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A frequent question from customers is "How often should my piano be tuned?" The textbook answer is "every six months". However, key factors are usage, temperature, humidity, location, room environmental controls, piano age, and the discerning preferences of the piano players. Some pianos go out of tune significantly in less than six months while other instruments hold fairly solid for a year. Over time your technician can help you determine the optimal  tuning schedule.

The Tempered Scale:
An piano "temperament" refers to the intervals between notes on the musical scale. Every pitch can be derived from a relationship with a chosen fixed pitch source. Temperament is also be a term in a sequence of piano tuning. When a piano has been tuned using an equal temperament, the octave intervals have been divided into smaller equal steps, each having equal frequency ratios between the adjacent notes. These are the smallest intervals in the tempered scale that is used in common modern music. Each of these intervals are 1/12 the width of the octave and are referred to as a semitone or half-step.
The tempered scale is commonly used today with the frequency between each interval being perceived as the same distance apart.

Before I learned about the tempered scale, I wondered why classical music often lists the key. For example, the title of the composition such as "Piano Concerto in A minor" or "Chopin's Piano Concerto in F minor" indicates the key. Why did these classical composers care what key? The answer lies in the historical temperaments of that era. There are many references to the tempered scale, its history, and examples of the historical temperaments. Importantly, there is no such thing as no temperament (See Figure 1) in a piano tuning scale. To accommodate the imperfections in the scale, there must be some "imperfections" built into the tuning. The various historical temperaments will cause a composition to sound different depending upon what key it is played in. If played in a modern equal tempered scale, the difference may be undetectable other than the relative pitch reference. But in the original classical temperaments, the difference would be notable.

You can easily find considerable information on the historical temperaments. If you really like to read the details, you can search on-line for "same song in historical temperaments" and you may find recordings where you can hear the differences. Below is a very simple diagram to show why there must be a temperament for the piano scale. But again, search for more information and you will find enough to keep you reading and listening for a long time.

Temperament Figure 1

Pitch, Inharmonicity & Tuning:
To fine-tune a piano, first the overall tension must be correct. If it is not correct, the instrument may need a "pitch-raise" to establish the correct tension and enable the instrument to hold a tuning. Once the correct tension is established, the technician must make very small adjustments to each string to fine-tune the instrument.  

Each piano is somewhat unique due to something called "inharmonicity". In addition to the full string length (the fundamental frequency), strings vibrate in a number of shorter sections separated by "nodes". The nodes divide up additional related frequencies that may be referred to as overtones, partials or harmonics.

We won't present an argument here regarding which term is correct (See figure 2 below). These related frequencies may not match up exactly with the mathematically determined harmonic frequencies due to a number of issues relating to the size, tension, length, materials and sometimes even imperfections in the steel strings. (If you want a very short demonstration of harmonics, ask me during your next tuning.)

The "scale" of the piano, the design that includes string length, diameter, materials, and tension, also impacts the inharmonicity and tuning approach. The tuner must deal with this unique "inharmonicity" in each piano. Therefore, the technician does not simply match the strings to a given set of pitches. Years ago there were some tuners who carried a set of 12 tuning forks to set the initial middle octave. Experience has shown how small changes are needed in individual pianos to adjust for this inherent inharmonicity that is different in each acoustic piano. Your tuner assesses this, via listening to the interaction among notes, and a slight variation is applied from the theoretical standard to make your piano sound its best.

Temperament Figure 2

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