Intonation

I like to break the topic of intonation down into two categories: linear and vertical.

Linear Intonation
I define linear intonation as the process of tuning a single line without any accompaniment. Essentially, one is comparing notes in the line to earlier notes.

Vertical Intonation
I define vertical intonation as the process of tuning your notes in the context of other notes sounding at the same time.

Linear Intonation

Many people now have and use electronic tuners to work on linear intonation. This is fine but remember ... Your ears are the tuner!

Use that electronic tuner to "calibrate" your ears. In other words:

Listen first, then look.

Try this: Ears first, then tuner!

After tuning your horn, play two notes a perfect fifth apart such as C and G. Using a tuner, carefully place the C in tune. Now move from the C to the G and rely solely upon your ears to check if the G is in tune. Once you think you've got it, glance at the tuner to check yourself. Also,try this with other intervals.

Try this: Aligning the "harmonic backbone"

Take a small segment of your music and look for primary tone / pure intervals in the melody (for example: scale degrees 1, 4 and 5). I sometime refer to these intervals as the "harmonic backbone" of the music. Align the backbone, and the other intervals have a way of falling into place more easily.
Play through the music, placing fermatas on the pure intervals. Using the same technique described in the tip above, carefully tune each of these pure intervals.
Once you have spent some time doing this, play straight through the music in time and see if you can carefully hear your intonation "on the fly."

Try this: Experiencing beats

Try playing a unison with someone else. As the other person holds constant, slowly move your slide away from their note. Listen carefully and you will hear the beats get faster as you move farther away.

Try this: Who's your tuning buddy?

Get together regularly to play together with a friend. Play easy duets, slow scales and arpeggios, or etudes in unison. Try playing scales in parallel fifths or thirds. Try having one person sustain a "drone" note (while using a tuner) while the other plays a slow arpeggio.
Be creative. Think of this as a "buddy system" for intonation. Do it several times a week if not daily.

Try this: Plunking on the piano

If an in-tune piano is available, play or buzz along with it. Even if a skilled pianist isn't available, you may be able to find a friend to simply roll major chords on the piano (holding down the sustain pedal) while you play slow arpeggios on your instrument. Make up simple one-harmony melodies with piano accompaniment. For more advanced keyboardists, learn the chord changes to simple folk songs and then take turns accompanying each other.

There are a few commercial products that can be of great assistance in practicing vertical intonation. Some of the Jamie Aebersold play along jazz CD's can be used for intonation practice. The "Tune-Up" CD-based intonation system is excellent for careful, methodical intonation practice. If you can afford it, the Smart Music Studio computerized accompaniment system (formerly known as Vivace) is an outstanding practice aid.

Equal Temperament vs. Just Intonation

When using a tuner, you are tuning to equal temperament. In other words, your intonation will be equally good in all keys but not ideal in any key. With the trombone slide, it is possible to slightly adjust notes for any given key in order to improve intonation.

When adjusting notes, it is useful to think of your adjustments in terms of "cents." Each half-step is divided into 100 cents. Thus if you play an "A" 50 cents sharp, you are halfway to a B-flat.

Here are some common adjustments that should be made in order to make intervals perfectly in tune. Each of these adjustments assumes that the bottom note is perfectly in tune and cannot be adjusted. Therefore you need to adjust the top note to arrive at a perfectly in-tune interval:

INTERVAL	ADJUSTMENT OF UPPER NOTE
Perfect Octave (for example C - C).	No adjustment
Perfect Fifth (for example C - G)	up 2 cents (almost nothing)
Perfect Fourth (for example C - F)	down 2 cents (almost nothing)
Major Third (for example C - E)	down 14 cents
Minor Third (for example C - E flat)	up 16 cents
Major Sixth (for example C - A)	down 16 cents
Minor Sixth (for example C - A flat)	up 14 cents
Minor Seventh (for example C - B flat)	down 29 cents* (useful in dominant seventh chords)

*There seems to be a some disagreement about this adjustment. Recently I have heard that perhaps this should be lowered by 31 cents.

Here's a good rule of thumb to remember all this:

Octaves, fifths and fourths ......... Almost no adjustment

Major thirds and major sixths ..... Top note down

Minor thirds and minor sixths ..... Top note up