How to play in tune: how do you know if you are in tune? Really in tune. What to listen for. What to do. How to do it. Nothing seems more impossible than learning to play really, truly, deeply, wonderfully in tune.
The key in this exercise is to listen for combination tones. It can be done with a partner or with double stops by yourself. Combination tones were discovered in the 18th century and written about by Tartini and Leopold Mozart. They are sometimes called Tartini tones.
They occur as part of the overtone series. When practicing with a chromatic tuner adjusted to equal temperament, these combination tones will not appear.
A perfect fifth is a ratio of 3:2, which means that the third partial is heard over the second partial. In simple English, if the root is a D, you find the 3:2 ratio by playing the second partial (D one octave higher) together with the third partial (A, one fifth higher than the D of the second partial). Take away two from three and you have one. One is the root note: D. Therefore, the Tartini tone, the combination tone, the difference tone of the a well tuned 3:2 ratio with a root of D will be D.
When played in canon at the measure, the following passages produce sequences of intervals: perfect fourths, major seconds, major sixths, unisons, perfect fifths, etc.
In this post, I will not burden the reader with the details of ratios and combination tones….just play it slowly together with a partner and listen for the third note, which will appear one or two octaves below the chord that you are playing together.
The second player enters at Bar 2. Other canonic options: at the half note or quarter note.
You can also practice this exercise solo in several ways. The easiest is just to constantly bow the A and D strings together. The first bar will be perfect fifths. The second will produce an octave (D), a major sixth (B/D), and another perfect fifth. Measure four generates a major second (A/G), a perfect fourth (A/E) and a perfect fifth (A/D).
These exercises come from See Saw Swings, available for violin, viola and cello. In the book, you can create canonic and solo intonation exercises in all twelve keys, on all three string pairs, and with a wide variety of melodic variations. I believe that this practice will be revolutionary for your intonation work, both alone and with your practice partner.