1.3. Tuning Your Ensemble

So how does the theory discussed in the previous two articles tie in with playing music in a real-life ensemble? Tuning of course! An important thing to remember is that musical instruments, from trumpets to guitars, only act to approximate the ideal 12-tone equal-tempered scale - they cannot be built to be perfectly in-tune; instead, it is up to the musician to make adjustments. But, even after the musician adjusts her instrument to an enharmonic 12-tone scale, she still must decide whether or not she wants to adjust to the more tonal just scale, or leave it in the more standard equal-tempered scale. These decisions, and the techniques required to accomplish them, will be discussed in this article.

1.3.1. Adjusting Your Instrument

Instruments are broken into three main classes based on how they produce sound: strings, winds and idiophones (or percussion). A huge number of variables go into the pitch produced by these instruments when they are stuck, plucked, bowed or blown - everything from room temperature to the specific shape of the individual instrument help to create distinct instrumental tones, and, less pleasantly, help to create an out-of-tune ensemble. Here is a brief overview of what precisely leads to poor intonation:

• Temperature:
• Temperature hurts ensembles made up of both winds and strings more than any other, as these instruments detune in opposite directions. Orchestras should retune after every piece of music to offset this effect, and instrumentalists should make a constant and conscious effort to adjust to their own changing instruments.
• Recall from section one that the pitch of a wind instrument is equal to the velocity of the air column over the wavelength of the sound. Fingerings, slide positions, and the lips determine wavelength, but atmospheric conditions determine air speed. At higher temperatures the air column moves faster, making the instrument sharper. This is counter to the common explanation that the metal or wood of the instrument expands in heat - this DOES happen, but it has a negligible effect, and actually makes the instrument flatter, not sharper. Musicians should adjust for heat by lipping notes up and down and, if the temperature is particularly nasty, by adjusting the tuning slide or mouthpiece.
• In general, wind instruments are designed to hit their true pitches after about five minutes of warming up. It's best to tune after this point.
• As temperature increases, pitch gets flatter In the stringed instruments - heat causes the strings to expand, resulting in less tension and lower pitch. Musicians should adjust fingerings to offset this effect.
• Idiophones are complicated and highly varied, but in general they get flatter in increased temperature.
• Extreme pitches and volumes (only winds):
• While strings and idiophones can change tone quality at these extremes, losing intonation is not a major problem. Winds, however, can be strongly affected.
• At both extreme high and low pitches, brass instruments tend to go sharp. Pinched lip shape at the top of the range drives pitch higher, and a failure to relax at the bottom of the range prevents the true enharmonic pitch from being produced. This is why practicing low notes on brass instruments can help high note intonation - it's all a matter of relaxing.
• At loud volumes, winds tend to go sharp, and the opposite happens in soft sections. This can be offset by maintaining a solid embouchure throughout, without letting it deform.
• Partials (only brass):
• The fifth and sixth partials tend to be flat and sharp respectively, with the latter being about 20 cents (hundredths of a half step) sharp. These notes should be lipped up or down, and a slide should be adjusted if possible.
• The third partial is slightly sharp. Brass instruments should not tune to a concert F as a result.
• Never use the seventh partial - it's about 30 cents flat. The Ab it produces should be played with an alternate fingering on the eighth partial. Trombones can use this partial to play G, Gb, etc., by virtue of the slide, but not even they can play that Ab in tune.

Be aware that these are only rules of thumb, and the individual instrument may vary. Get to know your particular instrument before committing these to memory.

1.3.2. Adjusting to the Ensemble

Getting an individual instrumentalist in tune is only half the battle - creating pleasant harmonies is a challenge on another level. If an ensemble is playing with a piano (or something similar) featured prominently, all instruments should adjust to match the piano, i.e. tune to equal temperament.

Otherwise, instruments should adjust to the just scale for its more pleasant harmonies. While performing, identify your position in the current chord. For example, if you have a major third, you should adjust it so that it is 14 cents flatter than usual to achieve that perfect harmonic sound. The following chart shows adjustments in cents from the equal tempered scale to the just scale, based on intervals:

Interval	Adjustment (in cents)
Minor second	-29
Major second	+4
Minor third	+16
Major third	-14
Perfect fourth	-2
Diminished fifth	-10
Perfect fifth	+2
Minor sixth	+14
Major sixth	-16
Minor seventh	+17
Major seventh	-12

To clarify, a positive value means that the note should be played sharper than normal, a negative value means the opposite.