3. Physiology of the Minor Chord. Among the most interesting of these discoveries is the reason of the heavy and quasi-dissonant effect produced by minor triads. Just intonation deepens the well-known grave, obscure, and mysterious character which belongs to minor chords; and the observations of Helmholtz on accurately tuned instruments have enabled him to trace this grave and obscure character to the presence of certain deep combinational tones, foreign to the chord, which are absent from major chords, and which without being near enough to beat, and thus actually to disturb the harmony, make themselves sufficiently audible, at least to a practised ear, as not belonging to the harmony. No minor chord can be obtained perfectly free from such false combinational tones. For the ordinary hearer the presence of these tones gives to the chord its well-known, obscure, and mysterious character, for which he is unable to account, because the weak combinational tones on which it depends are concealed by other louder tones. The fact that this unsatisfactory though not dissonant effect of the minor chord is deepened when the chord is played perfectly in tune, led musicians who wrote before the era of equal temperament to avoid the minor chord as a close, and to reserve the effect produced by minor chords for distinct passages or episodes in the composition, instead of using them in indiscriminate combination with major chords, as is the practice of ordinary modern composers. The 'Ave verum' of Mozart, and the choral hymn of Mendelssohn, 'Vaterland in deinen Gauen,' are good examples of this separation of major and minor effects as instinctively practised by the best writers.
4. Perception of musical tones by the human ear. Starting from the anatomical discoveries of the Marchese Corti, Helmholtz has shown how different parts of the ear are set in vibration by tones of different pitch. The human cochlea contains about 3000 of the rods or fibres known as 'Corti's arches.' The human ear, in fact, is a highly sensitive musical instrument, furnished with 3000 strings, which are set in motion by the concurrent vibration of external sonorous bodies, exactly in the same way in which the 'resonator' responds to a musical sound, or in which the strings of a silent violoncello or pianoforte are set in vibration by the production, in a sufficient degree of strength, of notes of equivalent pitch on any other instrument placed near it. On the perfect or imperfect anatomical constitution of these 3000 musical strings, and on their connection with the brain, depends the capacity in the human subject for the sensation of tune: probably in persons who have 'no ear' they are imperfectly developed. Deducting 200 for tones which lie beyond musical limits, there remain 2,800 for the seven octaves of musical pitch, that is, 400 for every octave. If the experiments of E. H. Weber are correct, sensitive and practised musicians can perceive a difference of pitch for which the vibrational numbers are as 1000 to 1001. Intervals so fine, falling between the pitch of two of Corti's arches, would probably set both arches unequally in vibration, that one vibrating most strongly which is nearest to the pitch of the tone.
5. Distribution of harmonic intervals. The common rule of avoiding close intervals in the bass, and of distributing intervals with tolerable evenness between the extreme tones, has long been arrived at by experience. Helmholtz has demonstrated its physiological basis to consist in the dissonant combinational tones which result from intervals otherwise distributed.For Professor Helmholtz's deduction of other rules of musical science from the physical nature of musical sounds, together with his historical exposition of the growth of melodic scales and of modern harmony, the reader is referred to his work, as already cited.
[ E. J. P.] ]
[ W. H. H. ]
[ W. S. R. ]
- From the Festgesang for the Printing Festival.