The sound of the piano and the other musical instruments sounds so natural to our ears that we often forget that tuning systems have actually changed over time. Behind each note that you hear is a rich story of music theory, math, and even philosophy. The two major concepts in this story are the historical tunings like just intonation, mean-tone, and Pythagorean tuning, along with equal temperament. You need to understand all these systems to better appreciate the notes as well as the character and the feeling of the music across different musical eras.

What Is Tuning in Music?

Tuning is a process where we adjust the pitches of the notes in relation to each other. An octave is a natural doubling of the frequency, so the problem lies in dividing that octave into smaller, usable pieces like the 12 notes on the chromatic scale. Depending on how you divide it, some intervals sound purer or in-tune, whereas others might sound off. Different tuning systems focus on different intervals, and this is where historical tunings and equal temperament differ.

Equal Temperament: The Modern Standard

Equal temperament, also known as the 12-tone equal temperament, aka the 12-TET, is a system that almost all Western music makes use of these days. In this system, they divide the octave into 12 exactly equal parts. Mathematically, each of the semitones is the twelfth root of two times the frequency of the previous note. However, this method compromises the natural purity of the intervals a little bit. For example, a different fifth in the equal temperament is a bit flatter compared to the pure fifth. Similarly, a major third is a bit sharper, but the advantage of the equal temperament is that it lets a musician play equally well in any key without having to retune the instrument.

If you play a piece that changes from C major to F# major on a modern keyboard without any tuning adjustments, you see the freedom that the equal temperament provides. It makes all keys usable and in tune equally.

Historical Tunings: Pursuit of Perfect Harmony

Before there was equal temperament, musicians used a variety of historical tuning systems. These systems focused on the pure-sounding intervals in certain keys. Each of these systems had its own compromises, but in a different way.

1.    Just Intonation

The oldest of these tuning systems is the Just Intonation, based on the simple ratios of the whole numbers. For example, a pure fifth has the frequency ratio of 3:2, whereas a pure major third has a ratio of 5:4. When one hears a chord tuned in just intonation, it resonates deeply like a harmonious ringing. The negative aspect of this is that it moves into a different key, and suddenly the notes sound sour and awkward as the pure intervals do not match any longer.

2.    Pythagorean tuning

This system was developed by the ancient Greeks and is named after Pythagoras, focusing on the fifths. It stacks the intervals of 3:2 to build a scale that results in amazing fifths but also a bit out-of-tune thirds. This tuning was favored for the medieval music, where perfect fifths overpowered the music, and the chords were not built around thirds.

3.    Mean-tone temperament

The last of the historical tunings is this one; it became popular during the Renaissance and the early Baroque periods. This system was used to balance things a little better and adjust the fifths a little. This was done to the major thirds, which sounded sweeter. It made music in the common keys sound beautiful but with wolf intervals.

Why the Shift to Equal Temperament?

By the end of the Baroque and the Classical periods, there were composers like J.S. Bach, who wrote music that explored the multiple keys for a single piece. His composition, ‘’Well-Tempered Clavier’’ showed the possibility of playing all keys. The real push for Equal Temperament came in the 18th and 19th centuries as the instrument became more standard and music needed to be more harmoniously flexible. Pipe organs, orchestra, and grand pianos all needed a universal system. Equal temperament allowed for smoother modulations between the keys and made the playing ensemble a bit more practical.

How It Affects the Sound and Emotion

Historical tuning allows each key to have its own personality, like the D Major might sound bright and happy, whereas an E-flat major sounds melancholic and warm. In equal temperaments, all keys would have the same character, and the emotional differences are due to compositional choices instead of tuning. Modern performers make use of historical tunings to perform their early music to catch that flavor of authenticity. However, the equal temperament has its beauty too, allowing for bold harmonic adventures such as shifting keys or chromatic wanderings.

Conclusion: A Trade-off Between Purity and Flexibility

The story of tuning is about compromising one thing for another. Historical tunings would offer exquisite purity in a limited content to create a sonic world with each key having its own meaning. Equal temperament had to sacrifice a bit of this purity for total harmonic freedom. When you understand both of these tuning systems, it improves your appreciation for the music you listen to. Whether it's tempered or pure, each note carries a world of history and invention.

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