EXERCISES
ORAL AND WRITTEN
1. Into how many parts does modern custom divide an octave?
2. What is each part called?
3. What is the difference between a chromatic scale and a diatonic scale?
4. How many forms of diatonic scales are there and what are their names?
5. Name and define the four ways in which the tones of the diatonic scales are named.
6. What is the key-tone?
7. Describe the movable and fixed systems.
8. Describe the major scale.
9. Describe the effect of a sharp; of a double sharp; of a flat; of a double flat; of a cancel.
10. State the rule for finding the key having the next number of sharps and the rule for finding the key having the next number of flats.
11. Write on the staff, using the treble clef, all the major keys to eleven sharps and eleven flats. Write several scales (the teacher deciding the number) using the bass and tenor clefs. (Show by curved line those notes situated one semi-tone apart.)
12. What is the order of the letters in the sharp signature? In the flat signature?
13. What is meant by enharmonic?
14. What are the enharmonic scales used in practice?
15. Give enharmonic letter names for each of the twelve keys.
16. What is the sum of sharp and flat signatures of enharmonic keys?
17. By the use of this enharmonic sum, find all the theoretical keys.
18. What is the construction of the harmonic minor scale? Of the melodic minor?
19. Write on the staff all the minor scales (both harmonic and melodic) to eleven sharps and eleven flats, letting the teacher determine which clef or clefs to use.
20. What is the reason for raising the seventh in harmonic minor?
21. What is the reason for raising the sixth in melodic minor?
22. Why does the descending form of melodic minor differ from the ascending form?
23. Why does not the raised sixth or seventh appear in the signature?
24. What is an accidental?
25. What is the relative minor and how is it found?
26. What is the parallel minor and how does its signature differ from its parallel major?
N. B. Before proceeding to the next chapter all these exercises should be properly answered and corrected by the teacher.
CHAPTER III.
INTERVALS AND INTRODUCTION TO CHORD BUILDING.
An interval is the distance between two tones; intervals are named by the ordinals. The number of letters comprised in the notation of two tones determines the ordinal name of the interval. Example:
c to d is an interval of a second because two letters are comprised. It makes no difference whether or not either or both of the above tones is affected by an accidental, the interval still comprises two letters and is a second.
Reckoning from the tonic of the major scale to each degree of the scale produces the following intervals:—
8th or prime. 2nd 3rd 4th 5th 6th 7th octave 9th
The interval of the ninth is often called a second, the octave not being considered.
These intervals are the normal intervals of the major scale. These normal intervals are qualified in two ways. The prime, fourth, fifth and octave are called perfect. The second, third, sixth and seventh are called major; thus:—
All intervals should be reckoned from the lower note, which is considered a major key-note. If the upper note is in the major scale of the lower note, the interval is normal; that is, either perfect or major. If the upper note is not in the major scale of the lower note, the interval is a derivative interval. The derivative intervals are called minor, diminished and augmented.
A minor interval is derived from a major interval and is one semi-tone smaller. By lowering the upper tone of any major interval one half step or by raising the lower tone of any major interval one half step (not altering the letter name in either case) a minor interval is formed, thus:—
A diminished interval is one half step smaller than a minor or a perfect interval. By lowering the upper tone of any minor or any perfect interval one half step, or by raising the lower tone of any minor or any perfect interval one half step (not altering the letter name in either case) a diminished interval is formed, thus:—
The tones of the diminished second are the same pitch, but must be called a second because two letters are comprised. The diminished prime is possible melodically, but harmonically, only in theory. It is
.
An augmented interval is one half step larger than a major or a perfect interval. By raising the upper tone of any major or perfect interval one half step, or by lowering the lower tone of any major or perfect interval one half step (not altering the letter name in either case) an augmented interval is formed, thus:—
Notice that the tones of the augmented seventh are the same pitch, but must be called a seventh as seven letters are comprised.
The following intervals are the same in sound, but not in name:—
| perfect prime | sounds | the | same | as | diminished 2nd |
| augmented prime | " | " | " | " | minor 2nd |
| diminished prime | " | " | " | " | minor 2nd |
| major 2nd | " | " | " | " | diminished 3rd |
| minor 3rd | " | " | " | " | augmented 2nd |
| major 3rd | " | " | " | " | diminished 4th |
| perfect 4th | " | " | " | " | augmented 3rd |
| augmented 4th | " | " | " | " | diminished 5th |
| perfect 5th | " | " | " | " | diminished 6th |
| minor 6th | " | " | " | " | augmented 5th |
| major 6th | " | " | " | " | diminished 7th |
| minor 7th | " | " | " | " | augmented 6th |
| major 7th | " | " | " | " | diminished 8th |
| perfect octave | " | " | " | " | augmented 7th |
From the preceding list the following rule is apparent:—
Rule 7. By Changing Enharmonically Either or Both of the Tones of an Interval, a Different Interval is Obtained Which Sounds the Same as the Original Interval.
The distance in semi-tones of all the intervals to an octave is as follows:—
| prime | = | unison | comprises | 1 | letter |
| augmented prime | = 1 | semi-tone | " | 1 | " |
| diminished 2nd | = | unison | " | 2 | letters |
| minor 2nd | = 1 | semi-tone | " | 2 | " |
| major 2nd | = 2 | semi-tones | " | 2 | " |
| augmented 2nd | = 3 | " | " | 2 | " |
| diminished 3rd | = 2 | " | " | 3 | " |
| minor 3rd | = 3 | " | " | 3 | " |
| major 3rd | = 4 | " | " | 3 | " |
| augmented 3rd | = 5 | " | " | 3 | " |
| diminished 4th | = 4 | " | " | 4 | " |
| perfect 4th | = 5 | " | " | 4 | " |
| augmented 4th | = 6 | " | " | 4 | " |
| diminished 5th | = 6 | " | " | 5 | " |
| perfect 5th | = 7 | " | " | 5 | " |
| augmented 5th | = 8 | " | " | 5 | " |
| diminished 6th | = 7 | " | " | 6 | " |
| minor 6th | = 8 | " | " | 6 | " |
| major 6th | = 9 | " | " | 6 | " |
| augmented 6th | = 10 | " | " | 6 | " |
| diminished 7th | = 9 | " | " | 7 | " |
| minor 7th | = 10 | " | " | 7 | " |
| major 7th | = 11 | " | " | 7 | " |
| augmented 7th | = 12 | " | " | 7 | " |
| diminished 8th | = 11 | " | " | 8 | " |
| perfect 8th | = 12 | " | " | 8 | " |
A quicker and better method of determining an interval than by committing to memory the above table is to consider the lower note the tonic of the major scale. If the upper note is in the major scale of the lower note, the interval is normal (major or perfect). After a little practice the number of letters in an interval can be determined at a glance. If the upper note is not in the major scale of the lower note the interval is derivative and is determined by the information heretofore given.