Translation of Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik. Includes bibliographical references and index.
Contents:
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 sympathetically ; 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.
Series:
Dover books on history of science and classics of science
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.