PART III. (pp. 234–371).

THE RELATIONSHIP OF MUSICAL TONES.

Scales and Tonality.

CHAPTER XIII. GENERAL VIEW OF THE DIFFERENT PRINCIPLES OF MUSICAL STYLE IN THE DEVELOPMENT OF MUSIC, pp. 234–249.

Difference between the physical and the esthetical method, 234
Scales, keys, and harmonic tissues depend upon esthetic principles of style as well as physical causes, 235
Illustration from the styles of architecture, 235
Three periods of music have to be distinguished, 236
    1. Homophonic music, 237
    2. Polyphonic music, 244
    3. Harmonic music, 246

CHAPTER XIV. THE TONALITY OF HOMOPHONIC MUSIC, pp. 250–290.

Esthetical reason for progression by intervals, 250
Tonal relationship in melody depends on the identity of two partial tones, 253
The octave, fifth, and fourth were thus first discovered, 253
Variations in thirds and sixths, 255
Scales of five tones Pentatonic scales., used by Chinese and Gaels, 258
The chromatic and enharmonic scales of the Greeks, 262
The Pythagorean scales of seven tones, 266
The Greek and ecclesiastical tonal modes, 267
Early ecclesiastical modes, 272
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, 272
Introduction of a more accurate notation for pitch, 276
Peculiar discovery of natural thirds in the Arabic and Persian tonal systems, 280
The meaning of the leading note and consequent alterations in the modern scales, 285

CHAPTER XV. THE CONSONANT CHORDS OF THE TONAL MODES, pp. 290–309.

Chords as the representatives of compound musical tones with peculiar qualities, 290
Reduction of all tones to the closest relationship in the popular harmonies of the major mode, 292
Ambiguity of minor chords, 294
The tonic chord as the centre of the sequence of chords, 296
Relationship of chords of the scale, 297
The major and minor modes are best suited for harmonization of all the ancient modes, 298
Modern remnants of the old tonal modes, 306

CHAPTER XVI. THE SYSTEM OF KEYS, pp. 310–330.

Relative and absolute character of the different keys, 310
Modulation leads to tempering the intonation of the intervals, 312
Hauptmann’s system admits of a simplification which makes its realization more practicable, 315
Description of an harmonium with just intonation, 316
Disadvantages of tempered intonation, 322
Modulation for just intonation, 327