SUBHARMONICS: A REVOLUTIONARY TECHNIQUE FOR THE VIOLIN
Mari Kimura
Abstract
In April 1994, at a solo recital given by Mari Kimura in New York City,
subharmonics were introduced to the musical community as a revolutionary
bowing technique to extend the violin's range by a full octave below on
the open G string without changing the tuning. Subharmonics require precise
control of the bow pressure and speed, in order to freely utilize this
extended bowing technique. Subharmonics can be used as a musical element
for composers to explore additional possibilities for the violin and other
string instruments. Kimura is further developing the technique and continues
to write works for the violin utilizing subharmonics.
Introduction
Subharmonics were introduced to the public as a musical element in the
third movement of ALT (1992) for solo violin written by Kimura.
This extended bowing technique allows one to play notes below the fundamental
by applying precise amount of bow pressure and speed. As a result, the
range of the violin was expanded one octave below the open G, the lowest
string of the instrument. The musical effects of subharmonics were noted
as a "revolutionary bowing technique [with] astonishing effect" [1]. During
the past year, subharmonics have been developed further. It is now possible
to control the various chromatic intervals below the fundamental pitch,
highly dependably for performance purposes. Each interval such as second,
third, fifth, and octave below the fundamental pitch, requires different
speed, pressure, and location of the bow on the string. One can isolate
different subharmonics by normalizing the speed and pressure of the bow
accordingly; precise control achieves regular, repeatable, and dependable
results.
Technique
Quality
Variables
Musical Creations
References
Acknowledgements
mari.kimura@nyu.edu
Some subharmonic intervals are obtained by exerting the same amount
of bow pressure. The only notable element that separates these intervals
is the slight shift in the emplacement of the bow on the string. [Fig.
1] shows the relative bow location on the string for playing different
subharmonics on open G string. ("open G" is called here as a musical note
"G2", and other notes are musically labeled along with each interval).
For example, subharmonic minor second (Sm2), major second (SM2), minor
third (Sm3) and major third (SM3) are obtained by using almost identical
bow pressure and speed, which is called {P1}(see [Fig.
1] No. 1) . Similarly, the bow pressure {P2} is identical for the subharmonic
perfect fifth (SP5), minor sixth (Sm6), diminished fifth (Sd5) (see [Fig.
1] No. 2), and so is the bow pressure {P3} for subharmonic octave (S8),
minor seventh (Sm7) and major seventh (SM7) (see [Fig. 1] No. 3). Larger
intervals such as ninth, eleventh (octave & third), and thirteenth
(octave & fifth), can be obtained in a similar manner.
The sound quality of subharmonics can be described as more nasal than
the violin played normally. The different proportions of harmonic components
shows a clear difference in sound quality. [Fig. 2] shows the FFT analysis
of open G "G2" ([Fig. 2] No. 1) and subharmonic octave "G1" ([Fig. 2] No.
1). The fundamental frequency of G2 is approximately 196Hz, followed by
the harmonics at 392Hz, 588Hz and 784Hz. The frequency that acts as the
fundamental frequency for the subharmonic octave "G1" is 98Hz, as is shown
in [Fig. 2] No. 2. The amplitude of the first harmonic of G1 at 196Hz,
which is also the fundamental frequency of G2, is suppressed almost as
half as much as the first harmonic of G2. The loudness of subharmonics
does not vary much and rather uniform; it is usually rather hard to control.
There are several variable elements that are included in order to obtain
subharmonics: the amount of rosin, the age and thickness of the string,
and the composition of the string. These variables are often combined and
create technical problems, mainly affecting the location of the bow on
the string. The amount of bow pressure is the most crucial element, however,
which one must imagine precisely before playing subharmonics.
Subharmonics usually sound somewhat harsher than notes played normally,
and they can be used as an effective element in musical compositions. Some
composers have written works for Kimura, utilizing subharmonics. For example,
Variants by Jean-Claude Risset (1994), and Effective by Robert
Rowe (1996), along with works by Kimura herself: ALT (1992, revised
1994), Gemini (1993) and Caprices (1996-).
[1] "A violinist test limits in music of her time". Edward Rothstein,
The New York Times , April 21, 1994.
I would like to thank Dr. Hideki Tachibana of Tokyo University and
Dr. Yoshio Yamazaki of Waseda University for their support for the acoustical
measurement.
© kimura@is.nyu.edu - March
1998