Michael Scott

The Problems of Intonation in Instrumental Ensemble Contexts

 

(From a Flute player’s perspective)

 

 

Equal temperament is a method of tuning keyboard instruments that allows them to be equally and approximately in tune (actually equally out of tune), in all keys. This is too complicated a subject to go into here, but it suffices to say that we cannot sustain chords in equal temperament without them sounding out of tune. As Piano sound decays quite rapidly, the problem is not so obvious, but sustained chords must be played in a more just (exact) temperament.

Prior to the development of equal temperament, different types of tempering were used which would work well in some keys and not so well in others, because of the impossibility of a fixed pitch for each note sounding acceptable in all circumstances.  Keyboard instruments would be re-tuned for compositions in different keys – still common practice today with the harpsichord in performances of early music.

 

 

An accomplished and expressive player with brilliant finger technique, etc., but unable to well play in-tune will have severely compromised prospects. Understanding the basic mechanics of tuning is a great advantage in dealing with this vexatious subject, but unfortunately intonation is rarely addressed at more than a superficial level. Since the whole purpose of learning to play a musical instrument is generally to play together with others, it’s a serious omission.

 

Experienced musicians will adjust their intonation instinctively. When moving from a chord which is perfectly in tune to another which is not, many will believe that because “they” were in tune in the last chord it must be somebody else’s fault (definitely not their own) that the next chord is out of tune. So they will adjust their note, very often grudgingly, believing that "they" were correct and somebody (even everybody) else is at fault.

It is simply not understood that the very nature of what they are doing demands large, sometimes unmanageable, alterations in the pitch of a note depending on its context in a chord.

 

Of great assistance in the process of training and refining the ear, is the “resultant” tone. This is heard in a suitable acoustic when any two notes sound together, it’s pitch being the difference between the frequencies of those two notes. Also known as a “difference” tone, it is either a buzz of indeterminate pitch, or it can be a third musical sound that might be another note - however, mostly it’s out of tune.

 

 

Example:

 

When tuned in Equal Temperament:

Pitch of "A" = 440 Hz.

Pitch of "E" = 659.3 Hz 

 

 

Sharpening "E" from its equal tempered frequency of 659.3 to 660 Hz, and playing it together with an “A” of 440 Hz will give an in-tune resultant, or difference tone, of 660 - 440 = 220 Hz. This is one octave below the original "A" (440) and is quite audible. It is easily demonstrated, sounding three notes from two players. Hence a perfect fifth has its name, with a mathematically perfect ratio of 3 / 2.

 

When the interval A - E (a perfect fifth), is to be played in tune, the E needs to be sharpened by 0.7 Hz compared with equal temperament.

 

A perfect fourth is the inversion of a fifth, and this interval will need to be flattened by an equivalent amount to give an in-tune resultant.

 

A - D is a perfect fourth.  The D will need to be flattened about 0.7 Hz from its equal tempered pitch, and the resultant tone will be D an octave lower.

 

Playing a fifth, the resultant tone is one octave below the lower note. Playing a fourth will produce a resultant tone one octave below the upper note.

 

Two players playing a perfect fifth followed by a perfect fourth, making the necessary adjustments, will hear the resultant tone change as follows:

 

A played together with E above: resultant = A one octave lower.

A played together with D above: resultant = D one octave lower.

 

 

Now adding a major third to an in-tune perfect fifth:

 

A major third needs to be flattened greater than seven times more than a fourth. Most instrumentalists don’t believe it at first and many find it impossible. Clarinet players, for example, have to work very hard to get this much adjustment, although for a flute player with a supple embouchure it is relatively manageable (see quartertone exercise below).

 

It can be easily demonstrated by playing a chord. For example: A and E, a perfect fifth, is first played in tune with the resultant tone sounding clearly. The major third, C#, is added, sounding very much out of tune until flattened sufficiently. At this point the chord of three notes will be beautifully in-tune, sounding like the humming top which many of us had as a child.  The pitch of an equal tempered C# is 555.3 Hz.  When flattened and in-tune in the chord, its pitch will be adjusted to 550 Hz, so that the various frequencies involved will be as follows:

 

E          660 Hz

C#       550

A         440

Resultant 1 =   220 (660 - 440) sounding “A” one octave lower.

Resultant 2 =   110 (660 – 550; also 550 – 440) sounding “A” a further octave lower.

 

Note that the difference between E and C# is the same as that between C# and A, at 110Hz. One octave below the first resultant, this is clearly audible in a suitable acoustic. The difference between the two resultant tones is also 110, so this frequency is strongly reinforced.

 

 

Exercises

 

Initially attempt these exercises with like instruments, and without any trace of vibrato

 

Understanding the above, a group of three players plays chord progressions as follows:

 

1:         Chord 1:          A - C# - E.                

 

Start with the fifth A – E, and get this in tune before adding the third. C# is a very sharp note on the flute and needs considerable flattening to get it in tune in this context. The first time attempted, players think it is ridiculously flat, until it suddenly snaps into focus – as long as those playing A and E haven’t lost their way in the confusion.

2:         Chord 2:          F# - A# - C#.              

 

This time the A# will need flattening, and C# will move up from its flattened pitch in Chord 1.

 

Move back and forth between the two chords slowly, taking time to adjust the pitch for each change.

 

The players could then take each pair of notes in turn, making the necessary adjustments to the pitch, as follows:

 

Player one plays:         A in chord 1;   A# in chord 2.

Player two plays:        C# in chord 1; C# in chord 2.

Player three plays:      E in chord 1;   (low) F# in chord 2.

 

Practice using other chord progressions in which the third of one chord becomes the fifth or the root of the next. For example:

 

Chord 1           A  C#  E

Chord 2           F#  A#  C#

Chord 3           E flat  G  B flat

           

The Player with C# in chord 1 plays C# in chord 2 adjusting the pitch upwards.

The Player with A# in chord 2 plays B flat in chord 3 adjusting the pitch upwards.

 

Rotate the notes among the players as before. Remember that the major third will always have to be flattened a lot and the fifth sharpened a little.

 

A Seventh will sound perfectly in tune when played suitably flat (even flatter than a major third), and softly, in an in-tune major chord: e.g. A - C# - E - G. Usually A and G played together will be discordant, but in this context the sound is harmonious and beautiful.

 

An equal tempered G has a frequency of 392Hz. If flattened by 7Hz (a lot), to 385 and played with an E (660) the resultant will be 275Hz. This is one octave below C# (550Hz).

 

 

The upper note of an octave needs to be flattened - the top note will need to be sharpened if sustained when the lower one stops, otherwise it will then sound flat. In an orchestra, the solo flute player, having the top line, will feel that all is well until suddenly he or she is the only one playing - and sounding flat. It’s necessary to raise the pitch in order to sound OK!

It helps a lot to know that this isn’t an aberration or a mistake, but is part of the very nature of our business.

 

At times the flute player is blamed for being out of tune when a chord in the lower woodwinds is faulty. For example, the bassoon and clarinet may play a major third out of tune and there is just nowhere for the flute player to place his or her note. It will sound wrong wherever it is pitched. Since the flute is on top and more easily heard this is where the finger is pointed! Piccolo players deserve a great deal of sympathy in this respect.

 

Exercising with chord progressions will develop skill and flexibility in understanding and adjusting intonation.

 

Flute players understand that when they are loud they are likely to be sharp, and when playing softly

they will be flat, which is exactly the opposite of every other member of the woodwind family (and the Brass). If you think that the Clarinets, Oboes and Bassoons (and Brass) are going to follow the flutes around - think again.

 

It is more difficult for all the other woodwinds to adjust their pitch, and flute players have the responsibility to help them out because for us it is very much less difficult.

 

 

 

 

Quarter-tone Exercise.        

 

In order to develop the flexibility and ability to play in tune under all circumstances, the following exercise is useful.

 

Throughout this exercise, sound quality is not important, and we should play without vibrato.

 

Starting with low A, play as sharp as possible.

 

Play B flat - as flat as possible, until the pitch is exactly the same as the sharpened A. Alternate between the two notes, matching the pitch, which will be a quartertone between the A and B flat.

 

Do whatever you need to make these extreme changes in pitch and forget about the quality of sound – the pitch is much more important.

 

Next:   Play B flat as sharp as possible.

Play B natural - flat, to meet the above.

 

This will produce a quartertone between B flat and B natural.

 

Proceed up and down the instrument, until quartertones are produced throughout the range as high and low as possible.

 

Tune your instrument to a piano. A good way is to play low D and top A on the flute, about mezzo forte, and get it in tune with a chord D F A on the piano (the D next to middle C). Next play the quarter-tone exercise, ignoring the piano.

 

When you get to the quarter-tone between E flat and E natural at the top of the stave, play it as softly as possible - ppp. The sharpened E flat is a quarter-tone sharp. So you believe. Now play an E flat major chord on the piano. Most flute players are surprised to find that their “sharpened” E flat (a quarter-tone sharp, remember?) when played ppp, is only just in tune with the piano’s E flat major chord!

 

When we are playing very softly, in order to correct the resulting flatness of our instrument, we will at times need to push the pitch up as much as a quarter-tone in order to simply stay in tune, and conversely when playing very loudly.

 

Instruments with different overtone structures (such as Bassoon and French Horn), at times find that their overtones are so powerful that they clash when playing a particular interval, even though the fundamentals are in tune. In such situations it can be next to impossible for them to sound really well in tune together.

 

When thinking of the accolades given to a well-intoned String Quartet, one does well to realise that a similar achievement from a Wind Quintet represents a far greater accomplishment. The wind instruments are more diverse and have different overtone structures. The wavelength from a flute is equal to its physical length (plus “end correction”, which we’ll ignore for now). The wavelength of a clarinet is double the instrument’s length, and for oboe & bassoon the wavelength is one and a quarter times their physical length. Variations in pitch caused by changes in temperature and humidity thus affect each instrument differently.

 

The international standard A = 440 Hz is specified at 21 degrees Centigrade. For every change in temperature of 2 degrees the frequency of the note produced by a specified tube length will change by 1 Hz. Thus at a temperature of 15 degrees, which is 6 below 21, the pitch we should tune to is 3 Hz lower, being A = 437 Hz.  At a temperature of 31 degrees, not uncommon in Australia, we should be tuning to A = 445 Hz. Attempting to play at A = 440 under these conditions will result in much greater difficulty and poor intonation. The relatively modern addition of air-conditioning to our performance spaces has brought much needed relief from these extremes.

 

 

The very sociability of making music together presents a plethora of problems. Differences of timbre, overtones, vibrato and temperature can present difficulties that appear to be quite insurmountable.

 

Intonation is everybody’s problem, and everybody’s responsibility.

 

 

Copyright: Michael Scott, 2002