Patent Application
20240312439
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A portion of the disclosure of this patent document contains material which is subject to intellectual property rights such as but not limited to copyright, trademark, and/or trade dress protection. The owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure as it appears in the Patent and Trademark Office patent files or records but otherwise reserves all rights whatsoever.
The present invention relates to improvements in tuning musical instruments. More particularly, the invention relates to improvements particularly suited for providing multiple instrument coordination and harmonics. In particular, the present invention relates specifically to a revised tuning system applicable across multiple instruments for band harmonies.
As will be appreciated by those skilled in the art, musical instruments are known in various forms. Patents disclosing information relevant to tuning musical instruments include: U.S. Pat. No. 2,221,523 issued on Nov. 12, 1940 to Railsback entitled Pitch Determining Apparatus; U.S. Pat. No. 2,679,782, issued on Jun. 1, 1956 to Ryder entitled Tuning Instrument; U.S. Pat. No. 3,968,719, issued to Sanderson on Jul. 13, 1976 entitled Method For Tuning Musical Instruments; U.S. Pat. No. 4,038,899, issued on Aug. 2, 1977 to Macmillan entitled Musical Instrument Tuning Apparatus; and U.S. Pat. No. 5,877,443, issued on Mar. 2, 1999 to Arends entitled Strobe Tuner. Each of these patents is hereby expressly incorporated by reference in their entirety.
For most instruments, the user tunes an instrument by turning pegs to change the tension of the string, adjusts the length of wind instruments, or by changing the tension of the drum head. Big instruments with multiple harmonic variables such as the piano or organ present a unique situation and have to be tuned by people who are specialists in tuning. During the course of music history there have been several systems of doing this. These different tuning systems are all about the exact scientific relationship between the notes of the scale. There has been an enormous amount of discussion among musicians about how best to tune instruments. Regardless of the system, there is a constant problem that forces compromises known since the time of Pythagoras.
To understand this problem, we begin with an understanding of basic tuning. In traditional western music, the diatonic scale is used C-D-E-F-G-A-B which then starts again at C for the next octave. Two notes are defined as “octave apart” when the higher note is vibrating at twice the speed of the lower note. For example: Middle C, known as C4, is 261.63 Hz versus 523.26 HZ for C5, the note one octave higher. Thirds, Fourths, Fifths, etc. . . . are also well defined. For example, a note at 1½ times the frequency of the basic note will be a perfect fifth higher. If one tunes a C, then tunes a G so that it is exactly 1½ times the frequency of the C, they can continue tuning in fifth up the octaves (a D, then an A etc.) until we should arrive back at C but octaves higher. However, for mathematical masons, the higher C is not in tune with the first C. This was discovered by Pythagoras and is called “the comma of Pythagoras”. The Pythagorean comma can also be thought of as the discrepancy between twelve justly tuned perfect fifths (ratio 3:2) and seven octaves (ratio 2:1) or 1.0136432647705078125. This interval has serious implications for the various tuning schemes of the chromatic scale, because in Western music, 12 perfect fifths and seven octaves are treated as the same interval.
Musical tuning systems throughout the centuries have tried to find ways of dealing with the Pythagorean comma problem. From the 16th century onwards several music theorists wrote long books about the best way to tune keyboard instruments. They often started by tuning up a fifth and down a fifth so that these notes were perfectly in tune (e.g. C, G and F), then they would continue (tuning the D to the G and B flat to the F) until they met in the middle around F sharp. Sometimes old organs today are tuned by such a method. Playing in keys with very few sharps or flats (such as C, G or F) sounds very beautiful, but playing in keys with lots of sharps or flats sounds horribly out of tune.
Here are some of the main ways of tuning the twelve-note chromatic scale which have been developed in order to get round the problem that an instrument cannot be tuned so that all intervals are “perfect”:
The ratios of the frequencies between all notes are based on whole numbers with relatively low prime factors, such as 3:2, 5:4, 7:4, or 64:45; or in which all pitches are based on the harmonic series, which are all whole number multiples of a single tone. Such a system can be used on instruments such as lutes, but not on keyboard instruments.
A type of just intonation in which the ratios of the frequencies between all notes are all based on powers of 2 and 3.
A system of tuning which averages out pairs of ratios used for the same interval (such as 9:8 and 10:9), thus making it possible to tune keyboard instruments.
Any one of a number of systems where the ratios between intervals are not equal to, but approximate to, ratios used in just intonation.
Standard equal temperament tuning (ET) of the range of frequencies for a diatonic scale piano uses the following frequencies:
One problem is specifically found in pianos because they have an inharmonicity in the strings. To cure this inharmonicity, piano tuners will “stretch” the tunings set around middle C (C4) on the piano. One type of stretch is known as a Railsback curve. An electric Fender Rhodes piano uses this type of tuning and this which may be seen in
On a different subject of mathematic ideas, we have the golden ratio and the Fibonacci sequence. In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities, (the ratio is a numeric value 1.618033988749 . . . ). Fibonacci numbers are found where each number is the sum of the two preceding ones in a sequence. These Fibonacci numbers form the Fibonacci sequence. Fibonacci started the sequence with 0 and 1, so that the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 . . . . When graphed, these form a Fibonacci spiral that is an approximation of the golden spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling. A golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio (That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
From these prior references it may be seen that these prior art patents are very limited in their teaching and utilization, and an improved musical instrument tuning is needed to overcome these limitations. Thus, the present application notes the limitations in these prior art tuning systems and presents a solution with a new unique tuning method and result.
The present invention is directed to an improved musical instrument tuning. In accordance with one exemplary embodiment of the present invention, the present invention teaches a fibratio tuning system for single and multiple instrument performances using the logarithmic spacing of equal temperament combined with both the golden ratio and the Fibonaccci sequence to change away from the linear logarithmic mapping of equal temperament to form a fibratio curve of sharps and flats in a fibratio spiral positioned at an inflection note to adjust above and below a chosen sharp and flat neutral intercept.
An octave system is utilized for compatibility with standard playing. Octave changes are adjusted using a Fibonacci sequence multiplied by the golden ratio. This combination of the golden ratio and the Fibonacci sequence is converted to get a decimal form to tune with sharps or flats from equal temperament to achieve the fibratio tuning curve with a neutral intercept A2. Finally, the entire fibratio tuning curve is shifted to adjust to a 440 Hz inflection point.
These and other objects and advantages of the present invention, along with features of novelty appurtenant thereto, will appear or become apparent by reviewing the following detailed description of the invention.
In the following drawings, which form a part of the specification and which are to be construed in conjunction therewith, and in which like reference numerals have been employed throughout wherever possible to indicate like parts in the various views:
As shown in
Piano Tuning with A2 110 Hz Inflection Point:
For the first example of
Step one: Begin with the Golden Ratio in numeric value:
Golden Ratio=GR=1.618033988749
Step two: Assign the Fibonacci sequence numbers to the octaves to get a Fibonacci octave number. We will begin with the lowest octave on a piano and assign it as the starting number of 1 in the Fibonacci sequence. Each octave above this will be assigned the next Fibonacci sequence number. Thus, the second octave is assigned a 2 and then the third octave is assigned a 3 and the fourth octave is assigned a 5, the fifth octave is assigned an 8 and so on. This is shown in Table 1:
Step three: Combine the Golden Ratio and the Assigned Fibonacci number and scale it to a decimal. The Golden Ratio GR is multiplied by the Fibonacci number AFN of the octave and then this is divided by 20 to scale it for a decimal form.
The results can be understood from the following table:
Now that we know a change per octave, we can calculate out a change per octave note. Because there are 12 notes per octave, we can simply divide by 12:
This can be understood by the following table:
With a change per octave note calculated, we can now use this to tune an instrument.
As a baseline for tuning, we can use equal temperament tuning to understand the new fibratio tuning. For nomenclature in this comparison, we will refer to equal temperament tuned notes as ET notes and fibratio tuned notes as FN notes. Thus, ETA2 is the Equal Temperament note with a standard A2, 110 Hz tuning. For this fibratio tuning example, we are using ETA4 as our inflection point and ETA2 as our neutral crossing point of flats and sharps. Thus, with ETA4 as our inflection point, we will add for notes with a higher frequency and subtract for notes with a lower frequency. Also, with the neutral crossing FNC set to the same frequency of 110 Hz its nomenclature will be FNA2 but it will have no cents adjustment from the equal temperament note. In this manner, both the inflection note and the neutral crossing note may be set. For every other note, we adjust the tuning up or down for each octave and each half step within a n octave as we move in a direction away from the inflection note FNA4. Each octave move will use the change per octave from the table above, similarly each change within a given octave will use the change per octave note from the table above. Thus, we use the following conversion formula:
In this example, with the neutral set at FNA2=ETA2, the note ETA2 #has an equal temperament frequency of 116.5410 Hz, ETA2 #is within the first octave adjacent to ETA2 such that no octave adjustment is needed, and ETA2 #is one half step up from ETA2 which places it in the change to the ETA3 octave with (From Table 3 above) a change per note of 0.0337. So we simply multiple the number of steps (1) against the octave CN 0.0337) and add that to the equal temperament frequency.
Thus, Fibratio A2 #(crossing A110)=116.5747 Hz. To continue with this example, we can go up two half steps from ETA2 to convert ETB2 to FNB2:
Thus, Fibratio B2(110)=123.5384 Hz. This continues through the twelve notes of the A3 octave until at A4 where we change into the next octave. This jump to the next octave requires an octave adjustment, resets the octave base for counting half steps, and resets the number of half notes to zero. Per the previous discussion, the CN conversion number for the next octave from ETA3 is now 0.4045. Thus, we can calculate using the formula:
Thus, Fibratio A3 (110)=220.4045 Hz.
Then for FNA3 #:
The following table outlines the conversions for a piano keyboard (ETA4 Inflection Note, and ETA2 crossing point). ETA2 was initially chosen because this is where the initial discrepancies in harmonics was heard as the most prominent:
By this system, we are based around the distance from 110 Hz such that the distance has primary control and not the octaves. Thus, fibratio tuning provides a completely different sound from the known equal temperament.
The A2 110 hz basis solved the harmonics problems with other instruments at that range, but an improved harmonic was discovered when the curve was shifted down and the neutral point was shifted to the inflection point at A4, 440 Hz.
The closest comparisons of this type of tuning in the known prior art is in a well tuned piano that tunes to perceived harmonics, and the Railsback curve style of stretch adjustment of an electric Fender Rhodes piano taught in the Prior Art. The following chart compares the different frequencies achieved in Hertz, and
As noted by
Next, we can look at the approximation of a Railsback curve in
Now that we understand how different the curvature of the Fibratio Tuning is from the prior art tunings, we can look to understand how to achieve this with individual instrument tunings.
Finally, we can note the comparison in
Additional instrument tunings for easy reference. First a guitar:
And variable tuning for DADGAD on guitar:
And also a CAPO 5 on the guitar:
From the foregoing, it will be seen that this invention well adapted to obtain all the ends and objects herein set forth, together with other advantages which are inherent to the structure. It will also be understood that certain features and subcombinations are of utility and may be employed without reference to other features and subcombinations. This is contemplated by and is within the scope of the claims. Many possible embodiments may be made of the invention without departing from the scope thereof. Therefore, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense.
When interpreting the claims of this application, method claims may be recognized by the explicit use of the word ‘method’ in the preamble of the claims and the use of the ‘ing’ tense of the active word. Method claims should not be interpreted to have particular steps in a particular order unless the claim element specifically refers to a previous element, a previous action, or the result of a previous action. Apparatus claims may be recognized by the use of the word ‘apparatus’ in the preamble of the claim and should not be interpreted to have ‘means plus function language’ unless the word ‘means’ is specifically used in the claim element. The words ‘defining,’ ‘having,’ or ‘including’ should be interpreted as open ended claim language that allows additional elements or structures. Finally, where the claims recite “a” or “a first” element of the equivalent thereof, such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements.
