Temperament: Information for real musical nerds

Understanding Piano Tuning Systems
By Henry Bahrou – Guitarist, Music Theorist, Music Academy Director

When it comes to tuning a piano, you might think that the perfect approach would be to tune every consonant interval — like fifths and thirds — so that no “beating” or wavering in the sound can be heard. While this might sound ideal, it turns out to be impossible on a keyboard limited to twelve notes per octave.

For example, you could tune an A perfectly so that it forms a beautiful sixth above C, and tune the G to create a clean fifth with C. You could also tune a D to sound good below A. But when you check the relationship between G and D, you’ll find it’s off — no matter how carefully you tuned. In short, you can’t have every interval perfect without duplicating notes. Historically, some instruments did just that by including extra keys for certain notes, but that’s not practical for the modern piano.

In early music history, musicians first solved this problem by tuning the fifths perfectly and accepting that the thirds and sixths would be out of tune. This system, known as Pythagorean tuning, dominated until around the 15th century. During that time, thirds and sixths were even considered dissonant — not consonant — because they sounded rougher than we’re used to today.

As the use of major and minor thirds became more musically important, a compromise was needed. Musicians began tuning certain notes to a midpoint between their ideal positions. This approach, called meantone temperament, made most thirds sound very pleasant and only slightly weakened the purity of the fifths. However, meantone temperament came with its own problems: some rarely-used keys sounded extremely bad, including what musicians called the “wolf fifth,” a jarring and unpleasant interval.

Over time, adjustments were made to even out these rough spots. New systems like Vallotti temperament and Kirnberger temperament tried to balance the purity of intervals across more keys. In these temperaments, the differences between keys became more noticeable, and musicians began associating emotional “characters” with different keys — like bright and happy C major versus the more somber F♯ major.

Eventually, equal temperament emerged as the standard, and it remains the dominant system today. In equal temperament, all intervals are slightly compromised so that music sounds reasonably good in every key. The fifths are kept strong and consistent, and although the thirds are a bit wider than ideal, they work well for both melody and harmony. Modern pianos, with their muted overtones compared to instruments like the harpsichord, make the slight imperfections even less noticeable.

With today’s digital technology, there is renewed interest in exploring historical tuning systems — even ones involving more than twelve notes per octave — allowing musicians to revisit older sounds with tools that were once impossible to implement.