The Well-Tempered Tune

Devoted to perfecting the sound of pianos and harpsichords
7D2_3547The Well-Tempered Tune
What is accomplished in a tuning?
(For tuners and the curious.)

“The piano is an untunable instrument." - Ed Foote

Although funny, this quote from Ed Foote summarizes the fact that the strings of a piano are not ideal oscillators and, strictly speaking, they cannot be tuned to be perfectly consistent with each other. Even in the case of unisons, some argue that the best sound is obtained if they intentionally not tuned to exactly the same frequency.

Ideally an aural tuner or an electronic tuning device (ETD) should take into account the intrinsic contradictions and imperfections of the piano. An ETD should be programmed to do what an aural tuner does while optimizing the tuning, and help the tuner rapidly (and reproducibly) achieve the optimization that you find most satisfying - that is, the perfect tune.

For those who are interested in what actually is done in piano tuning, I provide more information below and in the additional web pages under Tuning.

Piano tuning is not trivial

There are at least three reasons why tuning a piano is not trivial, i.e. you cannot use a Korg guitar tuner.

First, perfect intervals on the piano (e.g. the perfect fifth and the octave) are mutually incompatible. The problem is fundamental and has troubled philosophers for thousands of years, as far back as Pythagoras. One solution is to divide each octave into 12 equally spaced tones, i.e. adjust the
temperament to equal semitones. Unfortunately, the resulting equal temperament means that all intervals other than the octave are out of tune. The alternative is to allow some intervals to be closer to ideal than others, which was the approach used prior to around 1900. Some people find these “historic temperaments” to be a refreshing alternative to the more modern equal temperament. A nice visual summary of historic temperaments and the time period where they were used can be found here. Playing Beethoven or Bach with a temperament that they most likely used when writing their music can be very revealing, almost mystical. Tuning to a historical temperament is no more difficult than tuning to equal temperament with an ETD. Tuning to an historical temperament entirely by ear would be a major effort for most tuners since most are taught to only tune in equal temperament.

The second problem arises because of the significant stiffness of metal piano strings, which cause the
overtones above the fundamental to be increasingly sharp of the ideal harmonics. This inharmonicity means that not even the octaves can be perfect. The solution is to “stretch” the tuning of the octaves so that the dominant overtones of two or more notes in an interval are congruent (i.e. not beating wildly). The tuner must decide how to achieve the optimal compromise, i.e. tailor the stretch.

The third problem relates to how to tune the
unisons, the multiple strings (usually three) for each note. Some tuners believe that tuning each string slightly out of tune relative to the others leads to a richer sound with greater sustain.

The bottom line is that a good tune is actually an optimization to obtain the best of a bad situation, which explains why what sounds like a great tuning to one person, may be average for another. There is no single best tune.

The Veritune approach

I am a strong advocate of Dave Carpenter’s approach in the
Veritune software. His is one of the few ETDs to sample every note and not fit the tune to an idealized inharmonicity curve based on sampling just a few notes. Inharmonicities are not ideal, and one cannot expect to obtain an outstanding, sweet, aural quality tune if you smooth the inharmonicities with an ideal curve. All examples of ETD results presented in this website are therefore obtained using the Veritune software installed on an iPad.

You do not need to understand how an ETD works to use it. In fact the best are designed to be user-friendly and allow a complete tuning in about 1-2 hours, with the time determined largely by the quality that you desire and the condition of the piano when you begin. I typically take about 1.5 hours to do a tune, simply because I want it to be near perfect.