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The grandeur of this piece of music, and the facility with which it is apprehended by mankind in general, appear to be fully explained by the consideration of the numerical relations of the vibrations corresponding to the notes.

97. On Enriched Music, and Singing in Parts.

The melodies that we have considered, if played upon an instrument which does not necessarily at every touch or blast produce a combination of several harmonic notes, would seem too simple. It is necessary to ornament them by combining, with almost every note in the melody, a series of related notes, to be struck simultaneously with it. They are usually lower notes, in harmonic relation. The combined system, of the original note and these related notes, constitutes a "chord."

As instances of chords, we will exhibit (in the same form as in the last Article) the first part of "God save the Queen," and the second part of "Adeste fideles."

our gracious Queen Long live our noble Queen God save the Queen 2 2 3 1 2 2 22 4

God save
2 2 1 1 3 1 2

2

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EED E FED
сс св св CBC GG GG
60 60 54 60 64 60 54 60 64 60 54 48 45 48
48 48 48 45 48 45 48 45 48 36 36 36 36

E FE

DCB C

Dominum.

1 2 2 3

FEDC

CC B

64 6054 48

48 48 45

In the greater part of these chords, the proportions of the numbers of vibrations admit of being expressed

48

by very low numbers; for instance, the proportion 36 is

8

45

60

30

5

the same as 6; both 36 and 48 are the same as 4; and

5

27 36

3

so for others. On the first syllable of "Natum" in the second piece of music (to which syllable we have called attention before), the chord is the same as

3

72 48

or two notes at the interval of a Fifth, a most power

2' ful harmony. There are several chords containing

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54, 32 40

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harmonious; if, however, D be made = 56 (which, giving

7
6

a relation to the key note C, appears permissible), the

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This is an instance of what frequently occurs in musical composition, that the harmonious relation of two adjacent or simultaneous notes is more important than the harmonious relation of either note to the key-note.

45

45

56

64

The chords 32 or (as corrected) 32, 45' 45'

27

, appear to

28

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Singing in Parts may be understood as an exact imitation by different human voices of that which is done here by different fingers upon an instrument. The highest voice usually sings the notes as given in Article 96, or as in the upper line of the harmonized music just exhibited; the other voices at the same time sing notes represented by those of the second and third lines of the harmonized music. The skill of a composer of Music in Parts is shewn by his assigning, to those other voices, notes which will produce good harmony with each note of the highest voice, and which at the

same time will produce for each person, considered alone, a species of tune that can be followed correctly with

ease.

98. On the necessity for the supplementary notes called "flats" and “sharps.” .

We have exhibited to the reader two pieces of music in which every sound is expressed by a note of the diatonic scale. And the reason of our having been able sufficiently to express all by that scale is, that we have taken c for the key-note of our melodies; and that, in these special instances, that pitch has appeared so well suited to the subject that there has been no temptation to adopt any other key.

But it will easily be imagined that we cannot bind ourselves to this condition. We may desire to make our tune somewhat higher or somewhat lower, but we cannot venture to raise it an entire octave so as to have c for key-note, or to depress it by an entire octave so as to have C for key-note. And we may now consider how the power of using any other note as key-note can be obtained.

Proceeding upwards from c we have in the diatonic scale, two tones, then one semitone, then three tones, then one semitone. We desire to have a similar succession of intervals for any other key. Suppose, for instance, we adopt D as key-note.

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Here, the notes 1, 2, 4, 5, 6 on our new scale may be represented by D, E, G, a, b, on the old scale. The interval from 1 to 2 will not be precisely the same as that from C to D, and so in other parts of the scale; but they will be sufficiently near to them to pass (in ordinary estimation) for similar intervals, perhaps slightly altering the character of the music. But the notes 3, 7, on our new scale, have no representative on the old scale; and, for representing them, it is necessary to introduce a note nearly midway between F and G, and a note nearly midway between c and d (and similarly a note between C and D). The note between F and G is called indifferently F sharp, F#, or G flat, Gb; and that between C and D is called C or Db.

Now when we adopt other notes as key-notes, we find that we must interpose notes between various notes of the original diatonic scale; and ultimately we find that in every interval of a complete tone it is necessary to insert a new note. The whole scale, for one octave, then becomes this:

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This is sometimes called the chromatic scale.

The new notes are those corresponding to the black keys of a pianoforte.

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