(trick question)

The truth about pure temperament.

In the key of A major, A equals 440.  In the key of C major, A equals 440...right?   Wrong.  Now you may ask, "who cares" or "how does that affect me?"  If you are a wind, brass, or string player you should care, and it does affect you...more than you may think.

In the booklet to The Tuning C.D., a chart on scalar intonation is provided, as seen below.

Interval Name       To sound "in tune"...    

Major 2nd

is to be played 3.9 cents sharp.

minor 3rd

is to be played 15.6 cents sharp.

Major 3rd

is to be played 13.7 cents flat.

Perfect 4th

is to be played 2.0 cents flat.

Perfect 5th

is to be played 2.0 cents sharp.

Major 6th

is to be played 15.6 cents flat.

minor 7th

is to be played 17.6 cents sharp.

Major 7th

is to be played 11.6 cents flat.

As you can see an A, the major 6th in the key of C major, should be performed 15.6 cents flat.  In numerical terms, the same A that was equal to 440 in the key of A major must now bend down in pitch (436.06) to sound "in tune" for the key of C major. 

If you are in the key of F Major and perform an A...in order for it to sound "in tune" you must play the A, or Major 3rd, 13.7 cents flat (436.54).  If you do not, the note will sound "sour."  Technically, you will hear beats, or waves.

Most of the finer musicians bend their pitch naturally due to good intonation discrepancy, however for the rest of us...a Tuning C.D. will set us straight.

Try an experiment. 

You will need a synthesizer or keyboard with headphones and a digital or analog tuner.  

On the synthesizer and with headphones on, play a low C, middle C, and middle G at once.  Now sustain them.  Turn on the tuner.  While these notes are sustaining, play on your instrument a concert E and close your eyes.  Listen very closely to the keyboard and your instrument to get rid of the beats, or waves in the sound.  Once you have done this, open your eyes and look at the tuner.  You may find you are performing the concert E around 14 cents flat.

This is, in essence, what The Tuning C.D. is all about.  Ear training.   For good intonation you will not need to know the numbers above...you just need to use The Tuning C.D. for 5 to 10 minutes with your daily exercises.

(The keyboard is in equal temperament and instrumentalists need to train their ear in pure temperament.  The Tuning C.D. is in pure temperament.  If you experience any difficulty with the experiment above, it may be due to the fact that the G is 2.0 cents sharp.) 

For more information on intonation or different temperaments, simply click on one of the intonation links found on our main page.