A favorite topic of mine is about harmonics. Harmonics are where science and nature meet music. We are lucky as string players and especially as bass player that we are able to see the harmonic divisions occurring. Harmonics help us organize fingering systems. Harmonics also can help us to determine optimal bow placement.
1. The note that is two octaves above any open string is at a point which is one- quarter of the string length away from the bridge. Bowing an open string at this point creates a very pure soft sound since the string is vibrating mostly in one, two, and four parts.
2. Another fairly pure sound is created by bowing at the point which is one-sixth of the string length away from the bridge, the place of the harmonic which is two octave and a fifth above the open string. Bowing the string at this point causes the string to vibrate mostly in one, two, three and six parts.
3. Another pure yet brighter sound is created by bowing the open string at the point which is at the three octave harmonic, or one-eighth of the total string length away from the bridge.
Obviously if a note is stopped, the string length is shorter, and the fractions of that stopped string length are smaller. To maintain a consistent sound, the bow needs to travel nearer and further from the bridge, in order to stay at the two octave, two octave and fifth, or three octave mark above the stopped string length. The sound in #1 above is appropriate for an excerpt such as the opening of the Scherzo of Beethoven’s fifth symphony. #2 is good for fuller dynamics when a fast bow is desired. #3 is good for strong dynamics and requires a slower bow. This is good placement for an excerpt such as #9 in Strauss’s “Ein Heldenleben”.
There are other bow placements that work for other sounds, but knowing these three sounds is basic. Maybe next time I will share some ideas about how this relates to right hand placement for pizzicato. Practice well.