CHAPTER II.
THEORY OF SCALES.
MAJOR AND MINOR.
As stated before (Chapter I, page [4]), the rate of vibration is called pitch. Tones vibrating an equal number of times produce an unison which is a perfect concordance and is pleasant to the ear. Equally as pleasant to the ear is the ratio of two vibrations against one. A tone vibrating twice as fast as a given tone is called the given tone's octave. Between these two tones many tones may be found. For example, suppose a note vibrating two hundred times in a second, its octave would vibrate four hundred times in the second. Between these two tones there would be (avoiding fractions which would produce more different pitches) one hundred and ninety-nine tones of different pitch. The ear is incapable of locating all these tones and modern custom has divided all octaves into twelve parts, each part being called a half step or, literally incorrect, a semi-tone. These semi-tones sounded successively upwards or downwards from any tone to its octave produce the chromatic scale.[A]
A diatonic scale is a progression from any tone to its octave in which certain chromatic steps are omitted. In modern music there are three forms of diatonic scales, called:—
1. Major.
2. Harmonic minor.
3. Melodic minor.
All three forms have eight tones, the eighth being the octave of the first and is given the same name.
The tones of the diatonic scale are named in four different ways:—
1. by numerals (Arabic and Roman),
2. by the first seven letters of the alphabet,
3. by the Italian syllables (do, re, mi, fa, sol, la, si,) and
4. by the theory names (tonic, supertonic, mediant, subdominant,
dominant, submediant and subtonic).