Musical frequencies are based on Fibonacci ratios Notes in the scale of western music are based on natural harmonics that are created by ratios of frequencies. Ratios found in the first seven numbers of the Fibonacci series ( 0, 1, 1, 2, 3, 5, 8 ) are related to key frequencies of musical notes The calculated frequency above starts with A440 and applies the Fibonacci relationships. In practice, pianos are tuned to a “tempered” frequency, a man-made adaptation devised to provide improved tonality when playing in various keys. Pluck a string on a guitar, however, and search for the harmonics by lightly touching the string without making it touch the frets and you will find pure Fibonacci relationships. * A440 is an arbitrary standard. The American Federation of Musicians accepted the A440 as standard pitch in 1917. It was then accepted by the U.S. government its standard in 1920 and it was not until 1939 that this pitch was accepted internationally. Before recent times a variety of tunings were used. It has been suggested by James Furia and others that A432 be the standard. A432 was often used by classical composers and results in a tuning of the whole number frequencies that are connected to numbers used in the construction of a variety of ancient works and sacred sites, such as the Great Pyramid of Egypt. The controversy over Fibonacci Music Bellow is a list of three known methods used to compose Fibonacci music... Binary Method: When using the Binary Method a composer will create a piece consisting of a pattern that follows a 0 and 1 system. This system relates to the Fibonacci Sequence by allowing for a hierarchy that gets infinitely close to the golden ratio to occur. Since it is very difficult to subdivide this system into any time signature, the simplest course of action for an individual to take is to compose a musical build-up from a set foundation.[1] For example, a composer will choose the length of their smallest 0 and 1. ex. 0 = a 32nd note, 1 = a 16th note It is from this small increment that a composer will start to build upon by using the Fibonacci Sequence. As the piece progresses so do the length of the notes. The 0s at 32nd notes become 16th notes and 1s at 16th notes become 8th notes. The sequence is now underway as one can notice that the original 0 note length has grown by 2, while the original 1 note length has grown by 3 from that of the original 0s length. Next, the 0 will have grown by 3 beats while the 1 will have grown by 5 beats. The hierarchy continues in this fashion as the notes grow in accordance to the Fibonacci Sequence as do their measures as well. This method also allows for a composer to make variations with the layers at ease, thus making very melodic music possible. Note to Number Method: The Note to Number method involves creating a rhythm or melody by assigning a note to a number on the Fibonacci Sequence through Modular Arithmetic (sometimes also referred to as clock arithmetic). This is achievable due to the relation of Fibonacci numbers to a musical scale. Within a musical scale there are eight notes, the fifth and third notes of a scale create the basic foundation of all chords, which are based on the original whole tone that is located two steps from the root note, this note being the fist one in the scale.[2] To start, one would write out numbers on the Fibonacci Sequence at a length of their discretion. ex. 0, 1, 2, 3, 5, 8, 13, 21... Then, the individual would rework the numbers using clock arithmetic to receive a number on a scale from 0 to 7. ex. 1, 1, 2, 3, 5, 1, 2, 4... Next, the composer would pick a base or root note and then go up the scale from that root to the next octave. Since there are eight notes and the fist note would be starting from zero the results would have a note at every number up to seven. Fibonacci Piano A piano and its keys in relation to the Fibonacci Sequence. ex. : Number | Note 0 | G mid 1 | A 2 | B 3 | C 4 | D 5 | E 6 | F 7 | G high Beat Ratio Method: This method involves the use of beats within a musical time frame in order to achieve a golden ratio hierarchy through the Fibonacci Sequence. For example, one may chose to use 4/4 time, meaning 4 beats per measure, to compose their piece. In relation to the length of a note or beat an individual may have: 1 whole note per measure 2 half notes per measure 4 quarter notes per measure 8 eighth notes per measure 16 sixteenth notes per measure 32 thirty-second notes per measure 64 sixty-fourth notes per measure It is through tiers of measures and beat lengths that mimic the golden ratio, that allow for a sequential hierarchy to take place within the composition. In the first bar or measure, one would have a single whole note which would mark 4 beats. The next tier would incorporate two half notes marking the 4 beats. It is by the third measure that the golden ratio starts to form as a result of the sequence. In the third measure two quarter notes are used and one half note is used marking the 4 beats. The fourth measure will contain four eighth notes and one half note marking the 4 beats. The fifth will contain eight eighth notes marking the 4 beats. The next and final section will contain twelve sixteenth notes and one quarter note marking the 4 beats within a measure. It can be noted that the number of notes placed within each measure thus far has incorporated a number in the Fibonacci Sequence. Measure 1 = 1 note Measure 2 = 2 notes Measure 3 = 3 notes Measure 4 = 5 notes Measure 5 = 8 notes Measure 6 = 13 notes Once all of these measures are stacked upon each other, a musical hierarchy is reached and Fibonacci music is successfully composed.
Posted on: Thu, 09 Oct 2014 04:42:53 +0000