Look for information on "historically-informed performance practice" regarding keyboardists and composers in various musical style periods. This is a big topic and it will require research.
There are endless treatises on these various temperament systems, written hundreds of years ago. Most of these treatises include a lot of physics and mathematics that explain how the systems were derived.
But the good news with Pianoteq is that you don't have to understand any of the mathematics. You have a large list of presets from which to choose and with which to experiment.
Historically, these temperaments apply to keyboard instruments such as the pipe organ, harpsichord and fortepiano, but also to the harp, and the fretted instruments such as the lute, theorbo, Baroque guitar, and even the viola da gamba and the other viols.
In the Renaissance and early Baroque, the Valotti temperament was popular.
Bach used the "Well-Tempered" temperament system for his famous two folios that we know as the "Well-Tempered Clavier".
The Werkmeister III temperament was popular in the late Baroque and early Classical periods.
In various places and parts of the Renaissance, Baroque and Classical periods people worked with many different varieties of "mean-tone" temperament. There are so many different schemes for this that, personally, I would not know where to start.
In the 20th century, composers like Harry Partch and Wendy Carlos devised their own musical instruments (acoustic or digital) and their own tuning and temperamant schemes, some of which had many more than 12 notes in an octave. (I seem to recall that Harry Partch composed for instruments he designed that had 43 notes in an octave, or something crazy like that.) But working with those would require somebody to invest considerable time in learning very unconventional playing techniques.
Well, it is a large topic. Do not get too distracted from playing your piano!
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