Introduction

In April 1994, at a solo recital in New York City, I introduced subharmonics as a musical element to extend the violin's range by a full octave below the open G string without changing the tuning. The precise control of bow pressure and speed is necessary in order to play Subharmonics reliably and repeatedly on demand, especially in real performance situations.  Edward Rothstein of The New York Times described, "revolutionary technique" for the violin (Read the review “A Violinist Tests Limits In Music Of Her Time” here). Also: See STRINGS article on Subharmonics in June, 09 issue.

Discovery

I first discovered the technique from an age-old bowing exercise, a modified version of "Son Filé", drawing the bow very slowly but applying slightly more pressure.  The exercise was to make the sound steady on the upper E string notes while listening to a scratchy pitch generated one octave below, which I decided by chance to apply for the notes on the G string.  Eventually I managed to eliminate most of the "scratchy" transient noise, thus achieving solid low sounds one octave below on the G string.

The technique has been known among violinists as an exercise or some says even as a quirky 'joke'.  I took this obscure sounds and developed them further, not for the sake of novelty but to use them as a new element for the musical language for the violin. (You can read more about the story here).

"I wanted to free myself from the boundaries of Western musical idioms, associated with traditional violin literature, to reflect my own Japanese heritage in my compositions."

Research

Since 1994, I have given several presentations in the scientific communities such as Acoustic Society of America, and ASVA meeting presented by the Acoustic Society of Japan.

To read more about on how to play Subharmonics, please find the STRINGS magazine, August/September 2000 issue.  A scanned copy is sent along with the purchase of "The World Below G" CD. There is another article entitled "How to produce Subharmonics on the Violin" and you can listen to many sound examples, and see how I notate it on the score  (scroll down to the bottom of the page) It was publiId from the Journal of New Music Research (Routledge).

In 2008, Prof. Max Mathews, prof. Emeritus at Stanford University, visited me at Juilliard.  In February 2009, we took some measurements and video recordings of Subharmonics at Stanford.  On April 21st 2011, very sadly, Max Mathews passed away.  He was 84 years old.

November 2009: STRINGS magazine published an article and score examples of the Cadenza I wrote for Violin Concerto “SCHEMES” (2007) written for me by French composer Jean-Claude Risset.  The Cadenza is laced with subharmonic intervals and double stops that have never been seen on violin scores using pitches far below the normal range.

Development

During the past decade, I have been developing the technique even further. I am able to play not only an octave below, but also many intervals below the fundamental notes using carefully controlled bowing technique. Some excerpts are shown here to illustrate my method of notating subharmonics. These different subharmonics will also afford composers broader possibilities in creating their works previously impossible on the violin.  As I developed this technique on my own, I created musical works using Subharmonics, which is compiled in a self produced album entitled "The World Below G and Beyond".

I have been teaching many young violinists from all over the world, via internet, how to play Subharmonics.  It is not as hard as it might seem, but the real difficulty is in producing it on demand accurately at any circumstances; such as in any advanced violin technique.