!

Another-Scales Constructed from the Sense of Hearing, and All Scales Similar, therefore the Same Law Underlies them-Sounds Differ in Quality—Musical Sounds Result from Regularly Periodic Vibrations-Differences in Loudness from the Different Amplitude of Vibrations, and in Pitch from the Different Time of Vibrations -Differences in Quality from the Different Combinations of Vibrations-Vibrations Compounded, and Each of the Compounds Introduces into the Tone a Pitch or Partial Tone of its Own-Law of Sequence of the Upper Partial Tones of Musical Notes-Example in Music-Correspondence of the Earliest Greek Scale with the Chief Partial Tones of its Keynote-And of our Own Major Scale A Possible Scale of Ten Notes-Our Minor Scale-These Scales All Constructed on the Principle of Grouping Like Partial Effects of Unlike Complex Wholes-The Method in which the Greeks, Ignorant of Partial Tones, were Guided to these Results by their Sense of Hearing-How they Constructed, by Measuring the Length of Strings, the Lyre of Orpheus-Similar Results Reached by the Moderns through Counting Vibrations, and the Resulting Ratios-The Ratios of the Chinese Scale of Six Notes } as Developed by the Ancients-The Ratios of the Greek Scale of Seven Notes-Other Greek Scales-Deficiencies of the Greek Scale and the Development of the Modern Scales-Comparison between the Ratios of these and of the Pythagorean Scale-The Keys of the Piano and the Scales Played from the Different Keynotes-The Temperate Scale of the Present, and its Ratios as Compared with the Pythagorean, the Major, and the Minor.

XV.

PAGE

207-220

MUSICAL HARMONY AS DEVELOPED BY THE ART-
METHOD OF GROUPING LIKE PARTIAL EFFECTS
OF UNLIKE COMPLEX WHOLES
Historical Developments from Counteraction, etc., as Involved in
Polyphonic Music-Connection between the Concords and the
Lowest or Chief Partial Tones of a Compound Note-Harmony
Emphasizes the Fact that Like Partial Effects are Put with Like-
Visible Proof of this-All the Notes of a Scale Harmonized by
Using Chords Based on the Tonic, Dominant, and Subdominant
-Different Possible Arrangements of the Same Chord-The Ca-
dence and the Dissonance of the Seventh-The Principal Key-

Application of Subordination, Balance, Central-Point, Parallelism, Symmetry, Alternation, Massing, Complication, Continuity, etc. -And Other of the Methods of Art-Composition-Interchange as an Element of Modulation-And Gradation, Abruptness, Transition, and Progress-Interchange and Gradation in Sounding the Same Note in Successive Chords-In Passing from One Key to Another, by Making the Tonic or Subdominant of One Key the Dominant of Another-By Passing from Major to Minor, or Vice Versa-Further Exemplified and Explained-Relations of Different Chords to One Another-Abruptness in Transitions-The Chords Considered Separately-The Major Triad-The Chord of the Seventh-The Minor Triad-The Ratios of the Notes of these Chords when in the Same Octaves-Summary of the Ratios of Notes Causing Musical Concords.

XVI.

PAGE

221-228

PSYCHICAL AND PHYSICAL REASONS FOR THE EFFECTS OF MUSICAL FORM Relations of the Ratios Underlying Effects in Music to those in the Other Arts-Why is it Necessary that Notes should Chord ?-Psychological Reason-Correspondence of it to the Reason Given for Effects of Rhythm-Physiological Confirmation of this Reason— Beats Resulting from Discordant Notes-New Resulting Notes Formed by these Beats-In the Major Triad, the Resulting Note is itself the Tonic-Beats Disagreeable, because Interruptions of the Regularity of Periodic Vibrations-Cause Noise, not MusicBlending of Psychological and Physiological Reasons for Effects of Musical Form: Mind and Ear must Recognize that Like is Put with Like.

The Sustained Sounds of Singing and the Unsustained of Talking-The Former as Developed in Music and the Latter in Poetry

-Differences between these Two Methods of Vocal Representation -Music as Necessitating Sustained Sounds-The Germs of its Representations are mainly in Inarticulate Utterance, Instinctive and Associative, rather than Imitative and Comparative-The Representation of Speech, also Dependent partly upon Inarticulate Intonations-How these are Related to the Various Developments of Music-Representation in Music not Distinct and Definite, as in Words-Darwin's Theory of the Origin of Music-Gurney's Comment on this—Further Comments-Why Music is not Made Definitely Intelligible or Imitative-How it Represents both Mental Processes and Natural Surroundings-The Mind of the Composer not Necessarily in the Mood Naturally Represented by his Music-His Relation to this Mood that of a Painter to the Mood Represented in his Model's Pose.

II.

REPRESENTATION THROUGH MUSICAL DURATION AND

FORCE RHYTHM

PAGE

250-263

Similarity of Poetic and Musical Representation-Representative
Intonations of Elocution-Through Duration, Force, Pitch, and
Quality-Discoursive or Associative and Dramatic or Comparative
Elocution-Each Representative According to the Principle of Cor-
respondence-Musical Duration as Representative-Musical Dura-
tion as Representative of both Mental Moods and Natural Effects
-Illustrations-Musical Force as Representative of both Mental
Moods and Natural Effects-Rhythm as a Combination of Effects
of Duration and Force-Significance of Rhythm-As Representing
Moods of Buoyancy and Exhilaration-Confidence, Triumph-
Self-Poise, Dignity-The Gliding, Yielding, Graceful—Hesitation,
Doubt-Disturbance, Turmoil, Confusion-Imitative Effects-
Forging-Flight Downward-Upward-Snakes-Water-Flowing
Ease-Giants' Tread.

III.

264-273

REPRESENTATION THROUGH MUSICAL PITCH, HIGH
AND LOW, UPWARD AND DOWNWARD
Correspondences in the External World to High and Low Pitch—
And to Upward and Downward Directions of it-Further Explana-
tions-As Illustrated in Elocutionary Intonations—Gregorian

Chants as Developed from Elocutionary Laws-Upward Movements in Musical Questions—In Anticipative Expectancy—Downward Movements in Effects that are Conclusive-Affirmative and Positive -Combined Upward and Downward Movements in Effects both Anticipative and Conclusive-The Same Rendered EmphaticImitative Effects: Upward as in Rising-Downward as in Sinking-In Both Directions.

PAGE

IV.

REPRESENTATION THROUGH MUSICAL PITCH: COM-
BINED WAVE-MOVEMENTS.

274-279

The Meaning of the Elocutionary Circumflex or Wave-Movements
-Further Explanations-How these Conditions are Paralleled in
Music-Illustrations of Inconclusive Uncertainty Ending with
Positive and Decisive Effects-Of Anticipation Ending with
Finality-Of the Indecisive Ending with the Decisive Of Hope,
Ending with Doubt-Of Irony, Mockery-Other Illustrations.

V.

REPRESENTATION THROUGH BLENDING OF PITCH AS IN
MUSICAL HARMONY .

280-290

Elocutionary Use of Pitch, when Indicative of Suspense-Blending of Harmonic and Inharmonic Intervals of Pitch, as Analogous to Effects of Quality-Meanings in Speech of the Major and the Minor Interval-Their Meanings in Music-Further Explanations -The Subdominant, Dominant, and Tonic-Complete and Incomplete Cadence-Explanations of their Effects-Meanings of Upward and Downward Elocutionary Harmonic Cadences-Illustrations of the Satisfying Effects of Upward Musical Major Cadences-Unsatisfying Effects of Upward Minor Musical Cadences -Satisfying Effects of Downward Major Cadences—Unsatisfying Effects of Downward Minor Cadences-Wagner's Use of Upward Anticipative Movement Followed by Downward Minor Cadences.

VI.

REPRESENTATION THROUGH MUSICAL QUALITY.

PAGE

291-300

How Musical Quality is Determined-How Determined in the Human Voice-What Different Qualities of the Voice Represent -Their Correspondences in Nature-Analogies between Quality as Used in Elocution and in Music-Representation by Way of Association through the Use of Different Musical Instruments-The Same Continued-Representation through these by Way of Imitation-Other Examples.

VII.

MUSICAL REPRESENTATION IN SERIES OF PASSAGES WHEN
NOT IMITATIVE.

.

301-313

Series of Passages as Representative-By Way of Association as in Discoursive Elocution-As Illustrated by Haweis-By J. D. Rogers -Schumann's "In der Nacht"-Brahme's German Requiem-B. I. Gilman's Experiment-Explanation—Recorded Result―Deduction to be Drawn from these Quotations: In what Sense they Indicate that Music is Representative—Quotation from J. S. Dwight Interpreting the most Important of the Forms of Musical Composition-Program Music-Its Appropriate Use.

VIII.

MUSICAL REPRESENTATION IN SERIES OF PASSAGES WHEN
IMITATIVE, WIth Remarks ABOUT WAGNER

314-323

Influence upon Representation of Slight Imitative Effects-Examples: Barking of a Dog-Braying of an Ass-Nightingale's Song -Cackling of a Hen-Cluck of Same-Human Sounds-Laughter - Yawning-Sneezing-Coughing- Quarrelling-SobbingScolding-Moaning-Fondling - Playing - Frightening OthersPaganini's Testimony-The General Character of Wagner's Motives-His Peculiar Method of Using them-Result of this, Especially upon those not Previously Appreciating Music-His Tendency toward a Language of Music-Will Others Develop thisTwo Methods in which it may be Done with Safety-Conclusion.

INDEX

· 325