Math vs. art

Tuning into life. I often think about where science ends and spirituality begins. Or do they overlap? It seems that sometimes something considered to be woo woo is then found to have a basis in science. After all, the US government is now admitting that it has been tracking UFO’s for a very long time. The violin’s dimensions and the tuning of its strings is very mathematical but the emotional and spiritual connection the violinist has with his or her instrument manifests as art. 

String instruments can produce both natural and artificial harmonics. Natural harmonics are produced by placing your finger lightly on a node. A node is a location on a string where is does not vibrate. The tone of a harmonic is pure and somewhat airy. Natural harmonics that are the easiest to hear and produce are located at half the string length producing the tone an octave higher than the open string and at the quarter string length which is two octaves higher than the open string. There are myriad other natural harmonics which once discovered can make playing more “contemporary” music a lot easier even though the harmonic itself might not be entirely reliable. Artificial harmonics are produced by holding down most often the 1st finger and creating the quarter length with one’s 4th finger. It is kind of like the way guitar players use a capo. Otherwise the string length for natural harmonics is the distance from the nut to the bridge.

Shinichi Suzuki coined the term “tonalization” which grew out of the word vocalization. Singers have a series of vocal exercises they use to warm up the voice, develop health habits using the vocal anatomy, and extend the range, facility and power of the voice. Tonalization is the instrumentalist’s analog to this process. A Suzuki violin student’s first tonalization is the copying of the teacher’s tone using of the five Twinkle rhythms played on the open A and E strings. When one plays a tonalization, one is working on tone production. Here we are at that cross section of math and art on the violin. 

It seems to me that the basis of all tone production is the ability to get the deepest possible ring on the violin. “Ring tones” on the violin are created when a fingered note shares the same overtone series as one of the open strings. That is to say, any fingered note that is in unison or octave relation to an open string when played in tune will cause the open string to ring sympathetically. Once a ring tone is located, one should continue to search for the deepest possible ring.

I am constantly telling my students to check ring tones. I tell them that ensuring that these notes are always ringing, will help them play in tune and even improve the overall tone quality on their instruments. It can actually represent an epiphany to a violinist when the working on of ring tones becomes an integral part of one’s practice. Tuning in general for a musician is both math and art. Tuning is measurable, finite, and must be accurate. However, each instrument family presents its own bias due to the way its sound is produced. Being in tune with one’s own violin does not guarantee that you will always be in tune with, for example, the piano. The violin’s overtone series didn’t get the Baroque era memo about tempering the clavier so that so many boards and split keys wouldn’t be necessary. It is at this point that decisions need to be made about how to best serve the harmony presented. I have spent much rehearsal time asking a pianist to hold out harmonies so that I could find a way to insert passing notes to best color a harmony. It is so very complicated and beautiful at the same time.

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