Ever since the dawn of time and the birth of the first ever instrument, a 60,000-year-old Neanderthal flute, we have tried to understand sound. From production to communication, and from aesthetics to physics, we have been fascinated for centuries by what we call music. Music can be produced in many ways, and also organized in ways that we haven’t thought of before. Much of this has to do with physics. If a single note has its namesake counterpart higher or lower, we say that these two notes are separated by an octave. In modern Western music our octave is split in 12 notes, all equi-distance from each other. But why do they need to be equal distance from each other? The answer is they don’t. Historically speaking, the temperament that offers 12 equally spaced notes in a single octave is called an equal tempered tuning. There are, however, many others that were much more prominent and popular way back when.

Quarter-Comma Meantone Tuning

From the family of meantone temperaments, this one was by far the most commonly used. As in the equal temperament, where each interval of a fifth (C-G, A-E…) is adjusted by just a little bit (1/12 of a Phytagorean comma), resulting in all semi-tone intervals being equally spaced, the quarter-comma meantone system adjusts the fifth by a 1/4 of the syntonic comma. What that does is that it generates beautiful justly intonated thirds, which sound lush and rich.

Well-Tempered Tuning

The well-temperament means ‘good tuning’ and has had many iterations. Famous scholars who had given their versions of this tuning are Werckmeister, Kirnberger, Kellner, and Valloti. In this tuning the tempered fifths were treated in different ways, resulting in keys sounding acceptable when modulating, with those closer keys producing purer third relationships, and those distant less so. In other words, the goal of a well-tempered tuning was to be able to move from key to key, but the process isn’t as successfully polished as with later developed equal temperament. The well-tempered tunings are also some of most widely spread tunings, with the most diverse approaches and interpretations from scholars, as mentioned previously.

Phytagorean Tuning

Named after famous Greek philosopher, phytagorean tuning represents an organizational system, where all ratios note-to-note are based on the relationship of 3:2 on the natural overtone scale (a most perfect fifth). These pure fifths are then stacked one on top of the other, creating scales and sacrificing the purity of any other intervals in the scale. This is why music in phytogorean tuning prefers chords with only fifths and then octaves, insomuch to avoid the ‘out-of-tune’ thirds.

The important thing to note is that temperaments had creative purpose. For example, if the interval of a fifth were a pure interval, then we would had been one step closer to a divine being. If exploiting an out-of-tune interval (say the tritone), we would have created a dramatical value and a stronger but less pleasant imagery. Temperaments are ratios, but add drastically to interpretation and creativity. The modern equal temperament is one that is the least invasive to our ear, which is why it is the most popular one in Western music.