On the Sensations of Tone by Helmholtz, Hermann L.F. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Translator’s Notice to the Second English Edition Author’s Preface to the First German Edition Author’s Preface to the Third German Edition Author’s Preface to the Fourth German Edition Contents List of Figures List of Passages in Musical Notes List of Tables Introduction Relation of Musical Science to Acoustics Distinction between Physical and Physiological Acoustics Plan of the Investigation Part I On the Composition of Vibrations

Chapter I. On the Sensation of Sound in Genekal

Distinction between Noise and Musical Tone Musical Tone due to Periodic, Noise to non-Periodic Motions in the air General Property of Undulatory Motion : while Waves continually advance, the Particles of the Medium through which they pass execute Periodic Motions Differences in Musical Tones due to Force, Pitch, and Quality Force of Tone depends on Amplitude of Oscillation, Pitch on the length of the Period of Oscillation Simple relations of Vibrational Numbers for the Consonant Intervals Vibrational Numbers of Consonant Intervals calculated for the whole Scale Quality of Tone must depend on Vibrational Form Conception of and Graphical Representation of Vibrational Form Harmonic Upper Partial Tones Terms explained : Tone, Musical Tone, Simple Tone, Partial Tone, Compound Tone, Pitch of Compound Tone

Chapter II. On the Composition of Vibrations

Composition of Waves illustrated by waves of water The Heights of Superimposed Waves of Water are to be added algebraically Corresponding Superimposition of Waves of Sound in the air A Composite Mass of Musical Tones will give rise to a Periodic Vibration when their Pitch Numbers are Multiples of the same Number Every such Composite Mass of Tones may be considered to be composed of Simple Tones This Composition corresponds, according to G. S. Ohm, to the Composition of a Musical Tone from Simple Partial Tones

Chapter III. Analysis of Musical Tones by Sympathetic Resonance

Explanations of the Mechanics of Sympathetic Vibration Sympathetic Resonance occurs when the exciting vibrations contain a Simple Vibration corresponding to one of the Proper Vibrations of the Sympathising Body Difference in the Sympathetic Resonance of Tuning-forks and Membranes Description of Resonators for the more accurate Analysis of Musical Tones Sympathetic Vibration of Strings Objective existence of Partial Tones

Chapter IV. On the Analysis of Musical Tones by the Ear

Methods for observing Upper Partial Tones Proof of G. S. Ohm’s Law by means of the tones of Plucked Strings, of the Simple Tones of Tuning-forks, and of Resonators Difference between Compound and Simple Tones Seebeck’s Objections against Ohm’s Law The Difficulties experienced in perceiving Upper Partial Tones analytically depend upon a peculiarity common to all human sensations We practise observation on sensation only to the extent necessary for clearly apprehending the external world Analysis of Compound Sensations

Chapter V. On the Diffebences in the Quality of Musical Tones

Noises heard at the beginning or end of Tones, such as Consonants in Speech, or during Tones, such as Wind-rushes on Pipes, not included in the Musical Quality of Tone, which refers to the uniformly continuous musical sound Limitation of the conception of Musical Quality of Tone Investigation of the Upper Partial Tones which are present in different Musical Qualities of Tone

1. Musical Tones without Upper Partials 2. Musical Tones with Inharmonic Upper Partials 3. Musical Tones of Strings Strings excited by Striking Theoretical Intensity of the Partial Tones of Strings 4. Musical Tones of Bowed Instruments 5. Musical Tones of Flute or Flue Pipes 6. Musical Tones of Reed Pipes 7. Vowel Qualities of Tone

Results for the Character of Musical Tones in general

Chapter VI. On the Apprehension of Qualities of Tone

Does Quality of Tone depend on Difference of Phase? Electro-magnetic Apparatus for answering this question Artificial Vowels produced by Tuning-forks How to produce Difference of Phase Musical Quality of Tone independent of Difference of Phase Artificial Vowels produced by Organ Pipes The Hypothesis that a Series of Sympathetical Vibrators exist in the ear, explains its peculiar apprehension of Qualities of Tone Description of the parts of the internal ear which are capable of vibrating sympathetically Damping of Vibrations in the Ear Supposed Function of the Cochlea

Part II On the Interruptions of Harmony

Chapter VII. Combinational Tones

Combinational Tones arise when Vibrations which are not of infinitesimal magnitude are combined Description of Combinational Tones Law determining their Pitch Numbers Combinational Tones of different orders Difference of the strength of Combinational Tones on different instruments Occasional Generation of Combinational Tones in the ear itself

Chapter VIII. On the Beats of Simple Tones

Interference of two Simple Tones of the same pitch Description of the Polyphonic Siren, for experiments on Interference Reinforcement or Enfeeblement of Sound, due to difference of Phase Interference gives rise to Beats when the Pitch of the two Tones is slightly different Law for the Number of Beats Visible Beats on Bodies vibrating sympathetically Limits of Rapidity of Audible Beats

Chapter IX. Deep and Deepest Tones

Former Investigations were insufficient, because there was a possibility of the ear being deceived by Upper Partial Tones, as is shewn by the number of Beats on the Siren Tones of less than thirty Vibrations in a second fall into a Drone, of which it is nearly or quite impossible to determine the Pitch Beats of the Higher Upper Partials of one and the same Deep Compound Tone

Chapter X. Beats of the Upper Partial Tones

Any two Partial Tones of any two Compound Tones may beat if they are sufficiently near in pitch, but if they are of the same pitch there will be consonance Series of the different Consonances, in order of the Distinctness of their Delimitation Number of Beats which arise from Mistuning Consonances, and their effect in producing Roughness Disturbance of any Consonance by the adjacent Consonances Order of Consonances in respect to Harmoniousness

Chapter XI. Beats Due to Combinational Tones

The Differential Tones of the first order generated by two Partial Tones are capable of producing very distinct beats Differential Tones of higher orders produce weaker beats, even in the case of simple generating tones Influence of Quality of Tone on the Harshness of Dissonances and the Harmoniousness of Consonances

Chapter XII. Chords

Consonant Triads Major and Minor Triads distinguished by their Combinational Tones Relative Harmoniousness of Chords in different Inversions and Positions Retrospect on Preceding Investigations

Part II The Relationship of Musical Tones

Chapter XIII. General View of the Different Principles of Musical Style in the Development of Music

Difference between the Physical and the Esthetical Method Scales, Keys, and Harmonic Tissues depend upon esthetic Principles of Style as well as Physical Causes Illustration from the Styles of Architecture Three periods of Music have to be distinguished

1. Homophonic Music 2. Polyphonic Music 3. Harmonic Music

Chapter XIV. The Tonality of Homophonic Music

Esthetical Reason for Progression by Intervals Tonal Relationship in Melody depends on the identity of two partial tones The Octave, Fifth, and Fourth were thus first discovered Variations in Thirds and Sixths Scales of Five Tones, used by Chinese and Gaels The Chromatic and Enharmonic Scales of the Greeks The Pythagorean Scales of Seven tones The Greek and Ecclesiastical Tonal Modes Early Ecclesiastical Modes The Rational Construction of the Diatonic Scales by the principle of Tonal Relationship in the first and second degrees gives the five Ancient Melodic Scales Introduction of a more Accurate Notation for Pitch Peculiar discovery of natural Thirds in the Arabic and Persian Tonal Systems The meaning of the Leading Note and consequent alterations in the Modern Scales

Chapter XV. The Consonant Chords of the Tonal Modes

Chords as the Representatives of compound Musical Tones with peculiar qualities Reduction of all Tones to the closest relationship in the popular harmonies of the Major Mode Ambiguity of Minor Chords The Tonic Chord as the centre of the Sequence of Chords Relationship of Chords of the Scale The Major and Minor Modes are best suited for Harmonisation of all the Ancient Modes Modern Remnants of the old Tonal Modes

Chapter XVI. The System of Keys

Relative and Absolute Character of the different Keys Modulation leads to Tempering the Intonation of the Intervals Hauptmann’s System admits of a Simplification which makes its Realisation more Practicable Description of an Harmonium with Just Intonation Disadvantages of Tempered Intonation Modulation for Just Intonation

Chapter XVII. Of Discords

Enumeration of the Dissonant Intervals in the Scale Dissonant Triads Chords of the Seventh Conception of the Dissonant Note in a Discord Discords as representatives of compound tones

Chapter XVIII. Laws of Progression of Parts

The Musical Connection of the Notes in a Melody Consequent Rules for the Progression of Dissonant Notes Resolution of Discords Chordal Sequences and Resolution of Chords of the Seventh Prohibition of Consecutive Fifths and Octaves Hidden Fifths and Octaves False Relations

Chapter XIX. Esthetical Eelations

Review of Results obtained Law of Unconscious Order in Works of Art The Law of Melodic Succession depends on Sensation, not on Consciousness And similarly for Consonance and Dissonance Conclusion

Appendices

I. On an Electro-Magnetic Driving Machine for the Siren II. On the Size and Construction of Resonators III. On the Motion of Plucked Strings IV. On the Production of Simple Tones by Resonance V. On the Vibrational Forms of Pianoforte Strings VI. Analysis of the Motion of Violin Strings VII. On the Theory of Pipes

A. Influence of Resonance on Reed Pipes B. Theory of the Blowing of Pipes

I. The Blowing of Reed Pipes II. The Blowing of Flue Pipes [Additions by Translator]

VIII. Practical Directions for Performing the Experiments on the Composition of Vowels IX. On the Phases of Waves caused by Resonance X. Relation between the Strength of Sympathetic Resonance and the Length of Time required for the Tone to die away XI. Vibrations of the Membrana Basilaris in the Cochlea XII. Theory of Combinational Tones XIII. Description of the Mechanism employed for opening the several Series of Holes in the Polyphonic Siren XIV. Variation in the Pitch of Simple Tones that Beat XV. Calculation of the Intensity of the Beats of Different Intervals XVI. On Beats of Combinational Tones, and on Combinational Tones in the Siren and Harmonium XVII. Plan for Justly-Toned Instruments with a Single Manual XVIII. Just Intonation in Singing XIX. Plan of Mr. Bosanquet’s Manual XX. Additions by the Translator

[SECT. A. On Temperament [SECT. B. On the Determination of Pitch Numbers [SECT. C. On the Calculation of Cents from Interval Batios [SECT. D. Musical Intervals, not exceeding an Octave, arranged in order of Width [SECT. E. On Musical Duodenes, or the Development of Just Intonation for Harmony [SECT. F. Experimental Instruments for exhibiting the effects of Just Intonation [SECT. G. On Tuning and Intonation [SECT. H. The History of Musical Pitch in Europe [SECT. K. Non-Harmonio Scales [SECT. L. Recent Work on Beats and Combinational Tones [SECT. M. Analysis and Synthesis of Vowel Sounds [SECT. N. Miscellaneous Notes

Index

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