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Intonation and Tuning



There are two common tuning systems: Equal Tempered Intonation and Just Intonation.


Equal Tempered Intonation is what fixed-pitched instruments like piano, organ, and xylophone use.  Their notes are built-in and cannot be adjusted while being played.  Thus their notes are Equal Tempered, which means the octave is divided into twelve equal parts.  On these instruments no interval or chord is played perfectly in tune (the bad news), but no interval or chord is way out of tune (the good news).


In other words, everything played on all keyboard and other fixed-pitched instruments is slightly, but equally, out of tune.  Our ears have come to accept (and even enjoy) this common tuning system as long as it is coming from a fixed-pitched instrument like a piano or other keyboard.

Just Intonation is for singers, woodwind, brass and string players who can, by the nature of their instruments, adjust the pitch of each note as they perform it.  Thus in band or orchestra, we can, and are expected to, play and perform intervals and chords that are perfectly in tune, with no intonation beats marring the purity of the combined sounds.

What Creates Intonation Beats?

Assume that two musicians play the note A at the same time and that one of them plays the A at 440 Hz (vibrations / second) and the other at 441 Hz.  The one playing the A at 441 Hz would be sharp compared to the one playing at 440 Hz.  As the sound waves (or waveforms) of the two sound combine in the air, there will be points when the top of the sound waves (crests) of each waveform coincide.  This coincidence or combination creates an overall surge in the waveform’s amplitude (size of wave) and is called constructive interference.



Alternating with constructive interference is destructive interference.  This occurs when the trough or lowest point of the waveform (amplitude) of each wave coincide (or touch each other).  This coincidence of the troughs creates an overall dip in the amplitude.


The alternation of constructive and destructive interference creates a corresponding alteration of surges and dips (highs and lows) in the overall amplitude (size) of the combined sounds.  A pulsating loudness results that can usually be heard quite easily.  This effect is what is known as intonation beats.

Since one musician is playing the A at 440Hz and the other is playing it at 441Hz, 1 intonation beat will occur each second (441-440=1).  If one musician plays the A at 443 Hz and the other plays at 439 Hz, 4 intonation beats will occur each second (443-439=4).  Musicians use the number of intonation beats they hear as a guide to getting in tune.


How to tune using Intonation Beats:

1.     Listen very carefully to the other player or reference pitch.

2.     If the beats slow down, you are getting closer to being in tune.

3.     If the beats are getting faster, you are getting more out of tune.

4.     When the beats stop or disappear and you can only hear one pitch, you are in tune.


Using Just Intonation and Tuning

To achieve beat-less purity in Band or Orchestra, musicians must listen and adjust EACH note according to its harmonic context.  For example, an E in a C major chord* must be played lower than the same E in a C# minor chord.  Why?  Because of the acoustical (sound) relationship between notes.  To eliminate intonation beats the E has to be played lower if it is in the harmonic context of a major 3rd than if it is in the harmonic context of the a minor 3rd.


Don’t worry about all the acoustical details about Just Intonation and tuning in Band Class.  Just remember the following about tuning chords, intervals and notes in a harmonic context.


¨      Always listen to the people playing the same note on the same instrument as you first.  Eliminate intonation beats with them first.

¨      Listen across the band and match with other instruments playing your pitch. This is what we will call Horizontal Tuning.  Listening across the ensemble.

¨      Now, we will tune the chords and intervals using Vertical Tuning.  This eliminates the intonation beats in chords and intervals.

o   Major 3rds  must be reduced in size.  Lower the top note or raise the bottom note.

o   Minor 3rds  must be expanded in size. Raise the top note or lower the bottom note.

¨      Listen horizontally and vertically to eliminate intonation beats.  If your sounds disappears into the sound of the ensemble, you are most likely in tune.


How to read your Digital Tuner or Cents vs. Hertz


Cents is the distance between half tones (half-steps) (E to F or A to A# or Eb to E, etc.) divided into 100 equal parts.  When you see a tuner with a scale ranging from –50 to 0 to +50, that is the range between a quartertone flat up to a quartertone sharp.


Hertz, abbreviated as Hz, is the frequency of a waveform (sound wave) measured in cycles (vibrations) per second.  If an A is played at 440 Hz, it’s waveform is repeating 440 times per second.  An octave lower is 220 Hz, and an octave higher is 880 Hz.  Hertz is a standard measurement that can be accurately measured much like distance can be measured with a ruler or weight with a scale.

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