US2987950A

US2987950A - Wind instrument of the cup mouthpiece type

Info

Publication number: US2987950A
Application number: US731581A
Authority: US
Inventors: Earle L Kent
Original assignee: Conn Ltd C G
Current assignee: CG Conn Ltd
Priority date: 1958-04-24
Filing date: 1958-04-24
Publication date: 1961-06-13
Anticipated expiration: 1978-06-13

Description

June 13, 1961 E. L. KENT WIND INSTRUMENT OF THE CUP MOUTHPIECE TYPE 4 Sheets-Sheet 2 Filed April 24, 1958 INVENTOR.

Ear/e L. Kem BY m f June 13, 1961 E. L. KENT WIND INSTRUMENT OF THE CUP MOUTHPIECE TYPE Filed April 24, 1958 4 Sheets-Sheet 3 @EE E? n a P Ear/e L. Ken) United States Patent 2,987,950 WIND INSTRUMENT 0F THECUP MOUTHPIECE TYPE Earle L. Kent, Elkhart, Ind., assignor to C. G. Conn, Ltd., Elkhart, Ind., a corporation of Indiana Filed Apr. 24, 1958, Ser. No. 731,581 Claims. (Cl. 84-388) This invention relates generally to musical wind instruments of the type using cup-shaped mouthpieces, and more particularly to such an instrument in which the brass or metal tubing forming the same is constructed to provide better intonation and tone quality.

Musical wind instruments having cup-shaped mouthpieces have been constructed over a large number of years and are in quite widespread use. In such instruments various notes are played by use of frequency derived by resonance modes resulting from the length and general construction of the passage through the instrument. To provide other frequencies which may be spaced between these resonance modes, slides of different length are selectively connected into the passage of the instrument to change the effective length thereof. Resonance modes produced by these various lengths together with resonance modes at the basic length are used to provide the different tones of the instrument.

The frequencies of the tones of the equally tempered musical scale which it is desired to produce by musical instruments do not, however, correspond with the frequencies which are produced by the resonant modes.

Therefore the resonance frequencies produced by an instrument as mentioned above do not correspond accurately with the frequencies in the equally tempered musical scale. Further to limit the number of slides which change the length of the passage through an instrument, various slides are used in combination and by this arrangement compromises must be made resulting in variation in the lengths provided as compared with the desired lengths. These two factors contribute to provide the undesired result that the tones produced by cup-mouthpice type instruments do not accurately conform to the frequencies of the equally tempered musical scale, so that the notes are not completely in tune, the instrument does not respond as desired by the musician, and the tone quality is imperfect.

It is therefore an object of the present invention to provide an improved wind instrument of the cup-mouthpiece type which produces better intonation and tone quality.

Another object of the invention is to provide a cupmouthpiece type wind instrument wherein frequencies produced by resonance are modified to conform to the equally tempered musical scale.

The invention relates to wind instrument having valve slides which change the frequency thereof and which are used in combination to provide certain frequencies, but in which the frequencies produced by the slides differ from the desired frequencies, and it is a further object to compensate for such differences in frequency caused by the use of the valve slides.

Still another object of the invention is to provide an improved method of designing a cup-mouthpiece instrument-so that the instrument has better intonation.

A feature of the invention is the provision of a brass wind instrument of the cup-mouthpiece type which includes sections of varying diameter which change the effective. length of the instrument with the frequency of the tone played, to thereby compensate for differences between frequencies produced by resonance and the frequencies required by the equally tempered scale, and/ or differences due to the use of slides in combination which provide improper slide lengths.

A further feature of the invention is the provision of a brass type wind instrument having a mouthpiece, a mouthpipe and a bell which include tapered sections, with the tapers of the various sections being constructed to provide effective lengths of the over-all instrument which differ at different frequencies and fit a desired pattern. The bell may be formed of a plurality of portions each constructed to provide a desired change in the effective length of the instrument.

Another feature of the invention is the provision of a method of designing a cup mouthpiece instrument wherein the design variables for various parts are considered, and each part is constructed to have a particular elfective length characteristic with respect to frequency in conjunction with the remainder of the instrument, so that the instrument has the over-all elfective length to provide desired intonation characteristic over the entire range of the instrument. Nomograms may be used to determine changes in flared sections to provide the required changes in effective length to correct for intonation errors in an instrument.

A still further feature of the invention is the provision of an instrument as described above having a cavity formed by the mouthpiece and the mouthpipe, the size and shape of which may be controlled to adjust the. effective length of the instrument at different frequencies.

Still another feature of the invention is the provision of a brass type wind instrument having a mouthpiece in which the volume of the cup of the mouthpiece is so related to the orifice area of the mouthpiece to provide a change in the effective length of the instrument over a predetermined frequency band.

Further objects, features and the attending advantages of the invention will be apparent from a consideration of the following description when taken in connection with the accompanying drawings in which:

FIG. 1 is a perspective view of a comet constructed in accordance with the invention;

FIG. 2 shows in detail the taper of the various tubular portions of the comet of FIG. 1;

FIG. 3 illustrates the deviation in cents of the frequency of a cylinder open at both ends from the desired frequency over a frequency band;

FIG. 4 shows the effective length required in an instrument in accordance with the invention to produce tones in accordance with equally tempered scale;

FIG. 5 illustrates variations of the effective length of the mouthpieces having different constructions;

FIG. 6 illustrates the change of the effective length of the instrument as a function of frequency and shows variations resulting from change in the length of the cavity formed between the mouthpiece and the mouth- P P FIG. 7 illustrates the change of the effective length of the instrument as a function of frequency and shows variations resulting from changes in the length and taper of the mouthpipe;

FIG. 8 shows the variation of effective length of the instrument as a function of frequency, which may be produced by construction of the bell of the instrument;

FIG. 9 includes curves of the effective length of an instrument considered as a cylinder open at one end and shows the configuration required to provide the tones of the equally tempered musical scale;

FIG. includes curves illustrating changes in effective length with changes in physical length; and

FIG. 11 is a nomogram for use in calculating the effective length of flaring sections of an instrument.

In practicing the invention there is provided a musical instrument of the cup-mouthpiece type which in the en: ample illustrated is a cornet. This cornet is made up of a mouthpiece having a cup adapted to be positioned adjacent the lips of the person playing the instrument, a mouthpipe having a portion attached to one end thereof in which the mouthpiece is inserted, a length of cylindrical tubing to which additional slide portions may be selectively coupled by valves, and a bell connected to the cylindrical tubing and having a flaring end from which the musical tones are discharged. The mouthpiece, .the mouthpipe and the bell each have portions which are tapered, with the small ends being in the direction of the mouthpiece and the larger ends in the direction of the bell. The taper of these sections is effective to change the efiective length of the entire passage through the instrument with the frequency involved. The length of a cavity formed by the mouthpiece and mouthpipe may also be varied to change theefiecti've length of the instrument. The valve slides may also be constructed to have different effective lengths at dilferent frequencies. The bell may be constructed with three or more portions which are individually designed to provide further variables which may be controlled. Accordingly, the instrument has different eflective lengths at different frequencies and this feature is used to correct the effective length at particular notes where the actual length is improper'to provide the tone which fits in the equally tempered musical scale. This compensates for differences between the equally tempered musical scale and a series of frequencies produced by resonance, and also for improper length which results from the use of the valve slides.

Referring now to the drawings, in'iFlG. 1 there is illustrated a comet which is constructed in accordance with the invention. This instrument is made up of a mouthpiece 10, a mouthpipe ll, tubing sections 12 joining the mouthpipe in which valves 13 are provided for selectively connecting slides 14, 15 and 16 to the tubing 12.. The tubing 12 extends from the valve section and joins with the bell 17 which terminates in a flared end 18.

FIG. 2 shows the mouthpiece 10 more in detail and also shows in a schematic Way the mouthpipe 11, the uniform tubing 12 and the bell 18. As shown 'in FIG, 2, the mouthpiece includes a cup 26' adapted'to receive the lips of the person playing theinstrurnent. The cup has an orifice therein with a tapered back bore 21 extending therefrom which increases in diameter relatively rapidly. The mouthpipe 11 also increases in diameter but at a much lesser rate. The mouthpipe may extend all the way to the valve slides. The section 12 which is broken away and is indicated by the letter K is usually formed of cylindrical tubing which is all of constant diameter. The valve slides 14, 15 and 16 are usually of constant diameter. The bell 17 starts out at a relatively small taper and with the taper continually increasing until it becomes a very steep flare at the outlet or mouth of the bell.

Before considering the construction of the instrument further, it is necessary to consider the operation of the instrument which produces the problems solved by the invention. A cup mouthpiece instrument may be generally compared for analysis purposes to a cylindrical tube open at both ends. It is to be pointed out that the characteristics of'the instrument are not exactly the same as that of a uniform cylindrical tube open at both ends,-

and the instrument has some characteristics approaching that ofa cylindrical tube open at one end andclosed at d of frequencies which are the fundamental resonant frequency of the open tube and the harmonics thereof. The resonant frequencies of a tube open at both ends are indicated by the following simple formula:

where f, is the frequency of the harmonic, n is an integer corresponding to th e fundamental or harmonic frequency, c is the velocity ofsound in the tube, and L is the physical length of the tube. In order to provide the different tones needed in such an instrument, it is necessary to have tones in between the harmonics provided by the above formula and to accomplish this the slides are provided which change the physical length Lv so that additional series of harmonics are provided.

Considering first the problem of the resonant frequencies themselves, we may consider, for example, a cylinder of such a length that the fundamental frequency is 116.54 cycles per second. It will then resonate at the fgllowing harmonic frequencies:

Equally tempered scale frequency Harmonic Frequency The above table also lists the frequencies of the equally. tempered scale which itis desired to produce. Although some of the harmonic frequencies coincide exactly with the frequencies of the equally tempered scale, others .do not. It will be noted from the above that whereas A 13, Ant and A 5? are accurate, F is slightly off, D is substantially off, and F and C are slightly off.

As stated above, in order to provide frequencies inter mediate the frequencies produced by the harmonicsit is necessary to change the'length of the passage through the instrument and this is done'by the useof slides which may be selectively coupled to the instrument tubing. bly

val-vesor the like. It is necessary tov selectively add various different lengths to provide all of the tones .necessary to make up the equally tempered scale. Normally. it is deemed preferableto provide only three valves in such an instrument, and to do this three. diflferentaslide lengths may be provided. To produce other variations in length the slides are used' in combination. This introduces a 'problem since if the slides. .are the proper. length when used alone, the use of a plurality of slides to-p'rovide a different change in tone. is not accurate. and

does not provide the truelength required.

The reason that the slides areof improper length. when used in combination is that the slide lengths are. com puted as a percent of the fixed length of the instrument which is necessary to. change the tone by aparticularamount, .a semitone, two semitones, etc. However, when one slide is already inserted in the passage the fixed length is greater so that the operation ofa second slide does not increase the fixed length by the percent required to produce the change in tone normally provided by use of' such slide. Compromises are made by changing the slide lengths. so that they are slightly off-when used alone and are-reasonably close when used in combination. However, errors still exist' The following table shows the errors resulting when, the slide lengths aremade proper for. individual use and also the errors resulting when compromise slide. lengths are used. I-t-willbe-apparentthat the maximumerroris greatly reduced byJthe use ofcompromise slide lengths.

Stine LENGTH ACCURATE ron INDIVIDUAL USE As stated above, the errors resulting from the use of resonant frequencies which difier from the frequencies of the equally tempered scale and the errors resulting from theuse of slides which are somewhat inaccurate add together to produce improper tones. The following table lists the note, the frequency, the resonant mode, the valves used, the lengths provided, the lengths required and the errors in length for a cylinder open at both ends which has been described. The instrument simulated by this cylinder without use of valves has a natural resonant frequency of 116.54 cycles per second as in the previous example. The length of the tubing without use of slides is 58.56 inches. The length of the slides are the compromise lengths stated above; that is, slide No. 2 is 3.66 inches, slide No. 1 is 7.36 inches, and slide No. 3 is 11.77 inches.

of the valve slides. FIG. 3 is based on a cylinder open at both ends. The unit used in FIG. 3 is cents with 100 cents being equal to one semitone. This curve corresponds generally to the error in inches shown in the above table, but in FIG. 3 the error is shown in deviation of the tuning or intonation rather than in deviation of the length of the instrument. As stated above, the errors in tuning or intonation can be compensated for by changing the length of the instrument. It is, of course, not desired to make a physical change in the length of the instrument as this would require additional mechanisms, but it has been found that the effective length of the instrument can'be changed in various ways to provide an effective length. of the basic instrument which compensates for the errors referred to above to produce an instrument providing accurate tones at all the desired notes.

FIG. 4 shows the effective length of the basic open: cylinder which is necessary to provide accurate tones. In the example used, the instrument has a physical length of 58.56 inches without the use of slides. However, the effective length of the instrument must vary from inches at the low notes to less than 58 inches in the intermediate tones, with minor variations being required at various points along the musical scale.

I As shown by the formula presented above, the fr quency of a tone produced in an open cylinder dependsupon the velocity of the sound in the tube as well as upon the effective length of the tube. The velocity of sound. in turn varies with the frequency, in a tube wherein the walls flare. Accordingly, by providing flared portions in various sections of the instrument, the effective length of the instrument can be changed. In conic section the effective length also changes with frequency because of the changing phase relation between the outgoing wave. and the reflected wave. In accordance with the invention,

Length Length Length Change Note Frequency Mode Valve Attained Required Error RequiredlnLength I (open (open (Inches) for open Required cylinder) cylinder) cyhnder) (Percent) e asesaeaaaseaseaeeeseseeeesseaeaesse assessassesseseaeeaaseasaeeesaaaseaeea ae s geesasasseaseeeasaaeaeaeaeesaaaeee aaeoneeaaas:aaeeeaesaaaasaeeeeaeaameze H. 11! .++fl-.+: r t li fh 2sanaanoa;anasnaaaeoseaesseenaaczaeeee Valve slide lengths used#2=3.66". #l=7.36". #8=l1.77.

Referring now to FIG. 3 of the drawings, this curve shows the error in intonation (cents) resulting from the two factors mentioned above, that is, the difierence of the resonant frequencies and the frequencies of the equally tempered musical scale, and second the incorrect lengths the construction of the mouthpiece, the mouthpipe and the bell of the instrument are designed to provide configurations which control the effective length of themstrument. Between the mouthpipe and the bell is a section of tubing which is .of constant diameter and this sec,-

7 t er. a th us fi s g the n Produ e y not be modified to produce a change in the effective length. No. ub tantial ch e n ve it s p du ed y c n e in frequency in constant diameter tubing of the size gen-. erally used and in .order to produce the instrument con veniently this section to which the slides are coupled is retained at constant diameter. v i i V In some respects, it is more nearly a true analogy if the cylinder closed at one end is chosen as a reference 9 a GUI? m u hp ece inst ment. First, the cup-mouthp ece instruments have a pressure node at or near the bell of Elie instrument and a velocity node at or near the m uth ie e Sec dly. he e f t length of a cy n r, g qsst at ne a d u d need to increase wi h r q y if its resonant frequencies followed those required for the musical scale and this would mean that the effective velocity of sound in the tube would be an inverse function of frequency. In flaring horns, such as an exponential, this is actually the case.

It is well known that a cylinder closed at oneend resonates ,only at the odd integral multiples of the fundamental resonant frequency. Therefore, a cylinder closed at one end and of the proper length to resonate at, say, 116,54 cycles per second, as in the prior example, would resonate at 349.62 c.p.s., 582.70 c.p.s., 815.78 c.p.s. etc. if the physical length and the speed of sound in the cylinder are held constant. In order for this cylinder to resonate at 233.08 c.p.s. as required for A;;#, it would be necessary for its effective length to be increased as the frequency is increased so that by the time the frequency reaphed 233.08 c.p.s. the cylinder would be suitably longer it at 116.54 c.p.s. (the fundamental) and the next mode of resonance, which would be 349.62 c.p.s. if the length remained constant, is now 2.33.08 c.p.s.

The required effective length, L for the complete harmonic series is:

where n=odd integer indicating mode of vibration c=speed of sound f,=frequency at resonance.

T bus, to return to our example, the effective length required for a fundamental resonance (n=1) of 116.54 c.p.s. would be:

L 1 29.28 inches The effective length required to resonate at the second harmonic of 116.54 c.p.s., or 233.08 c.p.s., would be:

These calculations can be carried on as far as desired and an L will be a smoothly increasing function of frequency if the harmonic series is followed for the values of f As was mentioned before, the fifth mode of theinstru- L 2: =43.92 inches ment will resonate at too low a frequency if it follows the L 5= =52.7l inches 6 .5229 n hes,

This means that it would be necessary for the rate of a shoulder has been 1 nated C in FIG.

1 based on a cavity having a tubing shown increase in effective lengthto be reduced as the frequency v passes through the fifth 'mode,so that the instrument will resonate at the proper frequency to be in tune with the equally tempered scale. The solid curve of FIG. 9 shows the lengths required to provide the tones of the equally tempered scale and this is an irregular curve. The light smoothcurve follows the harmonic series.

Once it has been determined what the effective length should be for each frequency of the scale by this process, the "next step is to determine suitable parameters of here calibration to produce the correct variation of effective length as a function of frequency. Explanations of the effect o the d mensions of the r o s Parts of a ham on the effective length are set forth below. These apply to the analysis of a horn when considered either as a cylinder open at both ends or as a cylinder open only at one'end.

Considering first the mouthpiece of the instrument 11 2 it has been found that the effective length of the mouthpiece can be changed widely by control of the volume of the inlet cup in relation to the orifice area at the nost restricted point of the mouthpiece. FIG. 5 includes six curves which show the effective length of the mouthpiece, and show variation of the effective length with frequency with the length vs. frequency curve being of different shape for difierent ratios of cup volume to orifice area. Curve a is for a ratio of one, b for a ratio of two, 0 for a ratio of three, d for a ratio of four, e for a ratio of five, and curve 1 for a ratio of six. It will be apparent that the mouthpiece can be used to provide an increase in the elfective length in the region from 500 to 7-00 cycles per second as is shown to be needed by the curve of FIG. 4.

The taper of the mouthpiece back bore beyond the restrictive orifice may also be changed to change the effective length of the instrument. The change in taper changes the cutoff frequency and this changes the effective length for different frequencies. Increasing the cut off frequency decreases the effective length for lower frequencies and increases the effective length for higher frequencies. i

A second point in the instrument which may be controlled to change the effective length of the instrument is the small region at the end of the mouthpiece at its junction with the mouthpipe. A cavity with a square provided at this point which is desiga 2. Change in the volume and shape of this cavity will change the effective length of the instrumen. FIG. 6 shows changes in effective length result; ing f rom change in the length of this cavity. The center line designated g in FIG. 6, is, used as a reference and is length of inch which is illustrated in FIG. 2. To reduce this length by half results in the changes in effective length indicated by curve h, and to completely eliminate the cavity would produce the curve i. To increase the length of the cavity by 50% produces curve k and to increase the length of the cavity by would produce the curve I.

The next part of the instrument which can be con; trolled to provide change of effective length is the mouthpipe which has been designated 11. This is the portion of in FIG. 1 extending between the cavity designated C and the tubing of fixed diameter designated K. The shapeand length of the mouthpipe changes the effective length of the instrument and the use .Of a conical taper has been found to provide an improved result. In order to hold the diameters of the ends of the mouthpipe fixed and thereby'permit the use of a standard mouthpiece and standard bore for the tubing K. which, is of fixed diameter, the taper of the conical bore through the mouthpipe can be changed by changing the lengtht here of. In the mouthpipe shown in FIG. 2 the diameter at the small end is .330. inch and at the large end .438 inch. FIG. 7 shows the deviation in effective length resulting from change of the length of the mouthpipeifrom 8 inches to 12 inches. In FIG. 7 a standard mouthpipe '10 inches longis used as a reference and is designated by center line m. Curve n shows the deviation in frequency produced by a mouthpipe 8 inches long, curve is the deviation for a 9 inch mouthpipe, curve p the deviation for an 11 inch mouthpipe, and curve q the deviation for a 12 inch mouthpipe. It is obvious from the curves that relatively sharp changes in effective length can be produced by changing the length and thereby the taper of the mouthpipe, and this is particularly effective to bring the notes R ft, G it A and A 1? in tune.

It has been found that the use of a mouthpipe which is longer and has a smaller inlet has produced the required change in effective length to improve intonation in certain instruments which have been constructed. For example, the intonation of a euphonium was improved by reducing the small diameter of the mouthpipe from .437 to .418 inch and increasing the length thereof from 7.57 to 8.36 inches. The outlet diameter was retained at .555 inch to match the constant diameter tubing. In a trumpet designed in accordance with the invention, the mouthpipe inlet diameter was .330 inch as compared with .340 inch to .346 inch for prior accepted constructions. The mouthpipe inlet diameter at the junction with the cavity indicated c in FIG. 2 may be substantially the same as that of the outlet of the mouthpiece.

Although the constant diameter tubing which is represented in FIG. 2 as the section K is not usually modified to change the effective length or tone characteristics, this length must be adjusted to provide the required total length of the instrument. That is, when the length of the mouthpipe is changed as illustrated by FIG. 7, the length of the constant diameter tubing is subject to change to provide the required total fixed length. The following table shows the change in the constant diameter tubing K for changes in mouthpipe lengths.

Mouthplpe length, Constant Diameter inches Tubing, inches It may be desired to construct the third valve slide to provide a change in the effective length thereof with frequency to thereby compensate for incorrect effective length resulting from use of the third valve slide in com-, bination with other valve slides. Referring to FIGS. 3

fective length of the third valve slide which will be effec-' five for the frequency of B will have no effect on A it and therefore need not be so sensitive to frequency change.

The bell may also be constructed with the tapered and flaring portions selected to adjust the effective length of the over-all instrument at different frequencies. The bell may be considered as made up of three parts: first, the stem designated S which is made up of the full length shown in the third section of FIG. 2 and the portion designated S in the bottom section, second, the throat designated T in the bottom section, and third the mouth M which includes the remainder of the bell. The taper, length and cut-off frequency of each of these sections may be controlled to change the effective length of the hell. FIG. 8 illustrates the effective length at the various frequencies for the bell configuration as shown in FIG. 2. This shows that the effective length increases with frequency, and although there are no sudden changes in the eurvetit is not auniform curve, with thejriseat certain points being relatively steep and the curve atother points being substantially flat. This curve can be made to have wide variations by making the taper of the stem, where it:

I y=y cosh ms% sinh ms where y=diameter at any point s on section y =diameter of the small end of the section y =s1ope at the smaller end of the section m= f.,=parameter dependent on flare of section f =cut-ofi frequency of the section s=contour distance measured from smaller end of section c=velocity of sound=l3,650 inches per second Each section is, therefore, defined by four parameters, s, the contour length or distance from the small end of the section, m, the rate of flare, y the diameter of the small end of the section, and y' the slope at the small end of the section. Variation of any one of these parameters will cause a variation in the effective length of the section defined thereby. The section defined by the above equation may be conical, exponential, or catenoidal in shape depending upon the relative values of y y' and m. When m is zero and y' and y have a particular relation, the shape is conical, when y /y m=l, the section is exponential, and when y' /m equals zero, the shape is catenoidal.

The following equation defines the effective length of a first section open at its outlet and joined to a second section at its inlet, with the sections being of various shapes as encompassed by the above equation:

Note that if the second section is a cylinder, 73:0 and \/f2f12 (h T" L 27rf cot 1E? 00b 6 f f L As the velocity of sound is constant, the effective length as indicated by this equation is dependent upon the cutoff frequency 3, and the contour length L.

It will be apparent from the above that the equation, for determining the effective length of a flaring section as.

set forth above is quite diflicult to use. It has been found that nomograms can be prepared by the use of a computer to facilitate determination of the effective length of such a section at a particular frequency f. FIG. 11.

shows a nomogram which may be used for this purpose, and which applies to the length of a catenoidal section which is smoothly joined to another catenoidal section.

In using these curves, it is necessary to compute where h is the cutoff frequency of the section involved is used as the abscissa and the corresponding point is located on the curve which corresponds to the calculated value for curve corresponding to the calculated value of The abscissa for this point provides the value for so that .L the effective length, can be determined.

By use of the above equations and/ or the nomogram, it is possible to design an instrument, or correct the design of an instrument, so that it conforms more closely to the desired curve. This is illustrated in FIG. 9 wherein the dotted curve illustrates the effective length of an euphonium constructed prior to the invention and the dot-dash curve illustrates the effective length of the instrument when changed in accordance with the teachings of the invention. Although the dot-dash curve does; not coincide exactly with the desired cnrve shown by the heavy solid line, it will be apparent that it is much closer at certain critical notes. For example, B is considerably improved and Fi G A and Ai are all greatly improved. The improvement shown was achieved by changing the shape of the mouthpiece and the mouthpipe of the instrument, and by the use of a cavity between the mouthpiece and mouthpipe "havingsquare shoulders,

The deviations from the smooth resonance curve, as illutstrated by the heavy eurve in FIG. 9-, may be provided by making the cut-off frequencies of various sections out of line with the cut-off frequencies of other sections, and the equations setforth and the nomogram make it possible to determine the configuration which should be used. As an example, the three sections of the-bell described above may be constructed as catenoidal sections with cut-off frequencies having: such a relation that the effective length curve will be irregular at a particular-point where the equally tempered musical scale differs from a harmonic relationship.

' Deviations from the smooth curve can also be provided by joining sections of different shapes. For example, a catenoid smoothly joined to a cylinder will produce effective length variations as shown in FIG. 10. Such variations can be located at various points onthe curve by changing the physical lengths of the catenoidal section. In FIG. 10 the dottedcurve and the dot'dasli curve show deviations from the smooth solid curve, with the ca piece and mouthpipe configurations and control the efiec tive lengths thereof. These are the ratio of the volume of the mouthpiece .cup to the area of the mouthpiece.

orifice, the ratio of the diameter of the orifice to the. rate of taper of the mouthpiece back bore, the length of the back bore, the length of the cavity formed by the mouthpiece and mouthpipe, and the length and the rate of taper of the mouthpipe. This makes a total of 13 varithe dot-dash curve being produced by a catenoidal section I having twice the length of the section represented by the dotted curve.

A total of at least seven design variables determine the bell shape. These are rate of taper at the small end or stem of the bell and the cut-off frequencies and ables which may be changed to control the effective length. The bell may, of course, be divided into more sections to provide more variables. Also other parts of the instrument may be constructed to provide change in the effective length with change in frequency.

It will be apparent from a consideration of FIGS. 5,

6, 7 and 8 that by control of configuration of the mouth piece, mouthpipe and bell, the effective length of the instrument can be changed with frequency to provide the desired effective lengths at the frequencies of the various notes to be played so that :the notes produced have the desired tone frequencies to fit in the equally tempered musical scale. Due to variations produced by the musician and to changes in the velocity of sound in the instrument because of changes in temperature, and even due to acoustic coupling of waves, in a room into the instrument, the intonation is influenced in any given instrument construction. Accordingly variations of intonation apart from the design of the instrument can cause intonation discrepancies and therefore small intonation variations due to the instrument construction, such as :3 cents, become insignificant as compared to other influencing factors. It isv important however to eliminate large variations in intonation resulting from the design and construction of the instrument.

It is to be pointed out that the design variables mentioned above which can be chosen to provide optimum intonation may also effect the tone quality of the instrument and the response of the instrument (the feel) to the musician. Since there is no unique set of variables required to provide optimum intonation, the selection of variables should be made giving consideration to tone quality and feel as well as intonation. Improved intonation resulting from the teachings of this invention will however provide improved tone quality and feel when the selection of variables is properly made.

l. A musical instrument of the cup mouthpiece type, said instrument having at least four major tubular sections, said sections comprising a tapered bell, a valve section connected to said bell, a tapered mouthpipe connected to said valve section, and a mouthpiece, said valve section being of substantially cylindrical form, said mouthpipe having one end shaped to receive said mouthpiece, said bell having at least three sections, each of said bell sections having a progressively increasing diameter outwardly thereof, and the rate of increase in diameter'of each bell section extending outwardly from saidvalve section being of greater magnitude, the cut-off frequencies and the effective lengths of said three bellsections being different whereby the effective length of the instrument increases with the frequency of the instrument sothat the tones produced substantially follow the equally tempered musical scale.

2. A musical instrument of the cup mouthpiece type, said instrument having atleast four major tubular sections, said sections comprising a tapered bell; a valve sectionconnected to said bell, a tapered mouthpipeconnected to said valve section, and a mouthpiece, said valve section being of substantially cylindrical form, saidmouthpipe having one end shaped to receive said mouthpiece, said bell having at least three sections, each of said bellsectionshaving aprogressively increasing'diameter out? wardly thereof, and the rate of increase in diameter-"of each bell section being of greater magnitude as the bell sections are positioned outwardly from said valve section, the cut-off frequencies of said three bell sections being different and the effective length of each bell section varying with frequency, said mouthpipe and said mouthpiece also being shaped so that the effective lengths thereof vary with frequency, whereby the overall effective length of the instrument increases with frequency in an irregular manner and the effective length is different for different tones produced by the instrument so that the tones substantially follow the equally tempered musical scale.

3. A musical instrument in accordance with claim 2 wherein said one end of said mouthpipe which receives said mouthpiece has an annular recess therein forming a cavity with a square shoulder facing said mouthpiece.

4. A musical instrument as defined in claim 2 wherein the bore of said mouthpipe has a conical taper throughout its length.

5. A musical instrument in accordance with claim 2 wherein said one end of said mouthpipe which receives said mouthpiece has an annular recess therein forming a cavity with a square shoulder facing said mouthpiece, and the bore of said mouthpipe has a conical taper throughout its length.

6. A musical instrument as defined in claim 2 wherein said valve section includes a plurality of slides and valve means for selectively connecting said slides to increase the physical length of said valve section, with at least one of said slides being constructed to have an effective length which varies with frequency.

7. A musical instrument as defined in claim 2 wherein said mouthpiece includes a cup-shaped portion adapted to be placed against the lips of a person playing the instrument, an orifice at the base of said cup-shaped portion and a back bore extending from said orifice and tapering outwardly toward the end of said mouthpiece received in said mouthpipe, and wherein the ratio of the volume of said cup-shaped portion of said mouthpiece to the area of said orifice thereof is selected to provide different effective lengths of said mouthpiece for different tones played on the instrument.

8. A musical instrument as defined in claim 2 wherein said mouthpiece includes a cup-shaped portion adapted to be placed against the lips of a person playing the instrument, an orifice at the base of said cup-shaped portion and a back bore extending from said orifice and tapering outwardly toward the end of said mouthpiece received in said mouthpipe, and wherein said back bore of said mouthpiece is shaped to have a cut-off frequency which produces different effective lengths of said mouthpiece for different tones played on the instrument.

9. A musical instrument as defined in claim 2 wherein said tapered mouthpipe has a conical bore throughout its length and the end thereof which receives said mouthpiece has an annular recess therein forming a cavity with a square shoulder facing said mouthpiece, and wherein said mouthpiece includes a cup-shaped portion adapted to be placed against the lips of a person playing the instrument, an orifice at the base of said cup-shaped portion and a back bore extending from said orifice and tapering outwardly toward the end of said mouthpiece received in said mouthpipe, with the ratio of the volume of said cup-shaped portion of said mouthpiece to the area of said orifice thereof, and the cutoff frequency of said back bore thereof, providing different effective lengths of said mouthpiece for different tones played on the instrument.

10. A musical instrument as defined in claim 2 wherein said valve section includes a plurality of slides and valve means for selectively connecting said slides to increase the physical length of said valve section, at least one of said slides being constructed to have an effective length which varies with frequency, and wherein said tapered mouthpipe has a conical bore throughout its length and the end thereof which receives said mouthpiece has an annular recess therein forming a cavity with a square shoulder facing said mouthpiece, and wherein said mouthpiece includes a cup-shaped portion adapted to be placed against the lips of a person playing the instrument, an orifice at the base of said cup-shaped portion and a back bore extending from said orifice and tapering outwardly toward the end of said mouthpiece received in said mouthpipe, with the ratio of the volume of said cup-shaped portion of said mouthpiece to the area of said orifice thereof, and the cutoff frequency of said back bore thereof, providing different effective lengths of said mouthpiece for different tones played on the instrument.

References Cited in the file of this patent UNITED STATES PATENTS 1,509,104 Hickernell Sept. 23, 1924 1,759,824 Gulick May 20, 1930 2,033,183 Dewey Mar. 10, 1936 2,288,743 Reed July 7, 1942 2,376,453 Ruettiger May 22, 1945 2,504,336 Kleczka Apr. 18, 1950 FOREIGN PATENTS 378,157 France Aug. 1, 1907 198,960 Great Britain June 14, 1923 448,869 Germany Aug. 26, 1927