Sound and Music: An Elementary Treatise on the Physical Constitution of ...

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Chapter I. On Sound In General And The Mode Of Its Transmission

Sensation of Sound, and its cause, § 1 — Connexion of Sound with motion, § 2 — Velocity of Sound, § 3 — Stationary media of Sound, § 4 — Motion of sea-waves, § 5 — Description of a wave, § 6 — Length, amplitude and form of wave, § 7 — ^Water-waves, § 8 — Waves due to transverae vibrations, § 9-^Periodic vibrations, § 10 — Form of wave and mode of vibration, §§ 11, 12, 13 — Wave on the surface of a field of standing corn, § 14 — Longitudinal vibrations, §§ 15, 16 — Condensation and rarefaction, § 17 — Associated wave, § 18 — Law of pendulum- vibration, § 19 — Pressure and density of air; Ma/notte^8 law, § 20 — ^Transmission of sonorous waves along a tube of uniform bore, § 21 — Unconstrained motion of Sound-waves, § 22 — ^Musical and non-musical sounds, § 23. pp. 1 — 50

Chapter II. On Loudness And Pitch

Three elements of a musical sound, loudness, pitch and quality, § 24 — Loudness and extent of vibration, § 25 — Pitch and rapidity of vibration ; the Syren ; continuity of pitch, §§ 26, 27 — ^Measure of pitch; vibration-numbers, § 28 — Limits of musical sounds § 29 — Relative pitch; intervals, § 30 — Tonic intervals of the Major scale; concords and discords, § 31 — Additional notes required for the Minor scale, 32 — Measure of intervals, § 33 — Vibration-fractions, § 34 — Table of vibration-fractions for the tonic intervals of the Major and Minor scales, § 35 — Calculation of the vibration-numbers of all the notes in a scale from the vibration-number of its tonic, § 36. pp. 51 — 70

X CONTENTS,

Chapter III. On Resonance

Resonating pianoforte wires and tuning-forks; cause of the phenomenon, §§ 37, 38 — Resonance of a column of air; laws of its production, § 39 — Relation between the length of an air-column and the pitch of its note of maximum resonance, § 40 — Resonance-boxes, § 41 — Helmholtz's resonators, § 42.

pp. 71—83 CHAPTER IV.

ON QUALITY.

Composite nature of musical sounds in general ; series of constituent tones, and law which connects them, § 43 — Experimental analysis of musical sounds, §§ 44, 45 — Nomenclature of the subject, § 46 — Helmholtz's theory of musical quality as depending on the number, orders and relative intensities of the partial-tones present in any given clang, § 47. pp. 84 — 96

Chapter V

ON THE ESSENTIAL MECHANISM OF THE PRINCIPAL MUSICAL INSTRU- MENTS, CONSIDERED IN REFERENCE TO QUALITY.

Sounds of tuning-forks, § 48 — Modes of vibration of an elastic tube, § 49 — Meeting of equal and opposite pulses; formation of nodes, § 50 — ^Number of nodes formed, § 51 — Nature and rate of segmental vibration, §§52, 53 — Motion of a sounding string; quality and pitch of its note, §§ 54, 55 — The pianoforte, § 56 — Meeting of equal and opposite systems of longitudinal waves, § 57 — Reflexion of Sound at a closed and at an open oriflce, § 58 — Modes of segmental vibration in stopped and open pipes, §§59, 60 — Deepest note obtainable from a pipe, § 61 — Relation between length of pipe and pitch of note, § 62 — ^Theory of resonance-boxes, § 63 — Flue-pipes and reed-pipes, § 64 — Construction of flue-pipes and quality of their sounds, § 65 — Mechanism of a reed ; timbre of an independent reed, and of a reed associated with a pipe, § 66 — Orchestral wind-instruments, § 67 — ^Mechanism of the human voice, § 68 — Synthetic confirmation of Helm* holtz's theory of quality, § 69. pp. 97—138

CONTENTS. xi

Chapter VI. On The Connexion Between Quality And Mode Of Vibration

Composition of vibrations, §§70, 71 — Phase of a vibration; nondependence of quality on differences of phase among partial-tones, § 72 — Simple and resultant wave-forms ; Fowrier^8 theorem, § 73.

Chapter VII. On The Interference Of Sound, And On ^ Beats.'

Composition of vibrations of equal periods, § 74 — Two sounds producing silence, § 75 — Beats of simple tones, § 76 — Graphic representation of beats, § 77 — Experimental study of beats, § 78.

Chapter VIII. On Concord And Discord

Helmholtz's discovery of the nature of dissonance ; couditions under which it may arise between two simple tones, § 79 — Mode of determining the whole dissonance produced by two composite sounds, § 80 — Classification of the tonic intervals of the scale, according to their freedom from dissonance, §§ 81-86 — Picture of amounts of dissonance for all intei*vals not wider than one Octave, § 87 — Consonance dependent on quality, § 88 — Apparent objection to Helmholtz's theory of quality, § 89 — Combinationtones, § 90 — Their use in defining certain consonant intervals for simple tones, § 91 — Divergence from the views of musical theorists, § 92 — Dissonance due to combination- tones produced between the partial-tones of clangs forming a given interval, § 93.

xii CONTENTS.

OHAPTEK IX.

ON CONSTANT TRIADS.

Rules for the employment of vibration-fractions, ^ 94-96 — Inversion of intervals, § 97 — Definition of a consonant triad, § 98 — Determination of all the consonant tonic triads within one Octave, § 99 — Arrangement in two groups, § 100 — Mutual relation between the members of each group, § 101 — Notation of Thorough-Bass, § 102 — Fundamental and inverted positions of common-chords, § 103— Effects of Major and Minor chords, § 104.