Fibonacci’s Dream: Eclectic Modern Mathematical Compositions for the Acoustic Guitar All compositions written by Lawrence M. Blatt All instruments played by Lawrence M. Blatt Recorded in San Francisco (Knob and Tube) and Healdsburg, California Digital Recording, Mixing and Mastering by Gary Mankin (Knob & Tube) Photographs by Clint Graves (www.clintgraves.com) Prologue: We are always counting. We count the millennium, the centuries, the decades, the years, the months, the weeks, the days and the hours, minutes and seconds of every moment of our lives. Throughout each day, we perform hundreds of calculations without even thinking about it. We also have an eternal clock that guides us through our day called our circadian rhythm. We know, albeit subconsciously, that our hearts are beating and if you sit quietly you can even feel the pulse of your life force. You have been counting all of your life and that rhythm defines you. With all of this counting going on, I have realized that we are hard-wired for numbers. Numbers form the foundation of our physical world and it is the law of numbers, mathematics, which governs the universe. Many religions have also coveted numbers and have interlaced mathematics, wisdom and spirituality to help explain the mysteries of the world. I recently began to think about music and numbers. On the surface of it, one can easily see that music and math are intertwined. We count measures and notes and we play scales that are varied by tones defined by whole and half step increments. But I began to wonder: “What makes some music sound beautiful and sweet and other music sound out of tune or not well arranged?” You really do not need musical training to know. Most of us can tell when a singer is out of pitch or when a melody is pleasing or not. I began to question if we are hard-wired to know “good” music from “bad”. As I thought about the concept of musical hard-wiring, I began to examine the work of Leonardo Fibonacci, the extraordinary 13th Century Italian mathematician. During his life, Fibonacci traveled throughout the Mediterranean region and studied mathematics with several Arab scholars. By the age of 32, he published a book called “Liber Abaci” (Book of Calculation), and introduced Europeans to the use of Arabic numerals (the system we use today). In his book, Fibonacci explained the solution to the question of how fast a hypothetical population of rabbits could breed. The solution encompassed a derivation of a series of numbers that have far reaching implications to explain physical realities found throughout the universe. Assuming that there was one mating pair to start, Fibonacci calculated that each generation of rabbits would increase by the sum of the two preceding numbers of rabbits. Fibonacci derived a series of numbers using this formula. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,………………. Fibonacci further realized that these numbers could be expressed as a ratio, and he derived the calculation of Phi, “The Golden Ratio”. Expressed mathematically as: 1 +√5/2 The “Golden Ratio” is approximately equal to the number 1.618. OK, I know what you are saying—what does all this have to do with art and music? The answer is: EVERYTHING!!! Fibonacci ratios and numbers are found all over the natural world and in our every day lives. The petals of a Sunflower and the arrangement of seeds in a pinecone both contain Fibonacci numbers. The Golden Ratio is seen in the turns of a nautilus shell and the shape of cochlea inside our ears that both increase in size by a factor of 1.618 with every turn. The proportions of the human body are based on Phi and the Fibonacci number 5 and artists from Di Vinci to Seurat and Mondrian have utilized Fibonacci mathematics to improve the aesthetics of their artwork and designs. Much of musical theory follows Fibonacci mathematics. Musical scales are based on 8 notes and an Octave is separated by 12+ 1 tones (8 and 13 are Fibonacci numbers). The basic structure of a chord uses the Fibonacci sequence 1, 3 and 5. Many great composers from Mozart to Beethoven to Bob Dylan have either consciously or subconsciously applied Fibonacci mathematics to their music. With Fibonacci math in hand, I set out to compose this series of recordings. I have tried to lace Fibonacci numbers and ratios in each composition. To hear the Fibonacci influence, look for phrases that are repeated in a Fibonacci sequence of numbers, melodies that follow tonal intervals separated by Fibonacci numbers and verses increasing in length by the Golden Ratio. As with my first album, Out of the Woodwork please try to listen to this album, at least once, in its entirety as the compositions are carefully ordered to take you on a journey of my musical and mathematical world. I hope you enjoy my music…and the math. Compositions: Bern “The Bear” Time: 1:38 Tuning: DADGAD Instrument(s): Furch Stanford Acoustic Guitar Bern is the capital of Switzerland and the city is named after the bears that once roamed the mountains surrounding the city. If you go to Bern you can still see bears in display pits near the city center. It was on a recent visit to Bern that I wrote this song after visiting the bears. Una Vida (One Life) Time: 4:16 Tuning: Standard Instrument(s): EVD Custom Acoustic Nylon-stringed Guitar: Breedlove Acoustic Bass; Charango, Various Percussion Instruments If you live in California you cannot help but be influenced by the Latin world. Our architecture, the names of our cities, our food, culture and many of our people all have roots in Latin America. Una Vida (One Life) is a celebration of that influence and is a reminder of the fragility and uniqueness if each living soul. The last part of the piece is played on a charango, a South American 10-stringed instrument derived from the lute. In a Heartbeat Time: 2:00 Tuning: Drop-D Instrument(s): EVD Custom Steel-String Acoustic Guitar, Breedlove Acoustic Bass Life moves by so quickly. This composition, a short two minutes long, is a reminder that beautiful things can come and go “in a heartbeat”. Fibonacci’s Dream Time: 3:53 Tuning: Standard Instrument(s): Wingert Parlor Acoustic Guitar, Breedlove Acoustic Bass, EVD Custom Steel-String Acoustic Guitar, Various Percussion Instruments This composition is loaded with Fibonacci mathematics and was the first piece written for this album and the inspiration for the whole body of work. The middle section, utilizing a phased acoustic guitar, is called the “Dream Sequence” where Fibonacci congers up the solution to the rabbit breeding problem and the melody is played in a sequence of repeating Fibonacci numbered phrases. I Remember When Time: 2:20 Tuning: Hawaiian Taro-patch Instrument(s): Wingert Parlor Acoustic Guitar, Breedlove Acoustic Bass, Nahenahe 8-string Ukulele, Yamaha electric piano This piece was written on a trip to the Hawaiian island of Kauai. The reflective melody reminds me of places and people from the past. I’m Leaving Now Time: 2:48 Tuning: DADGAD Instrument(s): EVD Custom Steel-String Acoustic Guitar The one thing that is constant in life is that change will occur. With change comes challenges and with challenges new innovations can arise. It is sometimes necessary to leave a situation to allow for growth. This composition is about the turmoil of change and an ultimate decision to leave. Five Nights Time: 3:10 Tuning: Standard Instrument(s): EVD Custom Steel-String Acoustic Guitar, Various Percussion Instruments The 1981 Indiana University basketball team may have been one of the greatest teams of all time. Led by Isaiah Thomas, the team started the season poorly and did not function well together. Coach Bobby Night (yes- this is the guy that tossed the chair) pulled the team together and by the end of the year the five players functioned as a well-oiled machine that ended the season by winning the NCAA championship. This composition, which utilizes five melody lines, is a tribute to that team. See if you can hear how the “team” comes together in the end. Just Before Dawn Time: 3:40 Tuning: DADGAD Instrument(s): John How Custom Steel-String Acoustic Guitar As the old saying goes: “Sleep on it and things will become more clear in the morning.” In thinking about this album, one morning, just before dawn, after eight hours of sleep, the concept became crystallized and I had a true understanding of where I wanted to take the music. This piece was written in that moment. A Little More Sunshine Time: 3:09 Tuning: DADGAD Instrument(s): Stanford Acoustic Guitar, Breedlove Acoustic Bass, Various Percussion Instruments This composition evolved from an improvisation during a live performance of “Under the Sun” a piece from my first album Out of the Woodwork. Although this composition remains true to the original melody and phrasing, it has a slightly more jazzy feel and sound. Catalina Time: 2:57 Tuning: Drop-D Instrument(s): Furch Stanford Acoustic Guitar Santa Catalina Island is one of the eight islands that make up the California Channel Islands. The island was once owned by William Wrigley Jr., and he developed tile and pottery works there during the 1920’s. Catalina tile can now be found throughout the State of California adorning public buildings, churches and private homes. The tile often forms complex geometric patterns that can only be observed when several pieces are strung together and viewed from a distant vantage point. This composition evokes similar complex musical patterns as several guitars play different parts that unify to become the whole. Song for Chava Time: 3:00 Tuning: Standard Instrument(s): Wingert Parlor Acoustic Guitar; Breedlove Acoustic Bass, Charango, Ronroco, 1890 Ditson Mandolin, Various Percussion Instruments This composition is a gift for my daughter on her 13th birthday and is reminiscent of our Eastern European Heritage. La Selva (The Rainforest) Time: 2:04 Tuning: Standard Ronroco Instrument(s): Ronroco, Various South-American Percussion Instruments This composition is played on a ronroco, a South American stringed instrument that is related to the charango. This composition is a tribute La Selva, the Rainforest. I hope that it will serve as a reminder to the beauty and importance of the world’s rainforests, which are now in significant danger due to over forestation and pollution from fossil fuel exhaust. Move Um Out Time: 2:50 Tuning: DADGAD Instrument(s): EVD Custom Steel-String Acoustic Guitar, Various Percussion Instruments All of us have been affected by the terrible turmoil the world is now facing. If you live in the U.S., you may have known someone who died on 9-11-01 or you may have a family member or friend who is involved in the military service. Strangely though, all of this is quite removed from our everyday lives and our only true link to all the chaos is the footage on the news or a video on Youtube. This composition, “Move Um Out” is a reminder of the senselessness of war as the piece ends, metaphorically, in disarray. Acknowledgements and other stuff Thanks to Elyse, Zack and Zoe for allowing me the time away for recording sessions. Thanks to Gary Mankin of Knob & Tube for taking the time out of his busy schedule to record, mix and master this album and for helping me to get all of the instrument parts working in unison. Thanks to Kathy Wingert, Edward Dick, John How, and Frederick Furch for making my beautiful guitars. Thanks to all of you for listening to my music. If you would like to learn more about me please visit my website at http://www.lawrenceblatt.com or send me an email at Lawrence@lawrenceblatt.com LB Also available from Lawrence Blatt: Out of the Woodwork