There are several reasons for which the frequent playing of intervals is of the greatest importance.
For one, it will enable you to read music easily, to tell by looking at it how it will have to sound.
The difference between two notes, the distance at which the second note stands in pitch from the first, is called an interval.
In the first exercise, the first note is C and the second one is D. This is an interval of a second and the whole exercise consists of seconds. The first is printed as an 8th note with a dot, more to impress upon your mind that this note with the next one, which is printed as a whole note forms an interval of a second, than to show how it should be bowed.
In the 2nd exercise, the interval between the short note and the whole note is a third. One note between the two has been skipped.
In the 3rd exercise, the intervals are fourths. The lowest note is always counted as one, and the last note give you the name of the interval. FOr instance, C D E F is a fourth.
The last exercise is in thirds but written in the key of Bb.
Practice these exercises with different bowings. Play on interval at a time as if they notes were equal in time, to quarter notes for instance, and repeat it frequently, listening carefully to the differences between the higher note and the lower one at the same time saying to yourself, "I am playing a second or a third or a fourth, whatever it may be."
When you have done this play as the exercises are written. Play the short note with about half of the bow beginning at the middle, making a rapid short upward stroke and then play the whole note with the complete length of the bow but give the note at least the time of two seconds.
There is no time signature at the beginning.
One of these exercises should not be given less than a half hours time every day and not only for this week but for many weeks to come.
A dot and a curve signifies a pause. It means that you should at least double the time value of a note.
"The Invitation to the Dance" is your recreation, but at the same time an excellent exercise for intervals and slow bowing. You should use the full length of the bow for all the dotted half notes.
You will find the figure 4 frequently over notes that you might play on an open string, but that 4 tells you that instead of doing this, you must use the next lower string and play the note with the fourth finger.
The 4 placed over high C is not needed, it simply impresses it upon your mind that you will have to reach further with the fourth finger. If you have much time for practice, you should play and write similar exercises as those which are given at the beginning in all the scales that you have learned up to the present.
Dolce means softly, sweetly; p- (piano) means softly. Dim. means diminish the sound, getting softer.
Two lines joining in a point like a wedge means to swell the sound where the lines separate.