Understanding and Improving Intonation

INTRODUCTION
Playing with good intonation in an ensemble setting is a performance skill. It must be practiced diligently, just as you would practice scales, sight-reading, multiple tonguing, etc. Unfortunately, few of us practice “being in tune,” either because of an ignorance of its importance, or because of confusion on how best to proceed. The result is that over the course of a typical rehearsal, numerous unison lines remain out of tune, chords do not “ring true,” and performers do not get the best possible sound out of their instruments. ​

​Good intonation presupposes two ideas: 

1. You understand  the intonation deficiencies and tendencies of your instrument;
2. You know how to quickly correct them or compensate for them.

This entry will offer suggestions for training and improvement on both counts. As with anything else I ever post here, the subject material is drawn from myriad sources, including published research, colleague and mentor/teacher opinions, and experience conducting ensembles for the past twenty-five years. There is also a wealth of information to be found on YouTube - provided you can adequately sift through the information to find the important nuggets. However, this is not intended to be "the final word" regarding intonation - if you have anything to contribute, be it a correction, an emendation, or an addition, please don't be shy about replying and/or emailing me. I've been studying intonation for a long time, but will never fully master all there is to learn, and am always open to new ideas and opinions.

​FACTORS THAT CAUSE POOR INTONATION
It is important to understand why poor intonation is so prevalent. The following areas of concern can cause poor intonation by themselves, though they are (unfortunately) usually paired with other factors:

The Instrument/The Mouthpiece

• Poorly-constructed or low-quality instruments;
• Leaking pads, water keys, and/or joints (woodwinds);
• Worn out or cracked/chipped reeds (woodwinds);
• Incorrect reed strength or placement on mouthpiece (woodwinds);
• Stuck or dented tuning slides and valve slides (brass);
• Dents in the body of the instrument or on the mouthpiece (brass);
• Poor quality mouthpiece (brass, clarinets, saxophones);
• Shallow mouthpieces affect the basic overall intonation of the instrument, producing sharpness (brass instruments).

Dents in instruments cause intonation issues

Basic Playing Procedures

• Poor playing posture and/or hand or finger position;
• Poor embouchure formation;
• Insufficient air support - cold, fast air is required to set the air column vibrating…always use a focused, fast stream of air, even when playing softly (ESPECIALLY when playing softly!)

​
Not Playing in the Standard Tuning Frequency

• Wind instruments are manufactured to play in tune with the main tuning mechanism pulled part way out, allowing you to make minor adjustments;
• No instrument’s main tuning slide should ever be pushed all the way in, or pulled all the way out...if that is the only way for you to be in tune, it is indicative of a wider problem;
• The standard tuning frequency is 440Hz or cycles per second, which corresponds to our Concert A. Another frequently used tuning frequency is 442Hz. Deficient intonation may occur if you are tuning wind instruments to any other frequency.

Insufficient Warm-up Time

• Modern-day wind instruments are constructed to play in tune at an external temperature of 72 degrees Fahrenheit, at sea level, after a proper warm-up;
• Because the temperature of human breath is around 98.6, the breath gradually raises the temperature of the air inside a cold instrument, thus raising its pitch;
• Sound travels faster in warm air than in cold, because the air molecules are less densely packed together. This is the physical reason why wind instruments will sound flat when cold, and sharp when hot;
• Metal instruments warm up and cool down faster than instruments made of wood or plastic (flutes are the exception, as flutes do not tend to get much warmer because the performer is breathing across the mouth hole, not into the instrument itself, as with brass instruments); 
• Large instruments, such as the tuba, take longer to warm up than smaller instruments. For this reason, all wind players should warm up on their own at least five to ten minutes before tuning (chorales are great for this purpose in ensemble settings);
• During long rest passages, the internal instrument of your instrument can be maintained by softly and slowly blowing warm air through it. Flutes can keep their instrument warm by holding it close to the body or keeping hands on the instrument;
• Always be alert for environmental factors that may affect tuning (for example, a too-cold room, a warm, humid environment, heat from stage lights, etc.)

Psychological/Musical Phenomena

• While sound is a physical phenomenon (in the form of vibration), the interpretation of that sound by our brains is a completely psychological one, and is therefore subjective and can be manipulated in several ways;
• Octaves can often sound “stretched” to our ears: the higher octave will sometimes sound sharp, the lower octave will often sound flat. Both ends of the octave should always listen inward;
• Low tones played loudly tend to sound flat, while high tones played loudly tend to sound sharp;
• In general, humans tend to be more tolerant of sharpness than flatness in the middle and upper registers, and more tolerant of flatness than sharpness in the lower ranges.
• Playing with a tuner on your stand can be detrimental to the development of listening skills. Tuners should only be used to tune your overall instrument, not to attempt tuning every single note you play (especially when you are part of a chord). 

Not a great idea for being in tune in an ensemble setting...

Pitch Tendencies of Instruments and Performers

• Generally speaking, inexperienced wind players tend to play high notes sharp (pinching and tension) and low notes flat (not enough air support);
• Brass players and flautists tend to go sharp in crescendo, while clarinetists and saxophonists tend to go flat (the reverse is true in decrescendo);
• Regardless of quality or brand, every instrument has certain notes that are inherently out of tune with the equal tempered scale. Finding these troublesome notes and working out a solution to the problem should be paramount to all conscientious wind players…for this reason, it is highly suggested that you create a tuning tendency chart for yourself once a year, or anytime you get a new instrument, mouthpiece, etc.;
• Most performers will continue to grow sharp the longer they play, until a point of fatigue is reached at which point the instrument will begin to grow flat due to embouchure issues. Be aware of this tendency and compensate!

THE TUNING PROCESS
With the exception of oboes and bassoons, wind instruments are manufactured to play sharp when the headpiece, tuning joints, or slides are closed/pushed in. Therefore, players must lengthen their instrument by pulling out the main tuning mechanism, whatever it is for that instrument. When tuning in an ensemble setting, the following basic procedures should be followed by all wind players:

• Warm up thoroughly before tuning to make sure your instrument is at equilibrium temperature with the environment.
• Tune to a reliable frequency, and use the basic tuning notes recommended for your instrument (usually F for brass instruments and clarinets, A for most other woodwind instruments). Please note that while B-flat is an ok tuning note, it does induce a small element of strain in brass players, and F is a better tuning note (which also allows the clarinet to tune its barrel joint). 
• Tune at a mezzo-forte dynamic level, and do not use vibrato. 
• Humming the tuning note softly to yourself allows you to focus and internalize the pitch much better than simply “attacking” the note.
• Do not try to “humour” the tuning note…play it straight. Adjust the main tuning mechanism if your instrument is flat or sharp, do not “lip” the note into place.
• Adjusting the tuning note with your embouchure (“lipping”) does not mean you are in tune…it just means you have fixed that one single pitch, and that you will have to keep fixing it every time you come back to it! 
• The first effort you make while tuning should be to find out how far out of tune you are, and then make the length adjustment. The second effort should be to fine-tune any minor deficiencies, and the third effort should be to verify. A good player can do all of this in a few seconds. 
• In addition to tuning the main tube length of the instrument, brass players should tune the length of each individual valve in relationship to the overall length. Neglecting to do so may cause intonation deficiencies with individual fingering combinations.
• Softly re-articulate the tuning note from time to time at random. This will allow you to “get back in touch” with your own sound, which may have become blended into the overall sound of the ensemble (which is a good thing!)
• As soon as you’ve tuned – stop playing. The tuning process is not intended to be a long one. Ideally, you will already be close enough when the tuning note is sounded that it should not take you very long to ascertain where you are in relation to it.
• Use your tuning slides to fix the overall intonation on your instrument, and use your embouchure only for correcting small deficiencies on the go. Players should practice lowering and raising pitches using this physical technique without grossly distorting the tone quality or dynamic level.

THE HARMONIC SERIES
The Harmonic Series is a naturally occurring (i.e., not man-made) acoustic and mathematical phenomenon that is the underlying foundation for the construction of sound on string, woodwind, and brass instruments. The series consists of frequencies (pitches) that are related to each other via whole number ratios of the lowest possible frequency, which is known as the fundamental. 

For example, if the fundamental was 10Hz, then 20Hz (2xF), 30Hz (3xF), 50Hz (5xF), and 100 Hz (10xF), would allbe harmonic frequencies of the fundamental. 55 Hz would not be a part of the harmonic series, because it is not a whole number ratio to the fundamental (5.5xF). 55Hz would, however, be a part of the harmonic series if  the fundamental were 11Hz.

These frequencies, known as harmonics, are possible because of complex vibrations. All freely vibrating bodies (such as a piano string or an air column) vibrate not just along their entire length, but also in halves, thirds, fourths, etc., theoretically onward into infinity. The smaller each segment of string (or air column) vibrates, the higher the frequency (pitch) produced above its fundamental, hence the name we often use synonymously with harmonics: overtones.

Many of these overtones are inaudible to the human ear (just as many of the secondary vibrations are invisible to the eye). The lower the note played, the more obvious the overtones to our ears. This is why low notes on the piano, for example, tend to have such a vibrant and rich quality (try it out next time you are in a practice room...strike the lowest keys on the piano and strive to listen for the audible harmonics, particularly the fifth and the third of the fundamental).

As we progress up the Harmonic Series, the intervals between overtones get smaller and smaller (and some are not even intervals that we use in Western music). Any sound we hear contains all the notes in its harmonic series to varying degrees. That variability is the reason that instruments playing the same pitch sound different: Their harmonics have different strengths. For example, an oboe playing A440 has a rich, reedy, spicy sound, while a clarinet playing the same note has a much less vibrant tone, simply because the clarinet’s construction suppresses some of the overtones (the 2nd, 4th, and 6th especially) that would make it stand out more.

No matter how many overtones are present and audible, our ears tend to resolve all harmonically-related frequency components into a single sensation. Rather than perceiving all of the individual harmonics of a musical tone, we perceive them together as one pitch (the lowest one, or fundamental). Incredibly, this will happen if we hear just a few tones from the harmonic series…even if the fundamental is not actually sounding! This phenomenon is used in music recording, especially in low bass tones that are to be reproduced on small speakers such as earbuds or other headphones, and it fools your brain completely into thinking that the lowest tone is there, when in fact it is not.

 Yet another name often applied to the phenomenon of the harmonic series is partials. This is especially the case when speaking of the harmonic series in relation to brass instruments. For all intents and purposes, the terms harmonics, overtones, and partials are all interchangeable in this document. For brass players, these partials are particularly important, as they are the foundation to playing chromatically. Here are the first sixteen partials of the harmonic series (keep in mind that these partials go on, theoretically, into infinity):

• Partial 1 is the Fundamental (in brass instruments, often called pedal tones).
• Partial 2 is one octave above the Fundamental.
• Partial 3 is a Perfect Fifth above Partial 2.
• Partial 4 is a Perfect Fourth above Partial 3.
• Partial 5 is a Major Third above Partial 4.
• Partial 6 is a minor Third above Partial 5.
• Partial 7 is a minor Third above Partial 6.
• Partial 8 is a Major Second above Partial 7.
• Partial 9 is a Major Second above Partial 8.
• Partial 10 is a Major Second above Partial 9.
• Partial 11 is a Major Second above Partial 10.
• Partial 12 is a minor Second above Partial 11.

• Partial 13 is a Major Second above Partial 12.
• Partial 14 is a Minor Second above Partial 13.
• Partial 15 is a Minor Second above Partial 14.
• Partial 16 is a Minor Second above Partial 15.

If you were paying attention, you may have noticed that the first six partials of the harmonic series make up a Major Chord. In fact, many historians and theoreticians believe that the reason our harmony tends to be so heavily reliant on fifths, fourths, and thirds (i.e., major and minor chords) is because those are the most audible harmonics to the human ear. (This does not, however, explain why Asian and Arabic cultures use different harmonic models since they too would be able to hear the same harmonics as Western Europeans during the development of music).

Here are some other tips/tricks that will help you learn harmonics/partials:

• Partials 1, 2, 4, 8, and 16 are the Fundamental and its octaves. If the fundamental is B-flat, then the 2nd, 4th, 8th, and 16th, partials are also B-flat (and so is the 32nd, 64th, etc.)
• Partials 3, 6, and 12 are perfect fifths above the Fundamental (plus octaves). If the fundamental is B-flat, the 3rd, 6th, and 12th partial are F naturals (as are the 24th, 48th, etc.) – Note, the 3rd partial series is noticeably sharp on wind instruments.
• Partials 5 and 10 are Major thirds (plus octaves). If the fundamental is B-flat, the 5th and 10th partials are D naturals. So are the 20th, 40th, and 80th partials... Note- the 5th partial series is noticeably flat on wind instruments.
• Partial 7 is a minor seventh (plus octaves) above the fundamental. If the fundamental is B-flat, the 7th partial is an A-flat, and so is the 28th, 56th, etc. Note- the 7th partial series is extremely flat on wind instruments.
• 9 is a Major ninth (plus octaves). If the fundamental is B-flat, the 9th partial is a C, and so is the 18th, 36th, etc.
• Partial 11 is seldom used due to intonation deficiencies on most instruments. However, just for the sake of knowing it, it is a tri-tone plus an octave.
• If you “divide” a partial by two until it will no longer divide evenly, then you will really only have to learn Partials # 1, 3, 5, 7, and 9.

So why is any of this important to you? Well, knowledge of the harmonic series is how fingerings on brass, woodwind, and stringed instruments are derived. This knowledge could help you devise alternate fingerings for a troublesome spot, or decide a different way to voice a chord so that it sounds better in tune. But really, it is important to know because it is what music is all about, and knowledge for the sake of knowledge is still important. Knowing what we know now, we can see that the pitch “G,” for example, can be:

• The 1st, 2nd, 4th, or 8th partial of the G series...
• The 3rd, 6th, or 12th partial of the C series...
• The 5th or 10th partial of the E-flat series...
• The 7th partial of the A series...
• The 9th partial of the F series...
• The 11th partial of the C-sharp series...

= = =

“Every bit of playing we do today, be it good, bad, or indifferent, goes toward deciding what sort of player we will be tomorrow. A player who begins his day with a load of thoughtless, shoddy flourishes is simply perfecting their faults. Time spent trying to do simple things well is like putting money in the bank. Use your warmup time to do simple things well.”
– John Fletcher
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