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Firsts Seconds Thirds
Fourths Fifths Sixths
Sevenths Octaves
Ninths Tenths
When the interval extends above the tenth, it is then count-
ed from the octave of the fundamental note, and again called
fourth, fifth, &c. The smallest interval in general use, is the
semitone. All intervals must be reckoned from the lowest, up-
wards, unless the contrary be expressed. A semitone may be
major or minor. A minor or chromatic semitone is the difference
between two notes on the same degree, thus
A major or diatonic semitone is the difference between two notes
on different degrees, thus. A whole tone
consists of a minor and major semitone joined together; as in
the following example:
Inversion of Intervals
When the lower note of any interval is place an octave high-
er, or the higher note an octave lower, the change therby pro-
duced is called an Inversion. The 2d becomes a 7th, the 3d
a 6th, the 4th a 5th, the 5th a 4th, the 6th a 3d, the 7th 2d,
and the octave a unison. In the following example, the black
notes are direct intervals, and the white notes their inversions;
the lowest note, C, being placed an octave higher.
2d 7th 3d 6th 4th 5th 5th 4th
6th 3d 7th 2d 8th Unison.
Of the Scale, or Gamut
The seven notes, placed one after the other in regular suc-
cession with the octave to the first, form what is termed the
Gamut or Scale. The scale may be Diatonic or Chromatic.
The diatonic scale consists of five whole tones and two half
tones, which, accodring as the scale is major or minor, are dif-
ferently placed. In all the diatonic major scales, the semitones
are between the 3d and 4th, and 7th and 8th of the scale, both
ascending and descending. The following is the major scale
of C with the semitones marked with a slur: --
The minor scales have the same number of semitones as the
major, but differently placed. The semitones in all the minor
scales are between the 2d and 3d, and 7th and 8th of the scale
ascending, and between the 6th and 5th, and 3d and 2d, de-
scending. The semitones are marked with a slur.
The diatonic major key, or scale of C, which is the natural
key, may be transposed eleven times, and then it becomes ex-
hausted; and each of those keys has its relative minor; so
called in consequence of the signature being the same, and is
always found a minor third below its relative major. The last
note in every regular composition determines the key, and is
called the tonic or key note; and all scaled should commence
and end on the tonic, or key note. The first transposition in
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