Re: has anyone tried an Earvana nut?
Vincenzo Galilei (father of Galileo Galilei) may have been the first person to advocate equal temperament (in a 1581 treatise). The first person known to introduce a mathematically accurate specification for equal temperament is probably Chu Tsai-Yu (朱載堉) in the Ming Dynasty, who published a theory of the temperament in 1584. Soon after, European mathematicians Simon Stevin (1585, inspired by V. Galilei) and Marin Mersenne (1636) accurately described equal temperament.
In 1582, the great Chinese scholar of the Jesuits, Matteo Ricci, commenced his studies at Macao. From 1580, the Viceroy of the Cantonese province had established biannual 'trade fairs' lasting several weeks, at which Chinese and Westerners exchanged ideas and goods. The interchange between East and West was intense just at the moment when Chu Tsai-Yu went into print with his new theory. We do not know the exact mode of transmission of the idea to Europe. Within fifty-two years of Chu's publication, his ideas were published by Pere Marin Mersenne. The Ming Dynasty ended eight years later, but influenced musical theory for many years later.
Twelve tone equal temperament was introduced in the West to permit the playing of music in all keys with an equal amount of mis-tuning in each, without having to provide more than 12 pitches per octave on instruments, while still roughly approximating just intonation intervals. This allows much more facile harmonic motion, while losing some subtlety of intonation. True equal temperament was not available to musicians before about 1870 because scientific tuning and measurement was not available. And in fact, from about 1450 to about 1800 musicians tolerated even less mistuning in the most common keys, like C major. Instead, they used approximations that emphasized the tuning of thirds or fifths in these keys, such as meantone temperament.
At the time equal temperament was beginning to take hold in the West, many people perceived the much-increased mis-tuning of the music, relative to meantone temperament, as a disgrace. Those in opposition to equal temperament worried that the temperament, by degrading the purity of each chord, would degrade the purity of music. The composers against equal temperament included Giuseppe Tartini.
Equal temperament does have a weak point in tonal music. Group of musicians such as string ensemble or a capella, where tuning by microtones can be possible simultaneously during concerts, often prefer to tune the parts comprising each chord in just tuning relative to one another, in order to maximize the effect of consonance. Other instruments, such as wind, keyboard, and fretted-instruments, use equal temperament or quasi-equal temperament, when the instruments have technical limitations to be tuned exactly equal. The dissonance of such temperaments is known to be noticed by an average audience. Some claim that this is especially troubling in the lower register, and had somewhat constrained composers in the classical and romantic eras from writing chords narrower than octave for the left hand in keyboard music, while such examples in cello parts of string quartets are more common. Others hear the dissonance as most troubling in the higher register, where beating between harmonics of mistuned consonances is faster, and where combinational tones, often an entire semitone out-of-tune in equal temperament, are louder.
