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Müller, and Ferrari. The work commences with a Compendium of the Elements of Music. Following the elementary treatise, the Geneuphonic Grammar is divided into two parts. The first, called the Practical Treatise, commences with the section of Harmony. Harmony is defined to consist in the addition or agreeable union of one or more sounds previously determined upon for the melody, air, or singing part; but the melody being once invented, harmony exists without the composer's intervention. This dictum will startle an experienced and reflective reader, but let him proceed, and mark the lucidity and science as well as the simplicity with which the author establishes it as a fixed and invariable law. The oversight of those authors (and they are all that have written on this subject), not perceiving its truth, has led to all the complication that constitute the incongruous system generally received under the name of Thorough Bass. The want of this perception is the sole cause of those confused and confusing precepts by which it has in all times been attempted to construct an artificial, and to suppress or corrupt the natural law of harmony.
Virués starts with the proposition, that the grave or acute octaves of any perceptible sound have in euphony either melodic or harmonic, the same value as their denominative sound and as the unison, and proves this assertion by the octavism of the artificial perfect chord produced by resonance; and he draws the following conclusion, that all the rules of harmony must be necessarily contained within the narrow compass of one single octave of any scale. He goes on to say, that the harmonic generator is that which has hitherto been called dissonance-it arises from destruction, and brings with it reproduction. He discovers the fact, that the generation of harmony cannot be subject to or controlled by mathematical calculations; and this point of the new theory is lucidly and logically proved. He then proceeds to tell us that dissonance, from which all harmony arises, is the double sonorousness of the two ends of an interval smaller than the minor third, which he affirms to be doubly euphonic. From this he deduces what he terms the melo-harmonic typometre, and it determines the sounds which in harmony may be joined to each other. It is a distribution of the seven sounds of the scale into three harmonic groups, applicable to the forty-two scales or keys of music, and it clearly proves the incontestable superiority of the new system.
10Stationary 1 Descends a Semitone
7-Ascends a Semitone 10
10 Ascends one Tone 2 O Descends one Tone 1-0
APPLICABLE TO THE
FORTY-TWO SCALES OR KEYS OF MUSIC,
OR, Distribution of the Seven Sounds of the Scale into three Harmonical Groups.
Cadence is the chord called perfect, and is composed of the notes 1, 3, 5 of the heptachord, and has been known hitherto as the dominant. Transcadence is the chord hitherto termed the sub-dominant, and is composed of the notes 1, 4, 6 of the heptachord, and naturally follows the cadence; and precadence, hitherto the chord of the seventh, or sensible, is composed of the notes 2, 4, 5, 7 of the heptachord. Virués divides the “ Typometric Table”* into two divisions, the one for the major and the other for the minor mode. Each division is subdivided into three parts; the first one contains the names of the keys which are called natural, sharp, or flat, from the tonic bearing one or other of those three characters; the second part contains the three chords into which the melo-harmonic typometer divides the octave in every scale; and the third contains the indication of the other form, or forms, of every key. With the assistance
* Vide page 113 of the Book.
of this table, the author does not assert too much when he observes that the student will be enabled to harmonize every melody the key of which is not changed, i. e., in which no sounds enter but those belonging to the same scale; and the rules for harmonizing with such a transition follow in their natural order. The relations of the principal chords to the tonic, and to one another, are set forth in a few explicit and concise rules, which remove all uncertainty as to their use.
After these follows a table of all the scales, which is called the Table of Polytonogamism, and enables the student, who has carefully perused the preceding lessons, to determine, by momentary reference, what chords are admissible in the harmonies of any one of the forty-two scales, and what notes are incidental to any key according to the enharmonic division of the octave. From this the reader is led to some examples of the unconscious application of those principles by authors who had never thought of the theory, but followed it by an instinctive appreciation of its principles. We take the following illustration in a passage from a Cavatina by Paesiello: "Nel cor più non mi sento.” In this example the relative use of the transcadence and cadence, with preparation for the close, by the precadence, is placed very obviously before the student.
The author gives the whole of the piece, with highly edifying and conclusive remarks upon the composition, fully explaining thereby the practical applicability and perfection of the Geneuphony. Other examples, prepared for the purpose, follow, and are complete for the purpose of elucidation, to any scholar who applies a serious, though not necessarily a laborious attention to the study. From these lessons on rough harmony, he proceeds to the development of the system of counterpoint, by which, on Geneuphonic principles, uncouth and monotonous harmony is interrupted, modified, and polished. The chapter on this division of the subject is ample, and in the highest degree satisfactory, and prepares for the development of the Golden Rule, namely, “Never produce the intervals, or sounds, of fifths or octaves, by means of two voices, or parts, which ascend or descend together."
Further illustrations tend to confirm entirely the learner's confidence and satisfaction.
One is a somewhat pedantic quartett by Catel, which, however, even in its trivial formality, furnishes an excellent lesson for the practice of Geneuphonic Courterpoint. It is as follows: