Converting means and the stringed musical instrument that this converting means is installed
Technical field
The stringed musical instrument that the present invention relates to a kind of converting means and this converting means is installed relates to a kind of converting means of the tonequality that can improve the reproduction sound that obtains by the output from converting means and the stringed musical instrument that this converting means is installed in more detail.
Background technology
Stringed musical instrument as known all the time has acoustic guitars, promptly possesses the body of hollow shape and the plucked string instrument of many strings.The sound of directly hearing as playing this acoustic guitars enumerates that vibration by string causes air vibration and the vibration propagation of the sound that produces, string makes panel vibration to the panel of body and sound that the sound that produces, the sound hole by body produce.
But, in acoustic guitars, also have the converting means that the vibration of string is transformed to electric signal is set at body, can reproduce the type of electronics sound via amplifier etc.
At this, as the acoustic guitars that is provided with above-mentioned converting means, known have the existing structure 1 of the following stated (with reference to Fig. 6 and United States Patent (USP) the 5th, 123, (US the 5th for No. 325 instructionss, 123,325B)), existing structure 2 and existing structure 3 (opening flat 7-5881 communique (JP H7-5881A)) with reference to the spy.
As shown in Figure 6, in existing structure 1, the converting means 51 that is made of the piezoelectric element of shred shape is configured in the bottom of lower chord pillow 52.Particularly, hold converting means 51 and lower chord pillow 52 in the groove 53A of the qin bridge 53 on the panel that is installed in not shown body successively, thereby converting means 51 by qin bridge 53 and lower chord pillow 52 clampings.
In existing structure 2, converting means forms and includes the tabular of piezoelectric element, is installed in the body outside by bonding grade.
In existing structure 3, converting means has the coil case that is positioned at the sound hole inboard, the vibration of string can be transformed to electric signal by the electromagnetic induction of this coil case.
But, in above-mentioned existing structure 1, tension force by string gives the power of direction down to lower chord pillow 52, so more intense force of compression always acts on converting means 51, therefore can hinder converting means 51 and itself move freely, thereby have all unconvertible tendency of vibration of the panel of the complexity that causes by the performance behavior.Consequently, become in fact via the sound of reproductions such as amplifier and, exist infringement to play the problem of the repeatability of sound from tonequality and tone color that the performance sound that acoustic guitars is directly heard differs greatly.
In addition, in existing structure 2, though converting means detects the vibration of body, detected vibration changes greatly according to being installed in the position difference on the body.Therefore, in order to obtain good sound quality and tone color, the operation of adjusting the installation site of converting means becomes difficult and complicated, the problem that exists the needed burden of its operation to increase.
On the other hand, in existing structure 3, because do not detect the vibration of body, so tonequality and the tone color performance sound when not utilizing converting means is different.In other words, the sound of hearing when playing acoustic guitars mainly is the panel vibration of body and the sound that produces, therefore in the main existing structure 3 that detects the string vibration, and the problem that existence can not fully be reproduced.
In addition, in such plucked string instruments such as acoustic guitars, as the converting means such as acoustic pickup that the vibration of string can be transformed to electric signal, the known type that the piezoelectric element that possesses tabular or sheet is arranged.This piezoelectric element is installed on the body of stringed musical instrument by the bonding coat that is made of rubber, and is connected on amplifier etc. via lead.Therefore, the vibration of the string during performance propagates into body, bonding coat, piezoelectric element successively, thereby can reproduce the electronics sound according to the electric signal of this piezoelectric element output.
But, in this structure, the vibration of string is attenuated through bonding coat and propagates into piezoelectric element again, but only utilizes bonding coat to be difficult to obtain sufficient attenuation, thereby exist when using very not strong power to manipulate the strings, the output level of the electricity of piezoelectric element just becomes maximum situation.Therefore, when promptly use was manipulated the strings than this stronger power, output level was also constant big, changes hardly, thereby produces reproduced tone color or the inadequate defective of tonequality.
And, has the tendency that the frequency band of the good attenuation of performance becomes narrow, be difficult to obtain sufficient attenuation at the frequency band that will decay, consequently, for example at bonding coat, compare with high range, in low range can not fully obtain attenuation the time, between these ranges, output level changes artificially, and this also becomes the reason of tonequality or tone color deterioration.
Summary of the invention
The present invention proposes for solving the above problems, its purpose is the stringed musical instrument that a kind of converting means is provided and this converting means is installed, can alleviate required homework burdens such as adjustment, and make the sound that reproduces via converting means as much as possible near the sound of directly hearing from stringed musical instrument.
In order to realize this purpose, the stringed musical instrument that converting means of the present invention has been installed possesses: the many strings that are set up in parallel; The body that comprises the hollow shape of panel and backboard; Support the lower chord pillow in a distolateral zone of above-mentioned each string; Be set at the qin bridge that keeps above-mentioned lower chord pillow on the upper surface of above-mentioned panel.
Above-mentioned converting means has the installed surface with the opposed installation of lower surface of the panel of above-mentioned body, this installed surface be configured in the zone that includes the above-mentioned qin bridge of being provided with of above-mentioned panel under the zone.
Preferably the zone below the above-mentioned qin bridge of the above-mentioned panel lower surface of above-mentioned body has stiffener, and the installed surface of above-mentioned converting means is installed on this stiffener.
Can be that each above-mentioned many string gradually changes along its orientation pitch, above-mentioned converting means is provided with a plurality of, the above-mentioned installed surface of this each converting means be configured in respectively include above-mentioned lower chord pillow roughly under the zone and the zone of leaving to the both sides of above-mentioned orientation under above-mentioned each string.
In these stringed musical instruments, also can include above-mentioned lower chord pillow roughly under a plurality of above-mentioned converting means of area configurations.
In above-mentioned stringed musical instrument, the installed surface of above-mentioned converting means is formed by above-mentioned bonding coat.
In above-mentioned stringed musical instrument, can be that above-mentioned converting means comprises the bonding coat that forms above-mentioned installed surface and is installed to piezoelectric element on above-mentioned body or the stiffener via this bonding coat, be provided with the middle layer of one deck at least that forms by material with this bonding coat unlike material at the pars intermedia of the thickness direction of above-mentioned bonding coat.
The mounting structure of converting means of the present invention is that the converting means that the vibration of string is transformed to electric signal is installed on stringed musical instrument, and this stringed musical instrument possesses: the body that comprises the hollow shape of panel and backboard; Be set at the qin bridge that keeps lower chord pillow on the upper surface of above-mentioned panel; Supported by above-mentioned lower chord pillow, be set side by side with many string, it is characterized in that, above-mentioned converting means has the installed surface with the opposed installation of lower surface of the panel of above-mentioned body, this installed surface be configured in include above-mentioned panel be provided with above-mentioned qin bridge the zone under the zone.
And then preferably the zone below the above-mentioned qin bridge of the above-mentioned panel lower surface of above-mentioned body has stiffener, and the installed surface of above-mentioned converting means is installed on the above-mentioned stiffener.
In the mounting structure of these converting means, can be that above-mentioned converting means comprises the bonding coat that forms above-mentioned installed surface and is installed to piezoelectric element on the above-mentioned body via this bonding coat, be provided with the middle layer of one deck at least that forms by material with this bonding coat unlike material at the pars intermedia of the thickness direction of above-mentioned bonding coat.
Converting means of the present invention is the converting means that is installed on the body of stringed musical instrument and the vibration of string is transformed to electric signal, this converting means forms the tabular or sheet that flat shape is made circular, include sheet on the body of being installed to above-mentioned stringed musical instrument via bonding coat or tabular piezoelectric element, this bonding coat is arranged on the only one side side of above-mentioned sheet or tabular piezoelectric element, and, be provided with at least one middle layer that forms by material with this bonding coat unlike material at the pars intermedia of the thickness direction of this bonding coat.
The above-mentioned bonding coat of this converting means is formed by butyl rubber, and above-mentioned middle layer is formed by timber.
According to the present invention, because the installed surface of converting means is positioned at the following side of the panel of body, so when converting means uses sheet or laminal piezoelectric element, be not applied on the converting means by the preloading of opening the string generation, so the vibration former state of panel ground is passed to converting means.Thus, the sound that reproduces via converting means is similar to the performance sound of directly hearing from stringed musical instrument, thereby can improve the repeatability to this performance sound.
In addition and since the installed surface of converting means be positioned at include panel be provided with the qin bridge under the zone, so propagate into the structural influence that the vibration of converting means is difficult to be subjected to the power wood etc. of panel, thereby can realize the stabilization of the tonequality reproduced.
And, because converting means does not expose the outside at body, so thereby converting means can not become to hinder and can keep the state that is installed with, thereby can alleviate the burden of following adjustment operation that converting means is installed etc.
In addition, if the installed surface of converting means is installed, in body, because the relatively vibration in the zone of stable oscillation of converting means conversion so can prevent acoustic feedback, can further improve the tonequality of reproducing sound at stiffener.
And then, if with the installed surface of each converting means be configured in respectively include lower chord pillow roughly under the zone and the zone of leaving to the orientation both sides of string under each string, then can further improve above-mentioned repeatability.
Just because lower chord pillow supports string, so under it, utilize the vibration of string, panel easily the thickness direction almost parallel excite.Therefore, become the fundamental tone of the approaching sound that sends by the vibration of string at the electric signal that comprises this regional domain transformation.On the other hand, the electric signal that is transformed in the string side of sending out descant becomes the air vibration that comparison causes near the vibration by string and the reproduction sound of the sound that produces, and becomes the reproduction sound of the sound that comparison produces near the panel vibration of body at the electric signal of sending out the conversion of string side contrabass.
Like this, various types of vibrations electric signal can be transformed to, and the sound of the more approaching nature of directly hearing of reproduction sound of this electric signal can be made.And, can also adjust volume ratio by mixer device etc., and can easily carry out the setting of multiple tone color from the electric signal of each converting means.
In addition, include lower chord pillow roughly under a plurality of converting means of area configurations the time, can separate individually for example converting means of the change of the string of the converting means of the vibration of the string of main conversion treble side and main conversion bass side of configuration.Thus, the vibration detection stabilization of each string can be further made, thereby tonequality can be realized further improving.
Converting means of the present invention owing to utilize the middle layer can obtain the attenuating different with bonding coat, propagates into the vibration of piezoelectric element so can decay preferably when manipulating the strings energetically.Thus, can reduce the output level of piezoelectric element, realize output level, can improve the tone color and the tonequality of the sound that reproduces via circuit part and sound system corresponding to the power of manipulating the strings.
In addition, in middle layer and bonding coat, can adopt in the different mutually such designs of frequency band performance attenuation, thereby can enlarge the frequency band that obtains good attenuation.
Therefore, the variation of the output level that is caused by the difference of frequency band diminishes, and also can realize reproducing the raising of the tone color and the tonequality of sound thus.
And then, by the different converting means of the material for preparing multiple middle layer, can only replace these converting means and just obtain various attenuations, thereby easily carry out the adjustment of tone color etc.
In addition, in the scope of this instructions and claim, as do not have especially and express, " on ", D score, " left side ", " right side " be that benchmark uses with Fig. 4.In addition, " preceding " at the upside of Fig. 3, " back " at the downside of its opposition side and use.
Description of drawings
Fig. 1 is the outboard profile of an embodiment of expression stringed musical instrument of the present invention.
Fig. 2 is the vertical view of seeing from the top of Fig. 1.
Fig. 3 is the approximate vertical view of wanting portion that amplifies the mounting structure of stringed musical instrument shown in presentation graphs 1 and Fig. 2 and converting means.
Fig. 4 is along the cut-open view of the IV-IV line of Fig. 3, and an incomplete structure part is represented.
Fig. 5 is the sectional view of the layer structure of the converting means shown in presentation graphs 3 and Fig. 4.
Fig. 6 is the exploded perspective view of an example of mounting structure of the converting means of the existing stringed musical instrument of expression.
Embodiment
Below, the embodiment desirable at the present invention describes with reference to accompanying drawing.
At first, utilize Fig. 1 and Fig. 2 that the outward appearance of an embodiment of stringed musical instrument of the present invention is described.
Fig. 1 is the outboard profile of this stringed musical instrument, and Fig. 2 is the vertical view of seeing from the top of Fig. 1.
The stringed musical instrument 10 of this embodiment be with as the roughly the same structure of the acoustic guitars of representative plucked string instrument.Body 2 as this musical instrument main body has peripheral shape identical panel 15 and backboard 16, is the resonant of the hollow structure that the periphery of panel 15 and backboard 16 is bonded together of the side plate 17 by curve form.Central portion at the bulge of the smaller side of this panel 15 is formed with circular sound hole 14.
And, be fixed with at the leading section on the right side of Fig. 1 of this body 2 and Fig. 2 and possess the neck 3 of scroll head 5 at leading section when supporting fingerboard 4.In addition, on the upper surface 15a of panel 15, on the opposition side (left side of Fig. 1) opposite, support the qin bridge 13 of lower chord pillow 12 across sound hole 14 by being adhesively fixed with fingerboard 4.
Be provided with respectively 6 tuning keys 7 with the rotation of string button 9 interlocks at the scroll head 5 of the leading section of neck 3, at each tuning key 7 be inserted into to stretch tight between the string bolt 18 in 6 open-works that are formed on the qin bridge 13 and haul 6 strings of making by steel wire or intestines string etc. 11.And what be set at scroll head 5 and neck 3 borderlinely goes up the lower chord pillow 12 that capotasto 8 and qin bridge 13 supported and supports each string 11 respectively and give tension force.
Then, explain the part that the present invention relates in this stringed musical instrument with reference to Fig. 3 to Fig. 5.
The approximate vertical view of wanting portion of having represented to amplify the mounting structure of stringed musical instrument shown in Fig. 1 and Fig. 2 and converting means at Fig. 3 omits a part of structure at Fig. 4 and represents along the cut-open view of the IV-IV line of Fig. 1.
In the stringed musical instrument 10 that these figure represent, each string 11 is with along its orientation, promptly from left to right the mode that uprises gradually of pitch is set.At this, in each string 11, the string of the leftmost side is to send out string 11A (hereinafter referred to as double bass string 11A) contrabass, and the string of the rightmost side is the string 11B (hereinafter referred to as descant string 11B) that sends out descant.
When lower chord pillow 12 vertically is arranged on the qin bridge 13 along left and right directions, supporting the rear end side zone of each string 11 in the mode in the rear end side zone of each string 11 of bending in upper end side.The length of the orientation of the string 11 of lower chord pillow 12 is set in the mode that its two ends lay respectively at the outside of double bass string 11A and descant string 11B.
Qin bridge 13 there is no especially and to limit, and is for example made by ebony, forms tabular along the upper surface 15a of panel 15.This qin bridge 13 with along with away from lower chord pillow 12 thickness gradually the mode of attenuation form, the surface has a groove 13A that holds lower chord pillow 12 thereon.In addition, the rear side of the lower chord pillow 12 in this qin bridge 13 is provided with six hole 13B that insert string bolt 18, is kept the rear end side of string 11 by this string bolt 18.
On the upper surface 15a of the panel 15 of body 2 by the fixing qin bridge 13 of bonding grade.In the lower surface 15b of panel 15 side a plurality of power wood 19 that are used to strengthen this panel 15 are installed.The mode that two power wood 19A, 19A in these power wood 19 extend with the direction of intersecting between qin bridge 13 and sound hole 14 shown in Figure 2 and being provided with.
In addition, in the lower surface 15b of panel 15 side, zone between the wood of two power below the qin bridge 13 19A, 19A is provided with tabular stiffener 20, strengthens the installation region of qin bridge 13 that tension force because of string 11 is given the panel 15 of load by this stiffener 20.
Lower surface at this stiffener 20 is provided with a plurality of converting means 22 that the vibration of string 11 can be transformed to electric signal.
This each converting means 22 forms the tabular or sheet that flat shape is made circular respectively.The upper surface of each converting means 22 is the installed surface 22A that is installed in the lower surface of stiffener 20, and is relative with the lower surface 15b of panel 15.Each installed surface 22A is configured in the zone under the zone that is provided with qin bridge 13 that includes panel 15 respectively, particularly, under the state of Fig. 3 of seeing qin bridge 13 of bowing, disposes in the mode of roughly holding each installed surface 22A in the setting area of qin bridge 13.
3 these converting means 22 are set below lower chord pillow 12, simultaneously in the position of leaving towards the left side of double bass string 11A and the position of leaving towards the right side of descant string 11B 1 this converting means 22 respectively is set.The installed surface 22A of each converting means 22 of lower chord pillow 12 belows is configured in respectively and includes the zone of lower chord pillow 12 under roughly, and central part is respectively between the double bass string 11A string 11 adjacent with it, between the descant string 11B string 11 adjacent with it, between two strings of central portion in these faces.
The installed surface 22A of the converting means 22 in double bass string 11A left side be configured in this double bass string 11A and and the overlapping power wood 19A of the left end side of qin bridge 13 between.On the other hand, the installed surface 22A of the converting means 22 on the right side of descant string 11B be configured in this descant string 11B and and the right-hand member of the qin bridge 13 power wood 19A that stresses to fold between.
Each converting means 22 has layer structure shown in Figure 5.That is, possess at the bonding bonding coat 24 of the lower surface of stiffener 20, in the middle layer 25 of the thickness direction pars intermedia setting of this bonding coat 24, via the sheet metal of making by brass etc. 26 and be installed in sheet on the lower surface of bonding coat 24 or tabular piezoelectric element 27.
Bonding coat 24 is for example formed by butyl rubber.This butyl rubber has each kind by components matching, but is preferably the non-butyl rubber that adds the sulphur type and have self adhesion.Middle layer 25 usefulness form with the material of bonding coat 24 unlike materials, in this embodiment, use timber such as maple.On sheet metal 26, be connected with ground wire 29, on piezoelectric element 27, be connected with lead 30.
This piezoelectric element 27 detects the vibration of the panel 15 that the vibration by the string 11 that is struck causes, and is transformed to electric signal, and this electric signal is outputed to circuit part in the body 2 by lead 30.This circuit part will amplify and impedance conversion with operational amplifier etc. from the electric signal of each converting means 22 outputs, through mixting circuit and compensating circuit etc., can send to the sound system (amplifier and loudspeaker etc.) in the outer setting of stringed musical instrument 10.
In sound system, will amplify from the electric signal of stringed musical instrument 10 inputs with amplifier, carry out the electric acoustic conversion by loudspeaker, send the performance sound.
In above structure, when manipulating the strings for the performance of carrying out stringed musical instrument 10, the vibration of this string 11 propagates into lower chord pillow 12, qin bridge 13, panel 15, each converting means 22 successively, and is transformed into electric signal by each converting means 22.The electric signal that is transformed at each converting means 22 outputs to above-mentioned circuit part via lead 30, and the sound system by the outside reproduces sound again.
At this, the vibration that is transmitted to the panel 15 of each converting means 22 understand different owing to the position relation of the thickness of qin bridge 13 or each string 11 is different, thus also difference of the corresponding therewith and sound that reproduces.
In more detail, in the panel 15 of lower chord pillow 12 lower zones, because the thickness of the qin bridge 13 of its area just above is big, with the close together that becomes the lower chord pillow 12 that excites portion by support string 11, so easy and thickness direction almost parallel ground displacement vibration.Therefore, each converting means 22 of lower chord pillow 12 belows can stably detect and reproduce the tone color near the fundamental tone of the vibration of string 11.
In addition, the panel 15 of the left and right sides of lower chord pillow 12, qin bridge 13 attenuation of its area just above, below compared with lower chord pillow 12, the strength degradation of qin bridge 13, but owing to the distance with power wood 19A, 19A just increases more near intensity more, reverse a bit so vibrate displacement.Therefore, the homophonic composition of the converting means 22 in the left side of double bass string 11A increases, in addition, because near double bass string 11A, so can stably detect and reproduce the tone color of the sound of directly hearing that causes near vibration by panel 15.
On the other hand, the converting means 22 on the right side of descant string 11B also is since when homophonic composition increases near descant string 11B, approximate vibration by string causes air vibration and the tone color of the sound that produces so can stably detect and reproduce.
Like this, owing to can detect the vibration of different tone colors according to the installation site of converting means 22, so by the mixting circuit of above-mentioned circuit part, mix arbitrarily from the electric signal of each converting means 22 output and adjust, can carry out setting corresponding to the tone color of various music scenes.
For example, the volume with each converting means 22 below the lower chord pillow 12 be made as A, with the volume of the converting means 22 in the left side of double bass string 11A be made as B, when the volume of the converting means 22 on the right side of descant string 11B is made as C, if the ratio of these volumes is made as A: B: C=2: at 3: 5 o'clock, the tone color of the echo that stringed musical instrument 10 produces when becoming solo, if be made as A: B: C=3:, then can obtain the chord performance of sound grace on the whole at 2: 5 o'clock.
But at each converting means 22, the vibration that propagates into piezoelectric element 27 from installed surface 22A decays by bonding coat 24 and middle layer 25.Particularly the middle layer 25 of being made by maple is excited and consumes vibrational energy, the output level of piezoelectric element 27 can be dropped to below the certain value.Thus, even can avoid as existing structure, taking place increasing the situation that the power of manipulating the strings does not also exert an influence to output level, thereby can improve tone color and the tonequality of reproducing sound.
In addition,, can bring into play the attenuation in high range effectively, eliminate unnecessary lingering sound, and obtain smooth tone color at the bonding coat of making by butyl rubber 24.On the other hand, in the middle layer 25, obtain with the attenuation of bonding coat 24 different frequency bands, just obtaining the attenuation of low range and midrange or obtain butyl rubber not having and distinctive attenuation characteristic of maple and tone color correction effect.Therefore, can enlarge frequency band or the reduction or the adjustment of the good attenuation that obtains by this middle layer 25 to becoming unnecessary frequency content.Also can realize better tone color and tonequality thus.
In addition, according to present embodiment and since be positioned at lower chord pillow 12 under stiffener 20 on be provided with each converting means 22, so can pick up vibration in the zone of panel 15 stable oscillations, the generation of acoustic feedback can be prevented, and the tonequality and the tone color of electronic reproduction can be kept preferably.In addition, vibration has been attenuated by middle layer 25, so the electric signal that outputs to circuit part is changed according to the power of manipulating the strings.
And then, owing to each converting means 22 has been installed at the lower surface of the stiffener 20 of body 2 inside, so even under the situation of always keeping its installment state, converting means 22 can not become obstruction yet.Therefore, stringed musical instrument 10 is taken when taking out from box at every turn, do not needed to load and unload converting means 22 or adjust operation from the output of converting means 22.
And, since lower chord pillow 12 roughly under be provided with 3 converting means 22, so it is poor to prevent to produce volume at each string, thereby improve tonequality.
Though disclose the structure that is used to implement the best of the present invention and method etc. in above record, the present invention is not limited to this.
Promptly, the present invention illustrates and has illustrated the embodiment that certain is specific especially, these those skilled in the art can implement various distortion to shape, position, material or direction and other detailed structures of above-mentioned embodiment but only otherwise break away from the scope of technological thought of the present invention and purpose.
Therefore, the above-mentioned disclosed record that defines shape etc. is for easily understanding the exemplary record that the present invention makes, do not limit the present invention, so the record of making of the title of the part of the qualification of these shapes etc. or the member beyond whole qualifications is also contained among the present invention.
For example, in the mounting structure of stringed musical instrument of the present invention and converting means thereof, make the structure of having omitted stiffener 20, also can make the lower surface that the installed surface 22A of each converting means 22 is directly installed on panel 15, the structure of a converting means 22 perhaps only is set at the downside of lower chord pillow 12.But,, preferably as above-mentioned embodiment, adopt the structure that stiffener 20 is set and disposes a plurality of converting means 22 if want to obtain above-mentioned effect and effect.
In addition, quantity is set can changes of the converting means 22 of the below of lower chord pillow 12 for example can be made six or two.Preferably be provided with as follows: when converting means 22 is made six, in these faces the centre in each string 11 roughly under, when converting means 22 is made two, in these faces central part be positioned at respectively the adjacent separately string 11 of double bass string 11A and descant string 11B roughly under.
And then the present invention also goes for classical guitar or other various stringed musical instruments such as Ukuleles, mandolin.
Various changes can be carried out in the installation site of converting means 22 of the present invention, for example, can be installed in the places such as outside of the panel 15 or the backboard 16 of body 2.In addition, the material in the middle layer 25 that is provided with between bonding coat 24 is not limited to maple, also can use other timber etc., can be formed by various materials.
Therefore, replace this converting means 22, thereby can obtain the attenuation characteristic that the material by middle layer 25 causes or the variation of tone color, can easily carry out the adjustment and the correction of tone color by the different converting means 22 of material of preparing multiple middle layer.
And then, can form a plurality of middle layers 25, at this moment, bonding coat 24 is set between each middle layer again.In addition, the planar dimension in middle layer 25 is formed less than bonding coat 24, perhaps a plurality of middle layers 25 that form less than bonding coat 24 of configuration in same plane.