Music theory is the study of the elements and structure of music. The study of melody, harmony, notation, rhythm, musical form and analysis all fall under the purview of music theory. Understanding music theory benefits violin performance by helping the player understand why and how pieces of music work, and by helping the player transpose pieces to different keys when necessary.
The study of music theory should include aural training like dictation, piano or keyboard classes, sight-singing and ear training. For violin players, ear training is the most important part of music theory.
Violin players must have excellent "ears," or a very strong sense of pitch and rhythm recognition. Ear training develops a musician's ability to recognize intervals and rhythmic patterns. Through ear training, a musician can improve and perfect her sense of relative pitch.
The most basic ear training involves learning to recognize the intervals, or the constant relationships between pitches, that make up scales in Western tonal music. These intervals are usually taught through repetition and recognition drills. Basic rhythmic patterns may also be drilled.
Relative pitch is the ability to recognize and communicate intervals accurately given a starting pitch. While some people are born with perfect pitch, or the ability to identify a pitch without any outside reference, relative pitch can be learned.
Relative pitch is particularly important for violin players, as they must be able to tune the strings of their instrument, and because they rely on their fingers and ears to shorten their strings the appropriate amount to create changes in pitch.
Violin players should begin their ear training as soon as they start to learn the basics of their instrument. The Suzuki method is an excellent course for beginners (particularly children, although the exercises are beneficial to players of all ages) to follow as it combines lessons in basic technique with ear training. Suzuki training emphasizes learning to hear intervals and melodies before learning to read musical notation. Students play rhythmic and melodic patterns in unison with other students to learn those patterns and to train their ears to recognize them.
Beyond Suzuki, basic ear training may be accomplished in several different ways. A student may simply drill intervals one after another until he has learned the difference between them. A teacher and a well-tuned piano (or violin) or a computer program that plays and quizzes the student on different intervals will do this equally well. He may also learn to identify intervals by identifying the beginnings of popular melodies that begin with those intervals. For example, "Twinkle Twinkle Little Star" begins with a major fifth. As a violin student becomes more advanced in his ear training, he should be able to identify any interval that presents itself in the pieces that he is learning to play.