HERMANN HELMHOLTZ
. . . the inversion or transposition of an interval formed with the number 7 leads to intervals worse than itself. . . . The scales of modern music cannot possibly accept tones determined by the number 7. [Poole's scale f g a, 'bb c' d' e', f', and Bosanquet's and White's tempered imitation of b'b, propery 969¢, as 974¢ shew the feeling that exists for using the 7th harmonic, which is the only acoustical justification for the greatly harsher dominant Seventh.--Translator.] [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p228]

Rameau and d'Alembert lay down two facts as the foundation of their system. The first is that every resonant body audibly produces at the same time as the prime (générateur) its Twelfth and next higher Third, as upper partials (harmoniques). The second is that the resemblance between any tone and its Octave is generally apparent. The first fact is used to shew that the major chord is the most natural of all chords, and the second to establish the possibility of lowering the Fifth and the Third by one or two Octaves without altering the nature of the chord, and hence to obtain the major triad in all its different inversions and positions. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p232]

. . . what degree of roughness a hearer is inclined to endure as a means of musical expression depends on taste and habit; hence the boundary between consonances and dissonances has been frequently changed. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p234]

. . . the rules of any style of art . . . are rather the result of tentative exploration or the play of imagination, as the artists think out or execute their plans, and by trial gradually discover what kind or manner of performance best pleases them. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p235]
. . . many popular melodies, of older times or foreign origin, scarcely admit of any harmonic accompaniment at all, without injury to their character. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p253]
 . . . From youth upwards we are accustomed to accommodate our ears to the inaccuracies of equal temperament, and the whole of the former variety of tonal modes, with their different expression, has reduced itself to such an easily apprehended difference as that between major and minor. But the varied gradations of expressions which moderns attain by harmony and modulation, had to be effected by the Greeks and other nationals that use homophonic music, by a more delicate and varied gradation of the tonal modes. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p266]

The use of the major Seventh of the scale as a leading note to the tonic marks a new conception, . . . . The tone B1 in the major scale of C has the most distant relationship of all the tones to the tonic C, because as major Third of the dominant G, it has a less close connection with it than its Fifth D. We may perhaps assume this to be the reason why, when the sixth tone was introduced into some Gaelic airs, the Seventh was usually omitted. But, on the other hand, the major Seventh B1 developed a peculiar relation to the tonic, which in modern music is indicated by calling it the leading note.[Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, p285]

. . . the major Seventh in its character of leading note to the tonic acquires a new and closer relationship to it, unattainable by the minor Seventh. And in this way the note which is most distantly related to the tonic becomes peculiarly valuable in the scale. This circumstance has continually grown in importance in modern music, which aims at referring every tone to the tonic in the clearest possible manner; . . . .
  The general introduction of the leading tone represents, therefore, a continually increasing consistency in the development of a feeling for the predominance of the tonic in a scale. By this change, . . . the variety of character in the ancient tonal modes seriously injured, and the wealth of previous means of expression disrupted or disturbed. . . .
  In the gradual development of the diatonic system, therefore, the various links of the chain which bound the tones together were sacrificed successively to the desire of connecting all the tones in a scale with one central tone, the tonic. And in exact proportion to the degree with which this was carried out, the conception of tonality consciously developed itself in the minds of musicians. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, pp287-288]
. . . the melodic relationship of tones can be made to depend upon their upper partials, . . . . Now this method of explanation may in a certain sense be considered to agree with the favourite assertion that 'melody is resolved harmony,' . . . . According to our explanation, at least, the same physical peculiarities in the composition of musical tones, which determined consonances for tones struck simultaneously, would also determine melodic relations for tones struck in succession. The former then would not be the reason for the latter, as the above phrase suggests, but both would have a common cause in the natural formation of musical tones. [Helmholtz, Hermann, On the Sensations of Tone, Dover Publications, Inc., New York, 1954, pp288-289]
 
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