Intonation Problemsof the Euphonium

A tnorough discussion of the euphonium's intona-tion problems, along with their possible solutionsis a lengthy and complex undertaking. Such adiscussion involves an examination of several in-terrelated factors common to all brass instru-ments, especially those with valves. Instrumentmanufacturer and design considerations, the con-cept of compromise tuning, the individualplayer's intonation tendencies, mouthpiece size,temperature, and several other variables are apart of this complexity. Running throughout thisentire discussion is a thread of logic and relatedideas that will enable both the teacher and per-former to deal with the problems in a knowledge-able and confident manner. The intent of this arti-cle is to condense as much information as possibleinto simpler concepts — information that can befiled away in the immediate memory and used onrecall. The more a performer knows about the in-tonation tendencies of the euphonium, whether astudent or experienced teacher, the more easily hecan deal with day to day tuning problems. It ismuch easier to react quickly and confidently whenknowing what to expect in a given situation.

One of the first concepts a teacher or performermust understand is that of compromise tuning. In-strument manufacturers are faced with the factthat intonation on all brass instruments is in-herently imperfect. They can only try to minimize

Royce Lumpkin is a music faculty member atNorth Texas State University (Denton). He teachesapplied trombone, conducts the 30-piece N.T.S.U.Trombone Choir, performs in the North TexasBrass Quintet, and supervises instruction for thebrass methods courses. He received his degreesfrom North Texas State University and the Uni-versity uf Oklahoma

HarmoAnot

grasp tRoyce Lumpkin A harm

open Idescen1-2, 2-3

or balance out the tuning problems. In designingan instrument, the maker has to decide how sharphe can allow a given note to be, realizing that if helowers it any more he will make some other notetoo flat. Problems of this type fall into two basiccategories: (1) natural overtone series discrepan-cies; and, (2) valve combination discrepancies.

Overtone Series DiscrepanciesThe overtone series, also known as the harmonic

series, can best be defined as the various frequen-cies, from lowest to highest, that may begenerated in a given length of tubing. The over-tone series for euphonium displays the charac-teristic pattern of intervals that is common to al!

Example 1 . Overtone series for euphonium.

W be £ ? =

3*5=

the other brasses: the octave, perfect 5th, perfect4th, major 3rd, minor 3rd, minor 3rd, and major2nd, etc. The first note or partial is the fundamen-tal and is also referred to as a pedal tone. The sec-ond note is the second partial as well as the firstovertone. Because the notes of an overtone seriesare derived from laws of physics, various frequen-cies do not agree exactly with our man-madesystem of equal temperament, the division of theoctave into twelve equal parts. When comparedwith equal temperament, the following results areobtained:

• partials 1, 2, 4, and 8 are in tune with eachother and coincide with equal temperament (allBts)

• partials 3, 6, 9, and 12 are sharp to varyingdegrees (F's and high C)

• partials 5, 7, 10, and 11 are f la t to varyingdegrees (D's, At, and E).Because the bulk of the euphonium's standardplaying range falls between partials 1 and 8, a per-former can simplify and condense this informa-tion to the following:

• partials 1,2, 4, and 8 (all B^s) are in tune• partials 3 and 6 (F's) are sharp• partials 5 and 7 (D and At>) are flat.

Of these, partial 3 is so slightly sharp it can becorrected easily by the embouchure, while partial7 is too flat to be used. This leaves only partial 5(moderately flat) and partial 6 (noticeably sharp)that are of concern.

It is helpful to remember that the partials areout of tune to a degree that corresponds to theirnumerical order: partial 3 is the least out of tune,followed in order by partials 5, 6, and finally 7.

Example

Each n4th paFor exovertoimode ;as the -from tl

Valve (The

lems otion dstrum<comprmaketo lowvalve 5first v;valve <steps.binati<surfaclengththan t'alreadlength(perhacent cwholeseconishortecontirthe vaL. KeConn,ampleused i

Exampcorrect

1 8 THE INSTRUMtNTALISI /MAY HHI

iarmonic ModesAnother term needs to be defined in order to

rrasp the implications of the out-of-tune partials.\c mode results from the lowering of anyipen tone chromatically through the normalDescending chromatic valve sequence of open, 2, 1,[-2,2-3, 1-3, and 1-2-3.

xample 2. The fourth harmonic mode.

1 1-2 2-3 1-3 1 -2 -3

ti l>r»—

Each note of the harmonic mode is the respective4th partial of that valve setting's overtone series.For example, the G is the 4th partial of the 1-2overtone series. Each note in a given harmonicmode assumes the same intonation characteristicas the open valve note because they are all derivedfrom the same respective partial.

Valve Combination DiscrepanciesThe second major area of inherent tuning prob-

lems on the euphonium is that of valve combina-tion discrepancies. Manufacturers of valved in-struments have long wrestled with the problem ofcompromise tuning. They know that they canmake the separate valve slides the correct lengthto lower each valve an exact amount. The secondvalve slide lowers the open tone one-half step, thefirst valve slide lowers a whole step, and the thirdvalve slide lowers the open horn one and one-halfsteps. It is not until the valves are used in com-bination that serious intonation probems begin tosurface problems of proportionate tubinglength. If one starts with a longer piece of tubingthan the open horn (perhaps with the second valvealready down) it will obviously take a longerlength of tubing to lower the pitch a given amount(perhaps another whole step). If it takes four per-cent of the total tube length to lower the pitch awhole step, four percent of a longer tube (with thesecond valve down) is more than four percent of ashorter one (the open instrument). Therefore, wecontinually come up short of tubing when usingthe valves in combination. Example 3 from EarleL- Kent's The Inside Story of Brass Instruments,Conn, 1956, p. 3, shows valve slide length ex-amples chosen to give correct intonation whenused individually.

Example 3. Valve slide length examples — individuallycorrect intonation.

ValveUsed0~~

213

1-2

2-31-3] 0 oi -^-3

ValveSlideLength(inches)

5.9512.2518.9218.2024.8731.1737.12

ActualTotalLength(inches)

100105.95112.25118.92118.20124.87131.17137.12

CorrectTotalLength(inches)

100105.95112.251 18.92118.92125.99133.48141.42

TotalLengthError(inches)

0000

-0.72-1.12-2.31-4.30

TuningDiscrepancy(semitones)

0000

+ 0.11+ 0.15+ 0.30+ 0.54

The sharpness of all the combinations is readilyevident: 1-3 is almost a third of a semitone sharpand 1-2-3 is slightly more than a quarter stepsharp. Faced with this physics problem, instru-ment manufacturers resort to the idea of compro-mise tuning as a partial solution. This tuning is ac-complished by purposely making the various valveslides longer than they need to be. Depending onthe manufacturer the first and second valve slidesmay be lengthened slightly, while the third valveslide is always made longer. Because this valve isseldom used by itself, it can be made purposelyquite flat in an effort to lower the sharp 1-3 and1-2-3 combinations. Example 4, also from The In-side Story of Brass Instruments, shows valve slidelength examples chosen to give slide compromiseintonation.Example 4. Valve slide length examples — compromiseintonation.

ValveUsed

02131-22-31-31-2-3

ValveSlideLength(inches)

6.2512.5720.3518.8226.6032.9239.17

ActualTotalLength(inches)

100106.25112.57120.35118.82126.60132.92139.17

CorrectTotalLength(inches)

100105.95112.25118.92118.92125.99133.48141.42

TotalLengthError(inches)

0

-f 0.30+ 0.32+ 1.43-0.10+ 0.61-0.56-2.25

TuningDiscrepancy(semitones)

0-0.05-0.05-0.21+ 0.01-.08+ .07+ .28

The compromise tuning should be evident. Eachof the individual slides are tuned lower (an almostnegligible amount in the case of the first and sec-ond valves) to take some but not all of the sharp-ness out of 1-2, 1-3, and 1-2-3; however 2-3 becomesflat. No matter how each manufacturer goes aboutdesigning a three-valved instrument, he must stilldeal with this basic and inherent problem.

Cumulative EffectIn some cases the natural tendencies of valve

combination discrepancies and harmonic modediscrepancies may be opposite and therefore off-set each other. This phenomenon is illustrated inthe cumulative effect of the 3rd and 5th harmonicmodes.Example 5. Cumulative effect 3rd harmonic mode.

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8 ( 8 I it It

Example 6. Cumulative effect 5th harmonic mode.

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Assuming that "degree" is merely a relative term ofmeasurement, the third harmonic mode (example5) could be described as a one-half degree sharpharmonic mode. We can assume the following:

• a negligible first valve, second valve, and 1-2combination valve slide length error

MAY 19B1/THE INSTRUMENTALIST 19

• a one-half degree flat 2-3 fingering combina-tion error

• a one-half degree sharp 1-3 fingering combina-tion error

• a two degree sharp 1-2-3 combination error.The resultant numbers display the negating orcompounding effect of the two inherent intonationvariables. In example 6 assume a one degree flatharmonic mode with the same valve error factorsas above.

Although these inherent tuning problems are ofprime concern, there are obviously several otherfactors that influence intonation. Mechanical tun-ing devices, the addition of a fourth valve, com-pensating valve systems, environmental tempera-ture, mouthpiece and instrument design, andvarious physical considerations relating to lips,teeth, tongue, and air speed all have their effect onintonation.

Mechanical Devices — Added 4th ValveThrough the years a number of attempts have

been made to design adjustable kickslides for thethree-valved baritone or euphonium similar tothose found on the cornet and trumpet. Suchdevices were usually attached to the main tuningslide and were often spring-loaded in some man-ner. None have been widely accepted, perhapsbecause they proved too awkward to use. Becausea truly successful system was never adopted,there are countless three-valved baritones in usein the public schools today that are impossible toplay in tune. C3 and B2 are two of the most com-mon intonation problems on these three-valved in-struments. The notes are extremely sharp and theplayer can either lip them down, manually pull thethird valve slide, or do both. Because pulling theslide while playing is difficult to accomplish (if notimpossible on the typical school instrument), theplayer is left with little choice other than to lipdown as best he can.

Fortunately, there is another solution to thisparticular problem: adding a fourth valve to theinstrument. This valve lowers the open instrumenta fourth, making it an interchangeable fingeringfor 1-3. Because it is independent of the otherthree valves, the fourth valve slide can be made ofsufficient length to play C3 in tune. Similarly, theB2 may be played 2-4 rather than 1-2-3. Extendingthe lower register is another benefit of the addi-tional valve. Because the fourth valve (like thetrombone F-attachment) lowers the fundamental afourth to F2, a new overtone series is createdalong with a new set of harmonic modes. Thefollowing example shows the harmonic mode thatbridges, the gap chromatically from E2 to thepedal B b l .

Example 7. Fourth valve, second harmonic mode. Non-compensating f ingerings.

Not2 3 l\

available

Here again there are problems with the propot maker oftionate tubing length rationale the note careful arbecome sharper as the player proceeds downwar( promisesthrough the fingerings. By the time a euphqniumist reaches the D2 on a non-compensatinlphysical Cfour-valved instrument, he will likely have had t| Varioustry three fingerings, each Hatter than thjthe tuninpreceding one, before the pitch is lowered enough degree. Afor correct intonation. The D?2 usually requires!down,1-3-4 fingering and the C2 a 1-2-3-4 fingering, leaving no additional tubing for the Bl.

an

Compensating Valve SystemThe compensating valve system available 01

some euphoniums offers a practical solution ti

easier toonly so fafected, m;pitch adshould being the nfingering:the intonation problem by adding small knuckles;

of tubing to each of the valves. This extra tubing make sm£comes into play only when valves are used in comj • openibination, lowering the pitch when needed ana more opeenabling the player to use the normal descending • chan£chromatic valve sequence down through B1. | to an "EE

• varyi:

Example 8. Fourth valve, second harmonic mode. Compansating fingerings.

'•*

TemperatureThe effect of temperature on the pitch of the eu

phonium needs little explanation to those whhave marched at halftime on a Friday night in November, or sat on the concert stage under blazinglights in April. All brass instruments sharpen asthe temperature rises, and vice versa. Thi,phenomenon occurs because sound waves travefaster through warmer, less dense air. They strikthe ear at a faster rate, and the listener perceivethem as a higher frequency. Students sometimesattempt to explain the sharping phenomenon b)arguing that the rise in temperature causes thmolecules of the instrument to agitate, resultingin an expansion of the instrument's metal. A li t t lelogical thought should convince the student thaan expanded (larger) instrument would produce ilower sound, not a higher one.

Mouthpiece and Instrument DesignMouthpiece and instrument design also in

fluence intonation. It is beyond the scope of thiarticle to go into great detail concerning the man)variables. In dealing wi th mouthpieces, cup:volume is the most important consideration — thegreater the volume, the f la t t e r the pitch. The size!of the throat opening, and the size and shape of the;backbore also interact to influence intonation. In-designing an instrument, the manufacturer mayraise the flat f i f t h partial or lower the sharp sixtbpartial, but the inherent proportionate differencemust remain the same. Another manufacturermay f la t ten individual valves more than another,but the relationship between individual valves andvalves used in combination remains the same. Ineither situation the inevitable is compromise. The

blows sh;

Vibrato -Vibrate

common!satisfactceuphoniucontrollelower lipwill alte:center to(or perhcmoderatipriatene;hances ai

More ;ensembl<mute forthat the:pitch.

ImproviiIn the

encoura;on the rrfamiliarcouragevery st£pitcheseasier to

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20 !HE I N S T R U M E N T A L I S T , MAY 1'lm

breath (1lems wistream,euphonitonation

In latneeds toregularcourageto-day b

>r maker of fine instruments will have achieved ae careful and controlled balance when making com-fj promises for good intonation.

-). physical Considerationstr Various physical considerations also influencebt the tuning, though usually to only a moderatejj degree. All euphonium players must lip up or

I down, and they soon learn that it is generallyn easier to lip down than up. Obviously one can lip

I only so far before the tone quality is adversely af-! fected, making this technique best suited for small| pitch adjustments. Larger pitch adjustments

J snould be approached first through carefully tun-ic-ing the main tuning slide and/or using alternatee| fingerings. Other factors which may be used toIE make small adjustments in pitch include:4 • opening the teeth or dropping the jaw (theif more open, the more tendency to lower the pitch)

• changing the tongue position (arching more in-to an "EE" syllable tends to raise the pitch slightly)

• varying the air speed (the euphonium over-blows sharp and undersupports flat).

Vibrato — MutesVibrato and mutes also affect tuning. The most

commonly used and (in my opinion) the onlysatisfactory method of producing vibrato on theeuphonium is the lip-jaw vibrato. The slight andcontrolled up and down motion of the jaw andlower lip ("ya' ya, ya, ya") as the tone is sustainedwill alternately lower and raise the pitch from

jf- center to slightly below center and back to centercf (or perhaps even slightly above center). Done injf moderation and with regard to stylistic appro-aipriateness, this pleasant bending of the tone en-jl hances and warms the instrument's sound.ef More and more contemporary solo and largec| ensemble literature calls for the use of a straight

mute for the euphonium. Players should be awarethat these mutes generally tend to sharpen thepitch.

n

-Iu:jui

Improving IntonationIn the beginning stages of the student's training,

encourage the buzzing of various interval patternson the mouthpiece alone. Let young players buzzfamiliar tunes, scales, or other patterns that en-courage selectivity and accuracy of pitch from thevery start. When they attempt to reproducepitches on the instrument, they should find iteasier to center the pitch more accurately.

There is no substitute for teaching fundamen-tals in the first months of a student's experiencewith the euphonium. The young player must de-velop concepts of correct embouchure and properbreath (tonal) support. If there are no major prob-lems with embouchure and the use of the airstream, the student and teacher can expect theeuphonium to react predictably with regard to in-tonation.

In later stages of development, the teacher£eds to stress listening and matching pitches on a

regular basis. One of the best opportunities to en-courage this careful listening on a consistent day-to-day basis is in the warmup period, either in a

group or individually. Directors of large ensem-bles should devote 10 to 15 minutes of eachrehearsal (if time allows) to let students warm upon long tones, lip slurs, scales, unison studies, orchorales for the express purpose of balancing,blending, and matching pitch. The private teachershould encourage a similar warm up and occa-sionally play along with the student to provide apitch standard and encourage more discriminatelistening.

Directors should also devote an occasional sec-tion rehearsal to a lecture-demonstration on in-tonation to let the euphoniumists hear beats andmake necessary corrections. This is the ideal timeto sort out and correct intonation problems withinthe immediate section.

Once the player has achieved some maturity andstability in tonal production, he should be en-couraged to spend some time in front of an elec-tronic tuner and make out an intonation tendencychart. The procedure consists of writing out thechromatic scale for the basic range of theeuphonium and then notating whether each tonetends to be sharp or flat. An arrow pointing up ordown over the note could indicate sharpness orflatness and the length or size of the arrow couldindicate the degree of the tuning problem. If thisprocedure is repeated several times with a degreeof consistency, the student should see clearlyemerging tendencies in playing certain notes outof tune, with his personal set of variables (em-bouchure, air usage, mouthpiece, instrument,etc.). Once the student understands and identifiesthe problem, the correction process becomesmuch easier.

The tuner can be an immense help in thedevelopment of pitch awareness, but it is impor-tant for the student and teacher to avoid excessivedependence on the device. Tuners should be usedfor their intended purpose — a very importantguide to correct tuning and a point of departurefrom which the ear must take over. Accuracy ofpitch on the euphonium requires both muscularand aural memory. Lipping pitches in tune mustbe done before the pitches actually sound. Oncethe pitch has sounded, it can be fine tuned by us-ing the ear.

SummaryClearly a discussion of intonation problems in

any depth is destined to be lengthy. The many fac-tors that influence tuning are complexly inter-related, yet most can be distilled into a few easilyremembered facts once the concepts are under-stood:

• there are a handful of notes that are out oftune because they belong to an out of tune 5th or6th partial

• there are a handful of notes that are habituallyout of tune because they are played with valvecombinations that are predictably sharp or flat

• there is a cumulative effect resulting from theinteraction of the out-of-tune partials and the out-of-tune fingering combinations

• the fourth valve eliminates a major tuningproblem in that it can substi tute for the quitesharp 1-3 combination

• the compensating valve system on a four-valved instrument allows the notes from E2 topedal B^ 1 to be played with the normal fingerings

• temperature, various physical considerations,even vibrato and the use of mutes affect pitchmoderately and in a generally predictable man-ner.

If the student hears pitch reasonably well, con-scientiously tries to play in tune, produces thetone correctly, and has a reasonably well-made in-strument that is in tune with itself, there are onlya few notes that usually cause a large percentageof the tuning problems on the euphonium.

Example 9. Common intonation problems.

G3 in example 9 is often sharp in 1-2 and can bjlowered by substi tuting third valve. D3, C3, ari(jB2 are habitually sharp. The use of the third valv]substituting for 1-2 on D3, the fourth valve for C3!and 2-4 for B2 usually corrects these troublesorn|notes. The next three tones (D4, C#4, and C4) ar|usually flat because they are all 5th partial notes!Similarly, F4, E4, and EM are always sharjbecause they are all 6th partial notes. Alternatifingerings should be tried on all these notes unt jthe best intonation is obtained. The F4, E4, aniE'M can be lowered on some four-valved compensating system euphoniums by adding the fourtlvalve. The final five upper register notes in the e?ample may be fingered as marked if they are toi

It is genethe most iiplayer owntime helpinpensive itfdoesn't ha'necessary Vas well as ;

1 i-a

Tr/

flat in their normal fingerings. ctensticsteacher gui

Musicians w i l l never eliminate intonation probferrnou P1'lems from their playing. However, an effort t| Certain vunderstand the reasons tor basic tuning problems have predii

fro

-ff.' /

nr-i/ 2 2 - a \

1 -4 2-3 1 — [^~1 1 -2-3 r̂

can lead to marked improvement. No player oiteacher should be ignorant about how to achievfgood intonation. There are solutions to the probilems; we need only understand, listen, and appljwhat we know.

We'll starttendencies.

r i m

T.U.B.A. Stands for EuphoniumDon Little

The mass tuba-euphonium ensemble assembled at North Texas State University during the Second National Tuba-Euphonium Symposium-Workshop in May, 1980.

The Tubists Universal Brotherhood Associationspresents the interests and aspirations of nearly,000 euphoniumists and tubists in more than twoozen countries. Our constitution states thatf .U.B.A. is a worldwide organization of musi-ians. . .who take a significant interest in the in-fruments of the tuba and euphonium family. . . . "ven though "and euphonium" was added recentlyy a majority membership vote, the euphoniumas always been considered an equal partner inae association.This equality of emphasis is illustrated in

^veral ways. First, all musical works commis-.oned by T.U.B.A. have been evenly divided be-veen the euphonium and tuba, and the premiereDmmission was Four Dialogues, for euphoniumid marimba, by Samuel Adler. Second, the• L/.B.A. Journal devotes equal space to the con-;rns of the euphonium. In each quarterly issueicre are reviews of solo literature on the college,rofessional, and junior/senior high school levels;

reviews of tuba-euphonium ensemble literatureeuphonium disc reviews; plus articles, interviewsand announcements of interest to euphoniumists.

T.U.B.A. considers the euphonium to be a vita20th century instrument, and is working to give ila permanent and versatile position in the musicalworld. For more information about T.U.B.A., afree sample of the T.U.B.A. Journal, or an applicaition for membership write to Donald C. Little;Secretary-Treasurer of T.U.B.A., School of Music'North Texas State University, Denton, Texas. IIyou are a euphoniumist and are interested in thefuture of your instrument, we need you and youiideas, and you need us. In case you may have forgotten, we accept tubists for membership, too. •

Donald C. Little is assistant professor of tuba andeuphonium at North Texas State University and isprincipal tuba with the Fort Worth Symphony Or-chestra. He received his degrees from Peabody Con-servatory and Northwestern University.

IHE INS1RUMKNI ALIST, MAY 1'IHl

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