Quantifying Music: The Science of Music at the First Stage of Scientific Revolution 1580-1650

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Springer Science & Business Media, May 31, 1984 - History - 308 pages
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The soul rejoices in perceiving harmonious sound; when the sound is not harmonious it is grieved. From these affects of the soul are derived the name of consonances for the harmonic proportions, and the name of dissonances for the unharmonic proportions. When to this is added the other harmonie proportion whieh consists of the longer or shorter duration of musical sound, then the soul stirs the body to jumping dance, the tongue to inspired speech, according to the same laws. The artisans accommodate to these harmonies the blows of their hammers, the soldiers their pace. As long as the harmonies endure, everything is alive; everything stiffens, when they are disturbed.! Thus the German astronomer, Johannes Kepler, evokes the power of music. Where does this power come from? What properties of music enable it to stir up emotions which may go far beyond just feeling generally pleased, and which may express themselves, for instance, in weeping; in laughing; in trembling over the whole body; in a marked acceleration of breathing and heartbeat; in participating in the rhythm with the head, the hands, the arms, and the feet? From the beginning of musical theory the answer to this question has been sought in two different directions.
  

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Contents

DEFINING THE PROBLEM SITUATION
1
111 Zarlinos Redefinition of the Problem
3
112 Objections to the Senario
6
12 THE NATURE OF THE SCIENTIFIC REVOLUTION
7
121 The Science of Music around 1600
10
13 OUTLINE OF CHAPTERS 2 THROUGH 7
11
THE MATHEMATICAL APPROACH
13
211 The Empirical Foundation
15
41 ISAAC BEECKMAN
116
411 The Corpuscular Theory of Sound
120
412 The Nature of Consonance
127
413 Musical Instruments
147
Consolations for the Physicist
149
415 The Division of the Octave
151
416 Conclusions
157
42 RENE DESCARTES
161

212 Distinguishing Consonance from Dissonance
16
213 The Genesis of Harmony
23
214 Passing by Acoustics
29
215 Conclusions
32
22 THE DIVISION OF THE OCTAVE
34
221 The Incompatibility of the Pure Consonances
37
222 Summary
43
23 SIMON STEVIN
45
231 On the Theory of Music
48
233 The Octave Comprises 6 Equal Tones
51
234 The Octave Comprises 12 Equal Semitones
53
235 Sustaining Arguments
57
236 A Musicians Critique
61
237 Contemporary Music
63
238 Conclusions
67
THE EXPERIMENTAL APPROACH
75
32 VINCENZO GALILEI
78
321 The Singers Dilemma
79
322 Smashing the Senario
82
323 Summary and Conclusions
83
33 GALILEO GALILEI
85
331 Pendulums and Resonance
87
332 The Coincidence Theory of Consonance
90
333 Conclusions
92
34 THE NATURE OF THE COINCIDENCE THEORY
94
35 MARIN MERSENNE
97
351 The Abstract of Musical Theory
100
352 Some Properties of Sound
101
353 The Coincidence Theory Put to the Test
103
354 The Division of the Octave
111
355 Quantifying All Possible Music
112
356 Conclusions
114
THE MECHANISTIC APPROACH
115
422 The Scientific Analysis of Musical Beauty
166
423 The Perception of Consonance
172
424 Conclusions
175
CONTACTS AND CRITICISMS
180
51 THE RENAISSANCE THEORISTS
181
52 THE EARLY PHYSICISTS
182
521 Benedetti
183
53 THE MATHEMATICIANS
184
532 Kepler
185
54 THE MERSENNE CIRCLE
187
Beeckman Meets Young Descartes
188
542 Beeckman Descartes andMersenne
190
55 GALILEO GALILEI
201
56 CONCLUSION
202
AN EXAMPLE FROM THE SECOND GENERATION
205
61 THE PREVALENCE OF THE COINCIDENCE THEORY
206
62 CHRISTIAAN HUYGENS
209
621 The Theory of Consonance
210
622 The Division of the Octave
214
623 The Consonance of the Intervals with 7
225
624 Conclusion
228
CONCLUSIONS
231
712 What Was To Be Accomplished
234
IMPLICATIONS AND PERSPECTIVES
243
722 Music as an Art and Music as a Science
250
An Example of Theory Replacement
254
724 Quest Without End
258
NOTES
260
BIBLIOGRAPHY
296
NAME INDEX
303
SUBJECT INDEX
305
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