Perfect intonation Vs. Tempered Intonation
A visualization of the imperfections tempered tuning vs. perfect ration based intonation.
From Justonic(by way of Synthtopia):
With just tuning, composers were more or less locked into the key that a piece of music began in. This was not thought to be a problem until the rise of keyboard based instruments, which would sound out of tune if not played in their native key.
Equal-temperament– which remains the common tuning to this day– was developed in the 16th century as a compromise that allowed keyboard instruments to freely play in any key without being re-tuned. While this provided great freedom to composers to use any key and move between them with a piece of music, it has the side effect of making all music mathematically imperfect.
Wikipedia has a great chart demonstrating these imperfect ratios.
Most people– myself included– are used to it, but the musipheliacs at Justonic insist that this is the proper tuning(and their graphics make a hypnotizing argument.
