I. On the composition of vibrations: Upper partial tones, and qualities of tone : 1. On the sensation of sound in general : 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 -- 2. 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 -- 3. 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 sympathizing 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 -- 4. 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 practice observation on sensation only to the extent necessary for clearly apprehending the external world ; Analysis of compound sensations -- 5. On the differences 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 : Musical tones without upper partials ; Musical tones with inharmonic upper partials ; Musical tones of strings : Strings excited by striking ; Theoretical intensity of the partial tones of strings. Musical tones of bowed instruments ; Musical tones of flute or flue pipes ; Musical tones of reed pipes ; Vowel qualities of tone. Results for the character of musical tones in general -- 6. 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 car, explains its peculiar apprehension of qualities of tone ; Description of the parts of the internal ear which are capable of vibrating sympathetica lly ; Damping of vibrations in the ear ; Supposed function of the cochlea.
II. On the interruptions of harmony: Combinational tones and beats, consonance and dissonance : 7. 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 -- 8. 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 -- 9. 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 -- 10. 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 -- 11. 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 -- 12. 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.
III. The relationship of musical tones: scales and tonality : 13. 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. -- 14. 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 -- 15. 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 harmonization of all the ancient modes ; Modern remnants of the old tonal modes -- 16. 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 realization more practicable ; Description of an harmonium with just intonation ; Disadvantages of tempered intonation ; Modulation for just intonation -- 17. 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 -- 18. 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 -- 19. Esthetical relations : 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.
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