**Equal Temperament Piano Tuning-The Process ****By James Grebe ****www.grebepiano.com**

Since the late 1980’s we began using digital computers using programs written to them. In past years, piano tuners had their ears and reasoning ability along with aural tests to place the notes at the correct pitch of the tempered scale. Piano tuners now have devices to set numerically the correct pitch of every note with an accuracy of + or - 0.02%. The following is a brief explanation of how I tune your piano. Within the scale of 12 notes, musical mathematicians found a way to divide up the distance of an octave into 12 notes (1200 cents) with an equal distance between each note. Within this equally tempered scale, music can be played in all 12 keys and still sound equally correct. The process goes like this: since there are 12 notes they could take a starting pitch and multiply that figure by the 12^{th} root of 2 which is 1.0594631 and obtain the frequency of the next higher note. This method allows the notes to have the same proportion of cycles per second (or cents) as the previous noted dividing them. The next problem we have to deal with is the problem of inharmonicity, which is the distance between the theoretical frequency and the real world frequency of the harmonics present in the tone of each different piano. Because the wire in the piano is relatively short and stiff, the speaking lengths do not quite behave like the theoretical model. Following is a chart of the partials in musical tone that we use in piano tuning: 1^{st} partial - root or fundamental2^{nd} partial – octave pitch3^{rd} partial - octave + a 5^{th}4^{th} partial – double octave5^{th} partial – double octave + a 3rd6 partial - double octave + a 5^{th}7^{th} partial – not used8^{th} partial – triple octaveThese are the partials we use to tune pianos. If the piano behaved like the model, all these would be exact multiples. However, because of inharmonicity each partial up the ladder gets progressively stretched away from the model. In general, when we hear an aurally perfect octave, the sound of the 2^{nd} partial of the lower tone is equal to the 1^{st} partial of the higher tone. Because of inharmonicity, the 2^{nd} partial is stretched so the higher note has to be tuned slightly sharp to sound perfect, which means the 2^{nd} partial is equal to the 1^{st} partial of the lower note. This is what is meant **by stretching the octaves. **The preceding holds true for the middle and upper parts of the piano. In the bass section we generally tune the 6^{th} partial of the lower note to the 3^{rd} partial of the higher octave note because these partial are generally louder than the 1^{st} and 2^{nd} partial in the bass section and our ears listen for the louder partials present to determine if the note sounds flat or sharp. This is a general description of what we listen and measure to tune your piano to the highest standards possible. The instrument I use is a programmable digital computer (Sanderson Accu-Tuner III) with equal temperament in its memory with a quartz crystal built in with an accuracy of + or- 0.02%. With this instrument, combined with my over 46 years of experience tuning pianos, I can give your piano the best tunings it has ever had and also to be able to duplicate it each time I tune it. Here is the process I use: I set the device to F-5 and play the note F-3 and the note gets tuned to its 4th partial at a deviation of 0.0. Then I set the device to F-6 and measure the difference in cents. This measures the distance between the 4th and 8^{th} partial of F-3. I store that amount in the computer and proceed to A-4. I set the device to A-5 and tune A-4 to 0.0. Then I reset the device to A-6 and measure the difference in cents. That measures the distance between the 2^{nd} and 4^{th} partial of A-3. The device records that figure and then I proceed to C-6 and tune that note to 0.0 and reset the device to C-7 and record that amount. That measures the distance between the 1^{st} and 2^{nd} partials of C-6. With these 3 values the computes calculates the optimum tuning for that particular piano. Thus, we have measured the amount of inharmonicity in 3 places on your piano to be sure of the most balanced tuning for this instrument. I then end up with a tuning fulfilling the designers’ purpose, the manufacturers handiwork and my skill giving you the best tuning possible for your piano. The fact that I record these measurements in the devices memory bank is what ensures duplicity tuning for your piano. You will notice I keep a binder with the most popular recorded tunings already to go.

Copyright/2008/Yesterday Once More Publications,James Grebe