40 18 21 39 Klangfahbenmelodie 40 3 41 Violin IA4 47523 cpsviolin IIA4 45727 cpsviolin A4 44000 cps 130
7 MP3 131
21 WCSabine18681919 ILangmuir18811957 200 6 132
21 frequencycentdecibalphonsone 133
2 21 axiom 134
Veritas Musicae 1 WSU Columbia Princeton Composers Guild of New York Calabrese Brothers Music Mobart Music PublicationsAPNM Scarbo CRI 120 135
지식의지평 5 知平 200 8 편집인 김용준 편집위원 김광억, 김두철, 김혜숙, 이태수, 정운찬 편집주간 박은진 발행인 김정호 발행처 아카넷 발행일 2008 년 12 월 8 일 출판등록 2000 년 1 월 24일 ( 제2-3009 호 ) 주소 100-802 서울시중구남대문로 5가 526번지대우재단빌딩 8층대표전화 6366-0511 팩스 6366-0515 c 한국학술협의회, 2008 Printed in Seoul, Korea. ISBN 978-89-5733-143-9 03000
Orbis Sapientiae 5 by Korea Academic Research Council Copyright Korea Academic Research Council All rights reserved. ACANET, Seoul, Korea, 2008 이책은저작권법에따라보호를받는저작물이므로무단전재와무단복제를금하며, 이책내용의전부또는일부를이용하려면반드시저작권자와아카넷의동의를받아야합니다. 지식의지평 은대우재단과한국학술협의회가국내학문의발전과소통을위해발간합니다.