Technique
On instruments with a curved bridge, it is difficult to bow more than two strings simultaneously. The style of bow used until around the end of the 18th century, particularly in Germany, had the wood curved outwards (away from the hair), which made it somewhat easier to play three notes at the same time. However, most treatises written around the time make it clear that composers did not expect three notes to be played at once, even though the notes may be written in a way as to suggest this. Playing four notes at once is almost impossible, even with older bows. The normal way of playing three or four note chords is to sound the lower notes briefly and allow them to ring while the bow plays the upper notes (a broken chord). This gives the illusion of a true triple or quadruple stop. In forte, however, even with a modern violin and bow it is quite possible to play three notes at once, especially when played a little more towards the fingerboard. Obviously, with this technique, a little more pressure than usual is needed on the bow, so this cannot be practiced in softer passages. Of course, great skill is needed for the player to keep a beautiful sound. This technique is mainly used in music with great force, such as the cadenza-like solo at the beginning of the last movement of Tchaikovsky's violin concerto.
Josephine Trott's Melodious Double-Stops, Book I for Violin has been a classic string exercise book for decades. A more recent innovative teaching method for learning to play double stops, one which uses duets, was developed by Martha Yasuda; please see her Christmas Melodies: Double Stop Solos and Duets For Violin, Volume I. Martha Yasuda describes the theoretical underpinnings of this double stop method in her article entitled Double Stop Solos: How to Teach and Play using the Yasuda Double Stop Solos and Duets Approach.
Read more about this topic: Double Stop
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