Constructing the Just Major Third

Once the just major sixth has been mastered, the first bar of this passage can be used to construct the just major third:

The second bar in (4) can serve as verification by challenging students to begin with the major third and then release the third finger. If the resulting major sixth is at just consonance, the student knows that the just major third was correct. An entirely different construction of the just major third introduces the concept of “hunting”:

In this passage, the violin’s C♮ must be adjusted upward to make the just third. (With tempered open strings, Figures 1 and 2 show that the adjustment is 16%.) Passage (5) should be practiced in three variations:

1. 
   Do not sharpen the second finger until after the double stop with the open string has begun. This allows the student to “hunt” upward for the consonant sound.
   
2. 
   Sharpen the second finger before playing the double stop. This is more difficult and forces students to “learn the comma”.
   
3. 
   Play the passage in reverse order, with the strings tuned to equal tempered fifths. This challenges the student to create a deliberately dissonant major third that is a mere 2% wider than equal temperament.