The Tuning of Yamaha Percussion Instruments

Tuning a mallet instrument requires a deep understanding of complex physical phenomenon. The biggest question is, when does an instrument sound tuned? To answer this question, you need to align physical and subjective aspects.

When a piece of material is hit, naturally a lot of harmonics appear. With a sound bar, it is possible to bring this material to a suitable size in order to strengthen certain frequencies. Then, in the same way as a string, you can define and control the partials (or harmonics, overtones) at the appropriate part of the material. Most importantly, you can then approach the fundamental note plus e.g. the 3rd for quint tuning or the 4th for octave tuning.

So far, so good. Let´s tune the instrument in A=442hz. But wait! Isn´t there an enharmonic change or a problem with the fifths and thirds? Well, theoretically 12 perfect fifths would fit into 7 octaves.

Theoretically.

Practically one fifth is 702ct x 12 = 8424ct) while 7 octaves in equal temperament are 8400 cents (100 cent each half step). Which means there´s a gap of 24 cent within 7 octaves. For specialists: this is called the Pythagorean Comma (exactly 23,46 Cent). One of the many parameters to compromise. Then there´s such thing as inharmonicity of the overtones. Theoretically, each overtone should be a whole multiple of the fundamental frequency, e.g. a 3rd overtone vibrates 3x faster than fundamental, 12th overtone 12x faster than the fundamental and so on).

However, these overtones do what they want and they vibrate slightly faster (= higher) than they should. This inharmonicity defines the instrument´s character. Without it a marimba wouldn´t sound like a marimba. But in the end, another parameter to compromise. Finally, you need to deal with the used material, it´s thickness, hardness, stiffness, the size ratio, the temperature and humidity (esp. for wood) which also strongly influence the harmonics and sound.

Now let´s adopt these parameters to our human ear and to the western musical system. The most common tuning today is so called Streched Tuning, also known as S-Curve-Tuning. Executive summary: lower notes are tuned a bit lower, higher notes are tuned a bit higher (S-curve). Only the middle range of for example, a marimba is tuned exactly in e.g. A=442hz. A perfectly linear tuning would not sound in tune to human ears. Of course, the definite tuning graphs of each Instrument manufacturer are subject to confidentiality and part of the DNA of the brand´s individual signature sound.

Yamaha´s percussion instruments are tuned carefully by hand, computer controlled and based on our piano tuning graph. Each instrument is checked carefully by a specially trained technician before it leaves the factory. This quality check includes a bar selection, combining the best matching sound bars for an instrument´s set, plus a full instrument assembly to avoid any other problems.

This was only a very rough and brief introduction to a theme so rich and complex. Gain deeper knowledge checking some of the keywords in this text. It´s a world full of sound!

Christoph Müske works at Yamaha Music Europe since 2013 within the B&O division. He is responsible for product groups Strings and Percussion. One of his favourites is to re-tune the beautiful old bar sets of Yamaha Marimbas.