JP6906296B2 - Fret design method and fret stringed instrument - Google Patents

Description

The present invention relates to a fret on a fingerboard provided on a neck for a fret stringed instrument, and more particularly to a design and manufacture of a fret for obtaining a strict equal temperament scale.

FIG. 1 is an overall perspective view of an electric guitar shown as an example of a fret stringed instrument. Such an instrument is roughly composed of one body, two necks, and three heads. The basic idea and role of the neck 2 and the head 3 are the same for the classical guitar and the folk guitar, which are acoustic guitars.

The neck 2 fingerboard 9 is installed, metal frets 10 for constituting the pitch of each semitone (10 ₁ to 10 ₂₁₎ is installed present 19-22 by string-pressing. These generally have a linear shape parallel to the nut 6. The head 3 is mounted pegs (pincushion) 4 (4 ₁ to 4 _6), by changing the tension by winding the string 5 (5 ₁ to 5 ₆₎ perform articulation.

Classical guitars and folk guitars have a body 101 as shown in FIG. 2, an empty body 115 intended to resonate, and a sound hole 117 on the surface resonance plate 116, and have a mechanism for independently resonating live sound. Generally called an acoustic guitar. Further, there is a bridge 107 on the resonance plate 115, and a saddle 108 is installed on the bridge 107. Some electric guitars have an empty body 1 called a semi-acoustic guitar, but most of them are made of hard wood and are called solid guitars.

When a guitar string 5 (5 ₁ to 5 ₆₎ is stretched between the nut 6 and the saddle 8 placed to the bridge 7 (107) on the body 1 to be installed (108) as open string length at the top of the neck 2 ..

The guitar, open strings for twelve equal temperament scale from the first string 5 ₁ 6 string 5 ₆ (hereinafter, temperament scale abbreviated) of E4 (329.627557Hz), B3 (233.08188Hz ), G3 (195 .997718Hz), D3 (116.54094Hz), A2 (110.0Hz), E2 (82.40689Hz).

It is the vibration frequency of each string that determines the scale. This is related to the tension determined by the mass and length of the string and the amount of winding of the string by the peg, and is given as shown in Equation 1 in the ideal state where the rigidity and friction of the string are ignored. Here, n indicates the fret number, 10 _{n of} n = 0 is the nut 6, and f ₀ is the vibration frequency of the open string.

ここで、f_n：nフレット１０_nの振動周波数［Hz］
l_n：nフレット１０_nとサドル８間の弦長［ｍ］
T ：弦の張力［Ｎ］
σ：弦の線密度［Ｋｇ／ｍ］
である。即ち、弦の振動周波数は、重くて長いものほど低音となり、弦を巻き取ることにより張力を強くするほど、また弦長を短くするほど高音になる。

Here, the vibration frequency [Hz] of _{f n} : n fret 10 _n
l _n : n _{String length between fret 10 n} and saddle 8 [m]
T: String tension [N]
σ: Linear density of strings [Kg / m]
Is. That is, the heavier and longer the vibration frequency of the string, the lower the sound, the stronger the tension by winding the string, and the shorter the string length, the higher the sound.

The longest vibration length of each string is the open string length l ₀ between the nut 6 and the saddle 8, and the vibration frequency f _{0 at} this time is set as the lowest note as described above. _{A metal fret 10 n} is installed on the fingerboard so that the length l _n is narrowed and the vibration frequency f _{n for each semitone is obtained.}

As for the scale, the equal temperament scale is used like many other musical instruments. The equal temperament scale is based on the central A (la) note, which has a frequency of 440 Hz, and is an equal temperament divided into 12 octaves, which have a double frequency relationship. It is composed of each semitone frequency, which is 1 / 1th power and 2 minus 1/12 times on the bass side. Therefore, the vibration frequency f _{n of the fret 10 n} of the fret stringed instrument is defined as in Equation 2 with the vibration frequency determined by the open string lengths of the nut 6 and the saddle 8 as f _0. Therefore, when the open string length is l ₀ , the string length l _n of the n fret 10 _n and the saddle 8 is obtained as in equation 3, and the width between the _{n fret 10 n} and the n + 1 fret 10 _{n + 1 is a number.} Given as 4.

That is, in the nth fret 10 _n , n = 0 means the nut 6, but in the equation 3, the _{string length l n between the nth fret 10 n} and the saddle 8 is the string length of the n-1 fret 10 _n-1 . It means that it is obtained by multiplying l _{n-1 by 2 minus 1/12 (0.94387).} This is because, as shown in FIG. 3, the width between the nut 6 and the first fret l ₀ -l ₁ is taken as the height, and the height is taken as the radius in consideration of the right triangle with the open chord length l _{0 as the base. When a perpendicular line is drawn diagonally from the first fret chord length l 1} which is the intersection of the circle and the base, the right triangle newly created by the intersection is similar to the original triangle, and the circle and the base with this height as the radius width l ₁ -l ₂ intersections than the first fret 10 ₁ and between the second fret 10 ₂ of the sought. By repeating this operation, all fret positions are obtained, and the _{string length of the 12th fret 10 12} becomes half of the open string length. This fret design method is called the 18 rule because each fret width l _n -l _{n + 1} shown in Equation 4 is obtained by dividing each fret length l _{n by 17.8175, which is close to 18.} .. Generally, the fret position of a fret instrument is determined in this way.

By the way, although nylon strings are often used in classical guitars, steel strings are inevitably used in folk guitars and electric guitars, especially electric guitars because of their sounding principle. All strings, including nylon strings, are not completely flexible and have considerable rigidity, and due to this effect, the fundamental vibration frequency f is given as the number 5 when the string length is l (non-patented). Document 1).

ここで、Bは曲げ剛性による影響を表し、数６のように示される。

ここで、π：円周率
E ：ヤング率［Ｎ／ｍ²］
d ：弦径［ｍ］
である。

Here, B represents the effect of flexural rigidity and is shown as in Equation 6.

Where π: pi
E: Young's modulus [N / m ² ]
d: String diameter [m]
Is.

Therefore, even if the tension T is adjusted for the open string and the correct vibration frequency is given, the effect of rigidity differs depending on the string length as shown in Equation 5, so the vibration frequency obtained from Equation 1 is assumed. In the fret 10 designed according to the 18 rules, all vibration frequencies are higher than the frequency of the average rhythm scale.

In the music field, cents are used to express frequency deviations in detail. One octave has twice the frequency ratio, and a semitone is a geometric progression of one octave divided into twelve. The cent value of f with respect to the frequency f _{0 is defined as 1200 x log 2} (f / f ₀ ), but considering the frequency ratio of the previous semitone and one octave, the semitone is 100 cents and one octave is 1200 cents. Become.

In Fig. 4, for the string called the extra light gauge, which belongs to the thinnest string in the electric guitar, the effect of the rigidity represented by the equation 5 for the fret 10 designed by the 18 rule is defined as l → l _n for each fret. The deviation of the vibration frequency with respect to the number 1 is calculated by the cent value. It is confirmed that the thicker the string and the higher the fret, the larger the deviation of the vibration frequency with respect to the equal temperament scale. While indicating chord of specifications in Table 1, in the case of steel strings, third string 5 ₃ 6 string 5 ₆ or the fourth string 5 _4, is narrow with nickel and stainless steel core wire in order to increase the linear density A wound string with tightly wound wires is used. In the string 5 was used here, the fourth string 5 _4-6 string 5 ₆ has become a Makitsuru, since the influence of the stiffness considering the core, who from the third string ₃ of the fourth string 5 ₄ Indicates a small value. Since the target is a thin string, it cannot be said that it has a great influence, but it can be confirmed that it is a factor that causes a deviation from the equal temperament scale at all frets 10 except for the open string. ..

Next, the phenomenon generated by pressing the strings between the frets 10 will be considered. FIG. 5 is a model diagram showing the concept of string length by erection of strings 5 of a guitar or an electric guitar and pressing strings at frets 10. Tension is generated by winding the string 5 by a peg 4 located at the left support end of the open string. _{At this time, in the string 5, the portion l e} = l ₁ + l ₂ other than the open string length l between the nut 6 and the saddle 8 is also stretched, the string diameter is reduced, and the cross-sectional area and line of the string are reduced accordingly. The density is also slightly lower. The fingerboard 9 is installed with a slight inclination so that the string 5 of the vibrating part does not come into contact with the fret 10 due to the string pressing, and the string length l _n that determines the vibration frequency when the fret is pressed is horizontal. Although it is a slight difference, it is clearly different from the value determined by Equation 1 in the state.

In FIG. 6, after adjusting the tension with the peg 4 on the open string, when the string is pressed at each fret position determined by the 18 rule, the deviation of the vibration frequency obtained from Equation 5 from the equal temperament scale is obtained by the cent value. It is confirmed that the larger the string diameter, the larger the high frequency fret. The string height is set as shown in FIG. 7 with reference to the actually measured value of a commercially available electric guitar.

The problems caused by these 18 rules are known in the musical instrument industry, and in acoustic guitars, the saddle 108 is installed diagonally as shown in Fig. 2, so that the bass string with a larger string diameter has a longer string length. Is devised. Further, in the electric guitar, the position of the saddle 8 can be adjusted for each string 5 as shown in the enlarged view of the bridge in FIG. The positions of these saddles 8 _{are determined on the basis that the scale at the 12th fret 10 12} is one octave higher than the vibration frequency of the open string. That is, as shown in Equation 5 and FIG. 6, the vibration frequency that increases as the length of the string 5 is shorter and the string diameter is larger because the influence of rigidity is stronger is set to the string length when _{the 12th fret 10 12 is pressed.} Is corrected by stretching.

The above correction is called octave adjustment, which is the adjustment _{of the vibration frequency at the 12th fret 10 12} due to the movement of the saddle 8 and the adjustment of the tension by the peg 4 to correct the change in the vibration frequency of the open string that occurs as a result. Need to be repeated. Fig. 9 measures the vibration frequency of the electric guitar designed according to the 18 rules when the _{first , third} , and fifth strings 5 1, 5, 3, and ₅ are adjusted once, and deviates from the equal temperament scale. This is an example of finding. The 12th fret 10 ₁₂ is still not completely 0 cents and there is a sweetness of adjustment, but when compared with FIG. 6, there is almost no improvement in _{the low frequency range, especially in the 1st} to 7th frets 10 1 to 10 _7. The deviation is larger than expected, and the frequency becomes lower at the high frets. It is confirmed that even if the open strings and the 12th fret 10 ₁₂ are tuned to the desired equal temperament scale, the other frets 10 show a musical deviation that cannot be overlooked.

As a result, with the frets 10 designed according to the 18 rules, _{the vibration frequencies at the low frets and the high frets above the 20th fret 10 20} are considerably different from the equal temperament scale, even when the octave is adjusted. It remains. In connection with this fact, U.S. Pat. No. 5,404,783 (Patent Document 1) proposes a bridge that can adjust the saddle position for each string in an acoustic guitar, and has 18 rules. advocates can be improved by 3.3% the width of the first fret 10 ₁ and the nut 6 narrowed designed. Further, in US Pat. No. 5,814,745 (Patent Document 2), 3.3% is used for nylon strings of acoustic guitars, and 2.1% is used for electric guitars and light gauge strings whose third strings are not wound strings. , 1.4% correction is suitable for acoustic steel strings, bass guitars, and heavy gauge strings. However, since the fret 10 has a linear shape, it is unlikely that each string having different characteristics is uniformly corrected by the translation of the fret 10.

Subjecting the U.S. Patent 6,156,962 Pat (Patent Document 3) and U.S. Patent 6,433,264 Pat (Patent Document 4), a correction to narrow the nut 6 a first fret 10 ₁ to each string We are proposing a nut for this. Further, Japanese Patent Application Laid-Open No. 2005-275340 (Patent Document 5) proposes an auxiliary tool for correcting each string in consideration of rigidity and elongation of the string 5 due to string pressing. These matters also have correction for first fret 10 ₁ are mainly whole string 5, not to be improved for all fret 10.

As described above, the string used in the guitar is made thicker toward the first string 5 ₁ to the sixth string 5 _6, in the third string ₃ or the fourth string 5 _4, 6 string 5 ₆ Although wound strings are used, they are not designed in consideration of the characteristics shown in Equations 5 and 6. Therefore, even if the saddle 8 is adjusted for each string and the octave is adjusted so that _{the vibration frequencies of the open string and the 12th fret 10 12} can be matched to the equal temperament scale, the string 5 is as shown in FIG. The deviation of the vibration frequency differs depending on the characteristics of the above, and it is impossible to realize accurate tuning by the fret 10 having a uniform linear shape. Therefore, it seems certain that the claims of Patent Documents 1 to 5 mainly correct the pitch deviation of the lower frets of the bass strings, but all the proposals are based on the frets 10 designed based on the 18 rules. It is clear that there is still an error in the fine pitch of each string 5 and each fret 10.

Based on the above considerations, the fret 10 of a fret stringed instrument must have a curved shape, but in Japanese Patent Application Laid-Open No. 2009-532737 (Patent Document 6), the positions of each string and each fret are individually determined and they are used. We are developing a stepped curved fret that connects the two. Correct tuning is expected because it is considered to be in vertical contact with the strings directly under the strings, but this is not theoretically required, and for choking and vibrato performances where the pressed string position deviates significantly from directly below the open strings. It will be a big detriment.

_{In addition to the effects of rigidity and string pressing, there is also the effect of negative stiffness S n} [N / m], which is a coefficient of the dynamic component of the magnetic attraction of the pickup 11 in electric guitars. Assuming that the chord length is l [m], the tension is T [N], the linear density is σ [Kg / m], and c = (T / σ) ^1/2 [m / sec], the position a [m] from the saddle 8. ], The vibration frequency f [Hz] when the negative stiffness S _n acts satisfies the equation 7 with the angular vibration frequency ω = 2πf [rad / sec] (Non-Patent Document 2).

この解は、正弦関数が周期関数であることから、無限の周波数モードが存在する結果となる。剛性の無い柔軟な理想的な弦５では高次の振動周波数は倍音関係にあるが、剛性が存在することにより高次の成分は非調和性を生じる。このような高次成分は部分音と呼ばれ、楽音としての大きな特質となる。数７で示した負スチフネスの影響も、同様に非調和性を発生させ、楽音としての特徴を形成するが、調音の対象である基本振動周波数は、ピックアップ１１の位置や弦５の特質に応じて低下する。

This solution results in the existence of infinite frequency modes because the sine function is a periodic function. In an ideal string 5 that is flexible and has no rigidity, the higher-order vibration frequencies have a harmonic relationship, but the presence of rigidity causes anharmonicity in the higher-order components. Such higher-order components are called partial sounds, and are a major characteristic of musical sounds. The effect of negative stiffness shown in Equation 7 also causes anharmonicity and forms a characteristic as a musical tone, but the basic vibration frequency to be tuned depends on the position of the pickup 11 and the characteristics of the string 5. Decreases.

FIG. 10 shows the fundamental vibration frequencies of the fret 10 when the negative stiffness 2 [N / m] acts on the position a, which is a quarter of the chord length, from the saddle 8 for the chord 5 shown in Table 1. It seeks change. The longer the vibrating string length and the closer the point of action of negative stiffness to the center of the vibrating string length, the greater the decrease in the vibration frequency, and it is related to the chord diameter and tension, but here the effect on the second string is the greatest. Confirmed to be strong. It has been investigated that when a plurality of negative stiffnesses are present, when the deviation of the vibration frequency is considered by the cent value, it is obtained as a value obtained by approximately adding the cent values of each deviation (Non-Patent Document 3). Therefore, when a plurality of pick-up 11 (11 ₁ to 11 ₃₎ are present, reduction of the vibration frequency is too large to be overlooked.

As described above, in the current fret 10 design, a frequency error in each fret 10 is inevitably generated. Therefore, in order to obtain a strict musical tone based on the equal temperament scale, rigidity, string pressing, and multiple negative stiffnesses are required. A design that considers the effects theoretically and comprehensively is required.

U.S. Pat. No. 5,404,783 U.S. Pat. No. 5,814,745 U.S. Pat. No. 6,156,962 U.S. Pat. No. 6,433,264 JP-A-2005-275340 Special Table 2009-532737 Gazette

H. Fletcher, Journal of the Acoustical Society of Japan, Vol. 36, No. 1, p. 203-209 Masahiro Hara, et al., Journal of Acoustical Society of Japan, Vol. 36, No. 12, p. 615-623 Masahiro Hara, Journal of the Acoustical Society of Japan, Vol. 44, No. 3, p. 187-193

String specifications such as string diameter and wire density regarding the effects of string rigidity and string pressing, which are the causes of deviations from the average rhythm scale in current fret string instruments, and the effects of negative stiffness of electromagnetic pickups on electric guitars. A numerical value that determines the fret position to be tuned to the twelve average rhythm scale by formulating the string length between the saddle and the fret as a variable, taking into account that changes will also occur. Design and manufacture all fret positions and shapes on the fingerboard of fret instruments by creating a calculation program and performing numerical calculations.

The flow of problem solving is shown in FIG. First, in addition to the open string length erected between the nut 6 and the saddle 8, the string length between the pegs 4 of the head 3 and the saddle 8 of the nut 6 and the bridge 7 and the fixed part of the string shown in FIG. 5 is also added. The tuning with all string lengths is theoretically considered. That is, the peg 4 winds the string with respect to the total string length, and tension is generated in the string 5 according to its elastic modulus. At this time, the diameter of the string 5, therefore the cross-sectional area and the linear density, change, albeit minutely, but taking these into consideration, the vibration frequency of the string 5 affected by the tension and rigidity given by the winding of the string By making the tension to be satisfied equal, an equation with the take-up length as a variable is constructed and the take-up length is calculated. Next, when the specifications are renewed and the strings are pressed on each fret 10, the vibration frequency of the target fret is equal temperament scale, taking into account that the strings are stretched and the specifications are further changed. Under the condition that is equal to, an equation is constructed from the saddle 8 with the length between each fret as a variable. The equation is solved by creating a numerical calculation program. Furthermore, in an instrument such as an electric guitar that has an electromagnetic pickup, its negative stiffness reduces the vibration frequency of the strings according to the point of action, so the tension should be increased in advance to increase the decrease in the vibration frequency. The position of each fret is calculated by resolving the equation with the length between the frets from the saddle 8 of each string as a variable by numerical calculation in consideration of the changes in the specifications that occur at the same time.

That is, for the open string length l ₀ [m] of the nut 6 and saddle 8, the total external string length is l _e [m], the string diameter is d [m], and the cross-sectional area of the string is S [m ² ]. Then, the generation of tension T [N] due to the winding length dl [m] is given by the following relationship.

また、振動周波数を与える数５、６より、開放弦において張力は次の数９を満たさねばならない。

Further, from the numbers 5 and 6 that give the vibration frequency, the tension of the open string must satisfy the following number 9.

The initial chord diameter is d ₀ [m], the initial cross-sectional area is S ₀ [m ² ], and the linear density is _{divided into the core wire σ 0} [Kg / m] and the _{wound chord σ e} [Kg / m]. When, the extension of the string at the open string length (winding length) dl [M] is calculated by solving the following equation 10 obtained by placing the equations 8 and 9 in consideration of the changes in the chord diameter, the cross-sectional area, and the linear density.

但し、l_t ＝l₀ ＋l_eとした。

However, l _t = l ₀ + l _e .

In designing each string 5 and each fret 10, after the vibration frequency of the open string and the string height h _n [m] from the fret 10 are set, the tension between the saddle 8 and the fret 10 is taken into consideration in consideration of the increase in tension due to the string pressing. Determine the vibrating string length l _n [m]. _{The length l d} [m] between the n fret 10 _n and the nut 6 is given as in _{equation 11, and l n} is calculated numerically as a value satisfying equation 12.

ここでl_a［ｍ］は、先に求めた弦の巻き取り長をdlとして、次式で与えられる押弦時の全弦長を示す。

Here l _a [m] is the winding length of the string previously obtained as dl, indicating the total chord length at the depressed given by the following equation.

まず、開放弦において数７、あるいは数１４より負スチフネスによる周波数の低下を求め、平均律音階の周波数に合わせるための張力、これに基づき変化する諸元も新たに設定する。次に、先に求められたフレット位置について、作用点aに応じて各弦５、フレット１０毎に負スチフネスの影響により低下する周波数を算出する。そして、複数の負スチフネスによる変化分を求め、それを補償するように振動周波数を予め高めに設定し、押弦の影響を考慮して改めて数１２を解法することによりフレット位置を算出する。このとき、厳密に言及すれば、負スチフネスの影響を考慮する前後でフレット位置は若干異なるが、その差は各フレット１０での振動長lに対しては極めて微小であり、数７、１４及び図１０等を考慮する時、負スチフネスの影響による周波数の変化Δfは、殆ど同一であると考えることができる。 For guitars with electromagnetic pickups, the effect of their negative stiffness is compensated. Incidentally, the influence of the negative stiffness indicated by the number 7, the pickup 11 is normally used, considered _{^{2πσc 2 >> s n (l-}} a), the decrease amount Δf of the oscillation frequency of the fundamental first-order mode, the following It can be approximated by an equation.

First, the frequency drop due to negative stiffness is obtained from the number 7 or number 14 in the open string, and the tension for adjusting to the frequency of the equal temperament scale and the specifications that change based on this are newly set. Next, with respect to the previously obtained fret position, the frequency that decreases due to the influence of negative stiffness is calculated for each string 5 and fret 10 according to the point of action a. Then, the fret position is calculated by obtaining the change due to a plurality of negative stiffness, setting the vibration frequency higher in advance to compensate for it, and solving the equation 12 again in consideration of the influence of the string pressing. At this time, strictly speaking, the fret positions are slightly different before and after considering the influence of negative stiffness, but the difference is extremely small with respect to the vibration length l at each fret 10, and the numbers 7, 14 and When considering FIG. 10 and the like, it can be considered that the frequency changes Δf due to the influence of negative stiffness are almost the same.

FIG. 12 shows one of the examples of the present invention. The required fret position l _n of each string 5 gives the chord length from the saddle 208 to the last, but in this example, the nut 206 and the saddle 208 are intentionally set in a linear shape, and the arbitrary fret 210 line connecting the fret position l ₁ to l ₆ 6-string from the first string is not always smooth curve. In that case, in consideration of the convenience of playing, the frets 210 of each string are approximated to a smooth curve as shown in FIG. As a result, a string that does not follow the curve will cause a slight error, but this problem can be improved by setting an arbitrary fret 210 to a linear shape.

FIG. 13 shows a design example of each fret 310 including the nut 306 and the saddle 308 when the seventh fret 310 _{7 is set to a linear shape as the second embodiment.} The fret near the 7th fret 310 ₇ is almost straight, but the nut position and saddle 308 position of each string are not on a straight line, and the lower and higher frets such as _{the 1st fret 310 1 have a larger curvature.} It has a curved shape. In order to confirm subtle changes in the nuts 306, saddle 308, and frets 310, an enlarged view centering on the fingerboard is shown in FIG. The nut 306 is a vibrating end that supports a string erected with a recess, and has a stepped shape due to mechanical necessity.

The frets 310 of each string on the fingerboard designed by the present invention can all form a pitch that is infinitely equal to the equal temperament scale. The fret 310 has a curved shape with a small curvature, but an arbitrary n fret 310 _n can be set to a linear shape. In that case, the number of frets in the vicinity also becomes a shape close to a linear shape, and no inconvenience in performance occurs. Above all, it is possible to completely eliminate the frequency deviation that can be perceived by the low frequency fret and the high frequency fret. In addition, since it is possible to perform perfect tuning that matches the equal temperament scale, the high frequency such as the tuning curve (S curve) desired for a piano is set higher, and the low frequency is set lower, based on this. It is possible to easily design a fret 310 or the like with an arrangement such as setting.

FIG. 15 shows a prototype neck 302 created and the measured vibration frequency of each fret 310 for the third string compared to that of a commercial guitar. Since the prototype is handmade, there is still a problem in manufacturing accuracy, but the frequency deviation is greatly improved over all frets 310, and the effect of the present invention can be confirmed.

FIG. 1 is a perspective view of a general electric guitar on the market, showing an outline of the structure and components of each part. FIG. 2 is an example showing 101 parts of the body of an acoustic guitar. It shows the difference from the sound board 116 and the sound hole 115, especially the solid guitar of the saddle 108 in consideration of the influence of rigidity and the correction of the deviation of the vibration frequency due to the string pressing. FIG. 3 shows the concept of graphically designing the fret position called the 18 rule. FIG. 4 is a diagram showing in cents that in the case of the fret 10 designed based on the 18 rule, the vibration frequency shifts higher with respect to the equal temperament scale as the fret becomes higher in frequency due to the influence of rigidity. FIG. 5 is a model diagram for analysis of a fret stringed instrument showing the total string length and the arrangement relationship of the fingerboard 9. The fingerboard 9 carved with the frets 10 placed under the open string length between the nut 6 and the saddle 8 is slanted with respect to the strings 5 so that the strings 5 and the frets 10 do not come into contact with each other. In an electric guitar, a plurality of electromagnetic pickups 11 are placed on the side close to the saddle 8. When considering the extension due to the winding of the string 5, it is necessary to consider the extra lengths on the bridge 7 side and the nut 6 side in addition to the open string length between the nut 6 and the saddle 8. FIG. 6 shows the deviation of the vibration frequency with respect to the equal temperament scale when the fret 10 arranged according to the 18 rule is pressed on each string 5 and the fret 10 as a cent value. It is understood that if the octave adjustment at the 12th fret 10 ₁₂ is not performed, the frequency shift at the high fret becomes more remarkable in the bass string. If the chord length is calculated with the initial value, but the octave is adjusted, the frequency shift is improved by extending the chord length of the vibrating part with the saddle 8 and setting it to 0 cents at _{the 12th fret 10 12.} However, as shown in FIG. 9 below, it is not completely improved except for the _{open string sound and the 12th fret 10 12 sound.} FIG. 7 is a string height obtained by measuring the string height of a commercially available electric guitar and giving it as a regression curve. FIG. 8 is an example of a saddle 8 used in an electric guitar or the like. In the octave adjustment of each string 5, the string length is adjusted in order to correct the influence of rigidity and the deviation of the vibration frequency due to the pressing of the string. 9, as a target commercial guitar, in which the deviation of the oscillation frequency from the equal temperament scale when performing the octave adjustment for the second string 5 ₂ and 5-string 5 ₅ shown in cent value. FIG. 10 shows the change in the fundamental frequency that occurs in each string when the negative stiffness of the value of 2 [N / m] acts from the saddle 8 to the position of a quarter of the string length in cents. be. In the high frequency fret, the chord length between the fret 10 and the saddle 8 is shortened, and the action position of the negative stiffness is close to the support point, which indicates that the influence is reduced. FIG. 11 shows a flowchart of a process and a program for solving the problems of the present invention. FIG. 12 is one of the embodiments of the present invention, and shows each fret shape when the nut 206 and the saddle 208 are set to a linear shape. FIG. 13 is one of the embodiments of the present invention, _{and shows each fret shape when the seventh fret 310 7} is set to a linear shape. _{FIG. 14 is an enlarged view of the 7th fret 310 7} , the _{15th to 21st} frets 310 15 to 310 21, and the saddle 308 portion of FIG. 13, which is one of the embodiments of the present invention. Figure 15 is a prototype in order to confirm the effect of the present invention is obtained by measuring the frequency deviation of the frets 310 according to the invention the frets 10 designed by the third string ₃ for 18 rules. Since it is handmade, it seems that there is still a problem with the manufacturing accuracy, but it can be confirmed that the frequency deviation has been greatly improved over all frets 310.

FIG. 12 is an example showing each fret shape when the open string length of each string is set to be equal to l ₀ = 0.6477 m and the nut 206 and the saddle 208 are linearly shaped. Each fret 210 has a curved shape, and the curvature of the low-frequency strings of the _{5th , 6th} , 5th, and 5th strings is particularly large. Table 2 shows each fret width of each string 5 obtained in this example. Nut 206 and the first fret 210 _first width, in the 18 rules are 36.353Mm, in the present invention 35.64mm in the first string 5 ₁ a the sixth string 5 ₆ 33.895Mm sixth string 5 _The result of 6 is 1.745 mm narrower. Thus corrected by characteristics of the strings are different, the correction ratio 18 rules, sixth string 5 ₆ first fret 210 largest and _1, 6.761% of the next fifth string 5 ₅ first fret 210 _1, second fret 210 ₂ of the sixth string 5 _6, has a fourth string 5 ₄ of the first fret 210 ₁ forward, 4.967%, 4.372%, 3.589%, 3.28 It is%. Also, until the second fret 210 ₂ for all the strings, a third fret in 210 ₃ third string ₃ from 6-string 5 _6, fourth fret 210, ₄ only the sixth string 5 ₆ correction ratio of 1% or more ing. On the 5th fret 210 _{5 and} above, on the contrary, there are places where the fret width is widened, and some frets 210 show a correction value of a little over 1%, but in other cases, the fret width increases or decreases by 1% or less. ing.

In the first embodiment in which the nut 206 and the saddle 208 have a linear shape, it can be clearly seen that all the frets 210 have a curved shape, but even if the tuning is perfect, it is not always preferable in terms of performance. Therefore, as the second embodiment in FIG. 13, each fret 310 including the nut 306 and the saddle 308 is set with _{the seventh fret 310 7} as a linear shape without changing the width between the nut and each fret obtained in the first embodiment. It has been redone. Therefore, the width between the frets is the same as that of the first embodiment. In this example, the 7th fret 310 ₇ has a linear shape, but any fret 310 can have a linear shape. In addition, since the process is based on theoretical analysis, various selections such as changing the type of string 5 and the open string length for each string are possible, and design restrictions and performance benefits can be judged as appropriate. At the same time, the design contents can be solidified. The nuts 306, the _{first to seventh} frets 310 1 to 310 7, the high frequency frets, and the saddle 308 are enlarged and shown in FIG. The length between the nut 306 and the 7th fret 310 ₇ is shorter for the lower strings, and conversely the _{length between the 7th fret 310 7} and the saddle 308 is longer. The fret near the 7th fret 310 ₇ is almost linear, but the _{curvature of the 1st fret 310 1} is large, and it is confirmed that the high fret has an arc shape with a small curvature.

According to the embodiment of the present invention, since the vibration frequencies of all the strings 5 and the frets 310 are adjusted to match those of the equal temperament scale at the design stage, octave adjustment or the like is not necessary. However, since the specifications at the initial stage of design are the basis, the fingerboard 309 is specified with respect to the string 5 to be used. If you want strict tuning for different strings, you need to use a differently designed fingerboard. The basis of the present invention is to determine the set frequency of each string and then provide the optimum fret position and shape based on theoretical analysis. For example, the tuning curve (S curve) of a piano is arranged. It is also possible to design the fret 310.

The global market size of the musical instrument industry is said to be over 1 trillion yen. Yamaha, a comprehensive manufacturer of musical instruments, has the largest share of about 20%, followed by Gibson, Harman, Roland, Sennheiser, Fender, Kawai, Shure, and Stinway with about 2%. Looking at guitars and electric guitars, the market size is 300 billion yen, and Yamaha's market share is less than 10%. This is largely due to the fact that Fender's Stratocaster and Telecaster and Gibson's Les Paul are alive as mythically standard models. Of course, there are new attempts by emerging manufacturers for guitars and tones, but the old standard design method is firmly supported.

However, even if the genre of music has a strong fashion element, there is no reason why the absolute element of music, such as tone, can be disregarded, and many guitarists feel imperfections regarding the tone of the current guitar. It is certain that it is. The value of utilizing the present invention is great in improving the accuracy of musical instruments and improving the completeness of musical music. The problem is how to make the performer understand and experience the fact theoretically and how to combine the traditional sensibility and fashionability.

1 body 2 neck 3 head 4 pegs (pincushion)
4 ₁ 1 string peg ・
・
4 ₆ 6 string peg 5 string 5 ₁ 1st string ・
・
5 ₆ 6th string 6 nut 7 bridge 8 saddle 9 fingerboard
10 frets 10 ₁ 1st fret ・
・
10 ₂₁ 21st fret 11 Electromagnetic pickup 11 ₁ Electromagnetic pickup 1
11 ₂ Electromagnetic pickup 2
11 ₃ Electromagnetic pickup 3
12 Pick Guard 13 Octave Screw 101 Acoustic Guitar Body 102 Acoustic Guitar Neck 105 Acoustic Guitar String 105 ₁ Acoustic Guitar 1st String
・
105 ₆ Acoustic Guitar 6th String 107 Acoustic Guitar Bridge 108 Acoustic Guitar Saddle 109 Acoustic Guitar Fingerboard 110 Acoustic Guitar Fret 110 ₁₂ Acoustic Guitar 12th Fret
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110 ₂₀ Acoustic Guitar 20th Fret 112 Acoustic Guitar Pickguard 114 Strings Pin 115 Empty Body 116 Surface Plate (Soundboard)
117 Sound hole 202 Example 1 of the present invention ・ Neck 206 Example 1 of the present invention 1 ・ Nut 208 Example 1 of the present invention 1 ・ Saddle 209 Example 1 of the present invention 1 ・ Fingerboard 210 Example of the present invention 1 ・ Fret 210 ₁ Example of the present invention 1. 1st fret ・
・
210 ₂₁ Example 1 of the present invention ・ 21st fret 302 Example 2 of the present invention 2 ・ Neck 306 Example 2 of the present invention 2 ・ Nut 308 Example 2 of the present invention 2 ・ Saddle 309 Example 2 of the present invention 2 ・ Fingerboard 310 Example 2 of the present invention -Fret 310 ₁ Example 2 of the present invention-First fret-
・
310 ₂₁ Example 2 of the present invention, 21st fret

Claims (4)

In a fret stringed instrument such as a guitar composed of a body part, a neck part and a head part, the lowest pitch is set as the open vibration string length between the nut located at the uppermost part of the neck part and the saddle installed on the bridge on the body part. It is a fret that is installed so as to emit a pitch every half note by pressing a plurality of strings erected so as to emit a string on a fingerboard on the surface of the neck portion.
The total string length between the peg and the bridge was affected by the rigidity of the open vibrating string length due to the tension that takes into account the extension of the string length that accompanies the change in string diameter and linear density caused by the winding of the string. Under the condition that the vibration frequency is equal to that of the average rhythm scale, the winding length of the string is calculated by constructing an equation with the winding length of the string as a variable.
In addition to the obtained winding length of the string, the extension of the string length due to the change in string diameter and linear density caused by pressing the string at the target fret is also taken into consideration, and it is affected by the rigidity of the vibrating string length between the fret and the saddle. Under the condition that the vibrating frequency is equal to that of the average rhythmic scale, an equation with the vibrating string length as a variable is constructed, and the vibrating string length is calculated numerically.
For stringed instruments with electromagnetic pickups, the decrease in vibration frequency caused by negative stiffness shall be compensated in advance by increasing tension , and vibration shall be taken into consideration for changes in string diameter and linear density due to the accompanying extension of string length. The vibrating string length is recalculated by resolving the above equation with the string length as a variable.
Based on the vibrating string length calculated for all strings, any of the nuts, saddles, or arbitrary frets is made into a linear shape, and the frets other than the arbitrary frets are smoothly curved and installed, and all the frets are installed. Frets with the characteristic that the scale does not deviate from the equal temperament scale,
The neck of the stringed instrument that installed. A fret stringed instrument having the fret and neck according to claim 1. A fret stringed instrument having a fret and a neck designed to follow a specific tuning curve including an equal temperament scale in the fret and neck design stage according to claim 1. In fret stringed instrument such as a guitar consisting of a body portion and a neck portion and a head portion, and the nut of the neck portion, a fret and design method of the position and shape of the saddle of the body portion of the fingerboard,
The total string length between the peg and the bridge was affected by the rigidity of the open vibrating string length due to the tension that takes into account the extension of the string length that accompanies the change in string diameter and linear density caused by the winding of the string. Under the condition that the vibration frequency is equal to that of the desired tone scale, the winding length of the string is calculated by constructing an equation with the winding length of the string as a variable, and the winding length of the string is calculated.
In addition to the obtained winding length of the string, the extension of the string length due to the change in string diameter and linear density caused by pressing the string at the target fret is also taken into consideration, and it is affected by the rigidity of the vibrating string length between the fret and the saddle. Under the condition that the vibrating frequency is equal to that of the desired tone, construct an equation with the vibrating string length as a variable, and calculate the vibrating string length by numerical calculation.
For stringed instruments with electromagnetic pickups, the decrease in vibration frequency caused by negative stiffness shall be compensated in advance by increasing tension, and vibration shall be taken into consideration for changes in string diameter and linear density due to the accompanying extension of string length. Recalculating the vibrating string length by resolving the above equation with the string length as a variable,
Design method for the position and shape of nuts, frets and saddles, including.

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