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This book serves primarily the purpose of investigating tone in terms of musical values. Against the tendency to demonstrate “the science of music,” a subtitle like “the art of acoustics” might well have been chosen. Whatever the scientific involvements of the contents, the authors think of themselves as musicians writing for musicians and music lovers.
Our book follows Goethe in more than just general attitude. A short document by him exists, part of his correspondence with the Berlin Kapellmeister Karl Zelter, that outlines a theory of acoustics. In contrast to the rich and voluminous data presented by Goethe’s studies on optics, his papers on acoustics are sketchy and brief. But the essentials are clearly stated. The orientation, as in his theory of light, is gained from the concept of polarity. Tone is postulated as a given inner phenomenon. Hence, the main question is not what the phenomenon is but how it comes into being. After outlining the premises, Goethe presents the subject matter in three parts: organic (ear, voice, and body rhythm), mathematic (monochord), and mechanic (instruments). All sections point toward a contemplation of the work of art. In general conviction as well as in some specific details of organization, this book follows Goethe as a guide.
The authors are more immediately indebted to the contemporary Swiss philosopher Hans Kayser (who died in 1964 while this manuscript was being prepared). In his extensive writings, Kayser endeavored to develop an epistemological tool by proceeding from acoustics. He deserves credit for the modern exposition of the Pythagorean table (which had been rediscovered by Albert Freiherr von Thimus around the middle of the last century) its successful application as a key to Pythagorean philosophy and to number symbolism an explanation of the harmonical method used by Kepler in establishing his astronomic laws and, in general, the uncovering of a harmonical background in a wealth of phenomena. The connection with Goethe is evident from Kayser’s 'Harmonia Plantarum' (1943), for instance, where the norms recognized in and through tone are applied to the vegetable kingdom. But above all, Kayser—first against the modern scientific tendency to overemphasize the quantitative aspect of the world—insisted upon the autonomy and reality of tone as a value and upon the consequent “musicalization” of number. Without Kayser, the teaching of acoustics would probably still be what it was when the authors of this book were music students: a peripheral course dealing with some elementary notions about the physics of sound, lacking in inner significance because unfit to bridge the gap between physics and music, and conveying little importance to the musician. [ excerpt from the preface ]
Preface
Acknowledgments
Credits
Pitch Designations
Preamble
Premises
Sound and Vibration
The Monochord
Description and Construction
Division of the String
Division by 2
Division by 3
Division by 4
Division by 5
Division by 6
The Senarius
Division by 7
Division by Numbers above 7
The Pythagorean Table
Wave Properties
Sound Waves
Resonance
The Overtone Series
Tone Properties
General Characteristics
Pitch
Loudness
Timbre
Interference
The Human Voice
Organic Considerations
Pitch
Loudness
Timbre
Some Aesthetic Considerations
Music Instruments
Relation to Voice
Invention
Classification
Material and Form
Musical Character
Stringed Instruments (Other than Keyboard Instruments)
Construction
Pitch
Loudness
Timbre
Stringed Keyboard Instruments
Construction
Pitch
Loudness
Timbre
Piano Style: Aesthetic Considerations
Wind Instruments
Relation to Stringed Instruments
Construction
Pitch
Loudness
Timbre
Organ
Construction
Pitch
Loudness
Timbre
Percussion Instruments
Construction
Pitch
Loudness
Timbre
On the Function of the Ear
Acoustics of Halls
Musical Considerations
Acoustical Factors
Historical Survey
Music Theory
Major and Minor Mode
Consonance and Dissonance
Temperament
Conclusion: The Realm of Acoustics
Suggested Readings
Index