CONTENTS.

CHAPTER XVII. Of Discords, pp. 330-350.

Enumeration of the Dissonant Intervals in the Scale, 331
Dissonant Triads, 338
Chords of the Seventh, 341
Conception of the Dissonant Note in a Discord, 346
Discords as representatives of compound tones, 347

CHAPTER XVIII. Laws of Progression of Parts, pp. 350-362.

The Musical Connection of the Notes in a Melody, 350
Consequent Rules for the Progression of Dissonant Notes, 353
Resolution of Discords, 354
Choral Sequences and Resolution of Chords of the Seventh, 355
Prohibition of Consecutive Fifths and Octaves, 359
Hidden Fifths and Octaves, 361
False Relations, 361

CHAPTER XIX. Esthetical Relations, pp. 362-371.

Review of Results obtained, 362
Law of Unconscious Order in Works of Art, 366
The Law of Melodic Succession depends on Sensation, not on Consciousness, 368
And similarly for Consonance and Dissonance, 369
Conclusion, 371

APPENDICES, pp. 327-556.

I. On an Electro-Magnetic Driving Machine for the Siren, 372
II. On the Size and Construction of Resonators, 372
III. On the Motion of Plucked Strings, 374
IV. On the Production of Simple Tones by Resonance, 377
V. On the Vibrational Forms of Pianoforte Strings, 380
VI. Analysis of the Motion of Violin Strings, 384
VII. On the Theory of Pipes, 388
A. Influence of Resonance on Reed Pipes, 388
B. Theory of the Blowing of Pipes, 390
I. The Blowing of Reed Pipes, 390
II. The Blowing of Flue Pipes, 394
[Additions by Translator, 396]
VIII. Practical Directions for Performing the Experiments on the Composition of Vowels, 398
IX. On the Phases of Waves caused by Resonance, 400
X. Relation between the Strength of Sympathetic Resonance and the Length of Time required for the Tone to die away, 405
XI. Vibrations of the Membrana Basilaris in the Cochlea, 406
XII. Theory of Combinational Tones, 411
XIII. Description of the Mechanism employed for opening the several Series of Holes in the Polyphonic Siren, 413
XIV. Variation in the Pitch of Simple Tones that Beat, 414
XV. Calculation of the Intensity of the Beats of Different Intervals, 415
XVI. On Beats of Combinational Tones, and on Combinational Tones in the Siren and Harmonium, 418
XVII. Plan for Justly-Toned Instruments with a Single Manual, 421
XVIII. Just Intonation in Singing, 422
XIX. Plan of Mr. Bosanquet's Manual, 429
[XX. Additions by the Translator, 430-556

• * See separate Tables of Contents prefixed to each Section.
  [Sect. A. On Temperament, 430
  [Sect. B. On the Determination of Pitch Numbers, 441