Friday, December 28, 2012

Breaking the Limits of Music: Introducing the 14-Note Octave 7-Limit Just Intonation Guitar

Quick announcement: For the Spring Semester, starting in December, due to authors traveling abroad (to Italy, South Africa, France, and more!), Unleashed is being published once a month. 
Cheers to our first wonderful guest article of the New Year!


When the familiar becomes your only measuring tool, all creativity is lost-- this became my philosophy many years ago. Over ten years ago, I began a journey into the reexamination of the 6-string classical guitar. After having a serendipitous encounter with the Shaman of the 11-string arch guitar, James Kline, I was convinced my musical thought process needed reevaluation. Witnessing James Kline’s 11-string, its vast range of color, its harmonic and contrapuntal possibilities beyond the 6-string guitar, left me with no choice but to abandon my current parameters, which were imprisoning me. The emotional and spiritual depth found in the music of Ravel, Debussy, and Rachmanioff, would become my new inspiration for the next chapter in my musical life. I worked with Willits, Ca. luthier Greg Byers to construct a 7-string guitar with a lower bass string. We decided to add two extra frets on the 7th playing string making a scale length of 730mm from the other 6-playing strings at 650mm. Greg and I also added three extra frets on the 1st string, making a total of 22-frets or a high “D”, plus a sliding capo for the first five frets of the 7th string. I gave this guitar the name, Extended 7-String Guitar. I would be honored to share my adventure that gave birth to the 14-note octave just intonation guitar, an instrument of great complexity and spirituality.

As a performer of Indian classical music, I realized the limitations of my musical expression on a six or seven-string guitar set in equal temperament (E.T.). An interview with John Schneider about his microtonal guitars, inspired me to design a guitar that could express the gamut of Indian classical music. I worked with Fairfax, Ca. luthier Scott Richter to design a new guitar that fused the 7-string classical guitar and the Indian sarod into one creation. The raga guitar (the title I gave this instrument) has 7-playing, 12-sympathetic, 2-chikari, and 4-jawari strings making a total of 25-strings. We also included a just intonation fingerboard to accomplish the proper tuning of Indian music.

About two years ago, my raga guitar was partially destroyed in a freak accident. With his divine woodworking skills, Scott Richter was able to rebuild the raga guitar in nine months. In the meantime, I had a dozen Indian music concerts to perform. I needed some type of interim guitar. I had a 6-string guitar made by Greg Byers I intended to sell, so I asked Scott if he could remove the current fingerboard and replace it with a just intonation fingerboard to allow me to perform Indian music on some respectful level. Within one week Scott completed the task. At this point my guitar had a 12-note octave tuned in 5-limit just intonation. After having this guitar for five months I decided to add two additional notes to the palette, making a total of 14-notes per octave (1.). I gave this instrument the name: The 14-Note Octave 7-Limit Just Intonation Guitar. A new musical system was born.

I will give a brief overview of how just intonation works. Just intonation can be defined as small numbered whole number ratios based in the overtone series.  It can also be defined as musical intervals that are acoustically pure.  The relationships in the overtone series are given to us from the natural world; it cannot be altered on any imaginable level. J.I. can be expressed in whole number ratios or cents. For example: 3/2 is a just fifth measured at 702 cents, 5/4 is the just major third measured at 386 cents, and 7/4 is the septimal minor seventh measured at 969 cents.

There are advantages and disadvantages of both equal temperament (E.T.) and just intonation (J.I.). E.T. has the ability to perform in all the keys being “equally out of tune”, thus giving the illusion of perfect intonation. E.T. has homogenized all the pitches and have taking them away from their pure forms. However, the pitches are not taken to the gross level of a wolf interval. J.I. offers the purity and sacredness of pitch. All of the relationships are based from a fundamental tone and are tuned to low whole numbered ratios. If the music stays in one tonal center (not necessarily one key) the tuning is very pleasant to the ear. If the demands of the music require constant modulation, J.I. will start to produce some very gross wolf intervals that are not very pleasing. Neither J.I. nor E.T. can offer a universal solution for every musical system. This process becomes a personal preference of philosophy and musical aesthetics.

The path of developing a 14-note octave, was not an easy one. This instrument was originally intended to be my interim guitar for Indian classical music concerts until my raga guitar was rebuilt. It started with a 12-note octave in 5-limit J.I. After the interim period, I decided to include two additional notes to my octave, making 14-notes total. I added the ratios: 7/4 and 7/6 (septimal minor 7th and septimal minor 3rd) immediately to my palette of notes. I also considered adding: 9/7, 8/7, 12/7, and 11/8 (septimal major 3rd, septimal whole-tone, septimal major 6th, and 11-limit tri-tone) to my octave. One major hindrance was the frets being too close together, making it nearly impossible to play. I decided to make 36/35 (49 cents) my smallest interval on the fingerboard, thus maintaining a level of practicality for myself. The measurement of 36/35 can range from 9-16mm. The notes past the 12th fret return to a 12-note octave in 5-limit J.I. I started off with 12-notes per octave and then pushed for at least 18-notes per octave, thus settling for 14-notes per octave. Once I completely realized the complexity of 7-limit J.I., I was very happy to live humbly with 60 different sized musical intervals to master. J.I. allows for a distinctive voice in the creation of music. A musician is transported into their own musical universe through their choice of ratios. Most musicians stop at 5-limit J.I. When I heard 7/4 it was a mystical experience beyond words, I hade to have that note.

E.T. has only 12 different musical intervals. Every semi-tone (100 cents), whole-tone (200 cents), etc is the same distance in E.T. On my 14-note octave guitar, I have eight different sized half steps, ranging from 36/35 (49 cents) to 27/25 (133 cents). The inversion of the semi-tone, the major seventh has eight different sizes musical intervals as well. The augmented fourth has six different sizes ranging from 25/18 (568.7 cents) to 121/84 (632 cents). The major second, minor third, major third, minor sixth, major sixth, and minor seventh have five different sizes. The perfect fourth and perfect fifth both have four different sizes. From one perspective, the palette of musical intervals found in J.I. offers more color and emotional depth then E.T. has to offer.

The esoteric nature of J.I. provides the seeds for musical expression through musical composition. In Settings in a Utopian World for solo 14-Note Octave 7-Limit Just Intonation Guitar, I composed four movements: Prelude, Invocation, Intermezzo, and 7 Winds. The Prelude, Intermezzo, and 7 Winds are composed in 7-limit J.I. There are auspicious chords that reach into the depths of creation and transcend both time and space. Some harmonies are: 7/6, 4/3, 3/2, and 5/3 (simultaneously). Invocation utilizes the Dorian Mode in 5-limit J.I. One hears beautiful Em9 chords (6/5, 3/2, 9/5. and 9/8) justly tuned. There was a period I decided to try some “traditional” classical guitar music on this instrument. Interestingly enough, some of the music sounded very good. However, because of the fret placements, I found playing this repertory on this instrument to be very awkward. Music set with 12-notes per octave regardless of the temperament, is much more simple than my 14-note octave. One still needs to have an idiomatic nature to one’s instrument; musical performance needs to be accessible to one and all.

What type of notational system does one use for a 14-note octave guitar? I decided to list the ratios with the corresponding notes (i.e. E=2/1, F#=9/8, G=6/5, etc). This allows for a precise measurement of intonation. My instrument has two minor 3rds and two minor 7ths, if the desired piece of music utilizes both minor 3rds (G-note), I label above or below the written pitch either 7/6 (septimal minor 3rd) or 6/5 (just minor 3rd). This denotes what “shade” of “G” one should use. And similarly, I notate 7/4 (septimal minor 7th) and 9/5 (just minor 7th) to distinguish between the two “shades” of “D” or the minor 7th. My notational system allows for very little deviation from traditional notation. I hope this maintains a sense of familiarity, when one redefines their aesthetic.

My journey with the design of musical instruments has been an enlightening and peaceful journey for my soul. I feel “thinking outside of the box” is my general philosophy with life. The reexamination of what a musical instrument can or can’t do, is worth the time and effort. It colors our consciousness with contemplative thoughts about who we are as individuals. I believe we must understand our strengths and weaknesses as humans and be in touch we our “path” and live it to the fullest. This is what I see in my instruments.

1.)   Octave is a problematic term that makes no real sense outside of a system that uses 7-note scales. The precise measurement is 2/1, which expresses a frequency that doubles its vibration. I use the term “octave” as means of convenience to the reader.

About the Author
Born in 1972 of Chinese and Italian ancestry, Matthew Grasso began playing guitar at the age of twelve. He attended the San Francisco Conservatory of Music where he studied with Scott Tennant and Lawrence Ferrara. Matthew has participated in master classes by Eliot Fisk, David Russell, and the Los Angeles Guitar Quartet; he has further supplemented this training by studying the classical music of North India at the Ali Akbar College of Music with Ustad Ali Akbar Khan.

Moreover, Matthew has advanced the genre of world music by combining Eastern and Western traditions in both fixed compositions and improvised works for solo guitar and ensemble. He has developed a new style of playing entitled Indian classical fusion which combines elements of north and south Indian music, and has conceived new talas (rhythmic cycles) such as 10 1/2, 27 1/2, 9 1/4, and 26 1/4. This music can be heard with his group, The Nada Brahma Music Ensemble.

Matthew performs and lectures throughout Northern California. He has appeared as a soloist with the Solano Symphony and played with the Sacramento Youth Symphony Premier Orchestra. His recordings include two CDs of original compositions, Intimate Settings (1995) and Echoes of a Lake (1999) as well as his transcription of Mussorgsky's Pictures at an Exhibition (2001) for solo guitar. Matthew has self-published music scores of his compositions and transcriptions, and his CDs and sheet music are available from his publishing house:

Matthew teaches privately and is on the faculties of Sacramento City College and The Experimental College of U.C. Davis. He currently resides in Davis, California.

To learn more about Matthew Grasso and his music, please visit his website.

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