Intonation

Correct Note vs. Correct Pitch

* This page is a followup to the page About Trumpets. Also see Tuning. There is some overlap, for the sake of flow.

There is a difference between a Note and a Pitch. You are playing the right Note if you are using the right fingering (or have the trombone slide in the right position) and are playing the right harmonic. But this does not mean you sound good! If you are not playing in-tune with others in your group, the entire group will sound bad. Intonation is one of the main reasons that professional ensembles sound so much better even than a good high school group.

Intonation is about Pitch, which is the precise tuning of the note to the pitches being played around you. Your intonation can be off because your main tuning slide is in the wrong place, or because you are not playing in the focused, resonating center of the note, or because you are not applying your valve slides appropriately. But there are many times when you will have to fine-tune notes with your lip (actually a combination of your lip, wind, and tongue position). This is called “lipping it” into tune, and is why learning to bend notes is a worth your time.

A Word about "Perfect Pitch"

Some people have what is referred to as “perfect pitch”, which is really a very highly refined pitch memory. These people can name notes that they hear, and can often hear even tiny variations in a pitch from the standard A= 440 Hz reference. Perfect pitch can be learned — particularly if you start young, but even older people can develop it with practice.

I happen to think that perfect pitch is overrated. While convenient, it can also be a liability — I have known violinists with perfect pitch that had trouble playing with an orchestra that was playing slightly sharp (which they often are!). What is essential is not that you play in tune with a theoretical piano, but with the musicians that surround you! If it annoys you that they are not playing in “perfect pitch”, or you insist on playing “perfectly” while the overall pitch of the ensemble is higher or lower, it is you who will stand out as being out-of-tune.

The Harmonic Series

The harmonic series is simply the set of pitches whose frequencies are an integer multiple of a fundamental frequency. Each octave is a multiple of 2x the next lower octave. Three times (3x) the fundamental is an octave and a fifth above the fundamental (and a ratio of 3:2 to the next lower harmonic), etc. as show in the following image:

Intonation and the Harmonic Series

All of the notes of the harmonic series are perfectly in tune with each other, but they are not necessarily in tune with an equal-tempered instrument such as a piano, organ, or keyboard percussion. For example, if you tune your written C to the piano, you will find that, while all of the C’s are in tune, nevertheless:

Your fifths (3x, 6x, and 12x) are slightly sharp.
Your major thirds (5x, 10x) are flat.
Your 7th (high Bb), 11th (high F#), and 14th (double-high Bb) partials are VERY flat.
Your 13th (double-high Ab) is very sharp.

These tendencies are inherited by ALL of the valve and slide combinations, and are one of the main reasons we use alternate fingerings and valve slides.

The Harmonic Series and the Tuning of Chords

Interestingly, and very importantly, the harmonic series informs the way we tune chords. When we are tuning a major chord, for example, we want the ratios between the root, third and fifth of the chord to be precisely 4-to-5-to-6 (abbreviated 4:5:6).

Again, it’s Physics. When we play two or more pitches together, the wave pattern of high- and low-pressure interact. When the high-pressure peak of one wave meets the low-pressure trough of another, they will cancel each other out. When the peak pressure of two waves intersect, they will add together. A 4x wave will interact with a 5x wave to create an extra-high peak every 20 waves (the least common multiple). This creates a “virtual note” that is 1x — the fundamental, which is 2 octaves below the 4x note and the reinforces the root of the chord. When 5x and 6x interact, the result is the same — a 1x virtual note. When 4x and 6x interact, we get a 2x note — again, reinforcing the root at the intermediate octave. Note that the virtual note is the difference between the two real notes. It is referred to, appropriately, as the difference tone. So by playing C-E-G perfectly in tune, we get six notes! the three real notes, and three difference tones that reinforce the root of the chord.

This is why excellent choirs and instrumental ensembles sound so rich and deep… by singing and playing in tune, they can sound like a much larger group, because of the difference tones. Conversely, groups that play out-of-tune create virtual tones that conflict with their chords, sounding harsh and unmusical.

But what about chords that are not major chords? The same basic principle applies, but of course, we may want different resulting tones. The following chart shows the amount and direction that each note in a chord needs to move to play the chord perfectly in tune. The numbers are in “cents”… hundredths of a half step. From this, you can see that the fifth of the chord should always be slightly sharp (+2). But the third of a minor chord should be quite sharp, rather than flat as in the third of a major chord. It’s worth getting together with two or three (or four!) friends to try these out and see how they sound.

Using the Valve Slides

There is not a professional player in the world who does not make liberal use of the first and third valve slides to tune 1-2, 1-3, and 1-2-3 valve combinations, especially in the low register. These valve combinations (without using the slides) are inherently sharp due to compromises between the lengths of valve tubing and the need to make first valve and second valve fingerings in-tune with the open horn.

Why is this? As we have said, each valve makes the instrument a bit longer by diverting the vibration into an additional length of tubing, thus lowering the pitch. The exact lengths of each valve crook are designed to add a fraction/percentage to the length of the open instrument (no valves pressed).

HOWEVER, because 1 and 2 are sized for the open instrument, they are too short to lengthen an instrument that already has a valve pressed. Such an instrument is longer, so the added valve is a smaller percentage of that instrument than of an open instrument. We therefore need to add a little extra to the combinations to put them in tune, using the valve slides.

For example, the instrument with first valve pressed (e.g. when playing an F) is longer than the open instrument. Adding the second valve to the first valve adds a smaller percentage of the length of that longer instrument than it does to shorter, open horn. We therefore move the first valve slide out a bit to make the combined tubing slightly longer, putting it back in pitch.

Because third valve is typically used in combination with the 1st valve, the 2nd valve, or both 1+2, instrument manufacturers often make the 3rd valve slide just a bit longer than needed to lower the note 3 half steps from the open horn. While this means that the 2-3 combination is often nicely in-tune, it also means that playing an E (for example) with just the 3rd valve may tend to be flat. Unfortunately, it is not enough to make the 1-3 and 1-2-3 combinations in tune, so we must use the first and/or third valve slides to tune these combinations. In summary:

For 1-2, use the 1st valve slide
For 2-3, usually no slides required
For 1-3, use the 1st and/or 3rd valve slides (depending on the notes around them)
For 1-2-3, use both the 1st and 3rd valve slides (more than with 1-3)