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Musical scales are related to Fibonacci numbers.

The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as:

• There are 13 notes in the span of whatever notation through its octave.
• A scale is composed of 8 notes, of which the
• 5th and 3rd notes create the basic foundation of all chords, and
• are based on a tone which are combination of 2 steps and 1 step from the root tone, that is the 1st note of the scale.

Notation too how the piano keyboard scale of C to C above of 13 keys has viii white keys and five black keys, dissever into groups of 3 and 2.While some might "note" that in that location are but 12 "notes" in the scale, if you don't take a root and octave, a start and an stop, you have no means of calculating the gradations in between, and so this 13th annotation every bit the octave is essential to computing the frequencies of the other notes.  The word "octave" comes from the Latin word for viii, referring to the 8 tones of the complete musical calibration, which in the key of C are C-D-E-F-G-A-B-C.

In a scale, the dominant note is the fifth note of the major scale, which is also the eighth note of all xiii notes that comprise the octave.  This provides an added case of Fibonacci numbers in fundamental musical relationships.  Interestingly, 8/13 is .61538, which approximates phi.  What'due south more, the typical three chord song in the fundamental of A is made upwardly of A, its Fibonacci & phi partner E, and D, to which A bears the same relationship equally Eastward does to A. This is analogous to the "A is to B equally B is to C" basis for the gold section, or in this instance "D is to A as A is to E."

Here's another view of the Fibonacci human relationship presented by Gerben Schwab in his YouTube video. First, number the 8 notes of the octave scale. Next, number the 13 notes of the chromatic scale. The Fibonacci numbers, in crimson on both scales, fall on the same keys in both methods (C, D, East, One thousand and C). This creates the Fibonacci ratios of one:1, 2:3, 3:five, five:eight and viii:13:

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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 constitute in the first 7 numbers of the Fibonacci series ( 0, 1, i, 2, iii, 5, 8 ) are related to key frequencies of musical notes.

Fibonacci Ratio	Calculated Frequency	Tempered Frequency	Annotation in Calibration	Musical Relationship	When A=432 *	Octave below	Octave above
one/one	440	440.00	A	Root	432	216	864
2/one	880	880.00	A	Octave	864	432	1728
ii/three	293.33	293.66	D	Quaternary	288	144	576
ii/five	176	174.62	F	Aug Fifth	172.8	86.four	345.vi
3/2	660	659.26	East	Fifth	648	324	1296
three/v	264	261.63	C	Minor Third	259.2	129.6	518.4
three/8	165	164.82	E	Fifth	162 (Phi)	81	324
5/2	1,100.00	1,108.72	C#	Third	1080	540	2160
5/3	733.33	740.00	F#	Sixth	720	360	1440
5/8	275	277.18	C#	Tertiary	270	135	540
eight/3	1,173.33	1,174.64	D	4th	1152	576	2304
8/5	704	698.46	F	Aug. Fifth	691.2	345.half-dozen	1382.four

The calculated frequency higher up 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 cord on a guitar, notwithstanding, and search for the harmonics by lightly touching the string without making it touch the frets and you lot will observe pure Fibonacci relationships.

* A440 is an arbitrary standard.  The American Federation of Musicians accepted the A440 as standard pitch in 1917.  Information technology was then accustomed by the U.Southward. government its standard in 1920 and information technology was not until 1939 that this pitch was accustomed 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 oftentimes used by classical composers and results in a tuning of the whole number frequencies that are continued to numbers used in the construction of a variety of ancient works and sacred sites, such as the Great Pyramid of Arab republic of egypt.  The controversy over tuning nonetheless rages, with proponents of A432 or C256 as being more natural tunings than the current standard.

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Musical compositions oftentimes reverberate Fibonacci numbers and phi

Fibonacci and phi relationships are often found in the timing of musical compositions.  As an instance, the climax of songs is ofttimes found at roughly the phi betoken (61.8%) of the song, as opposed to the center or stop of the song.  In a 32 bar song, this would occur in the 20th bar.

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 Musical instrument blueprint is often based on phi, the golden ratio

Fibonacci and phi are used in the pattern of violins and even in the design of high quality speaker wire.

Insight on Fibonacci relationship to dominant 5th in major scale contributed by Sheila Yurick.

Practice you know of other examples of the golden ratio in music?  Submit them below.

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Source: https://www.goldennumber.net/music/

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