Bird's eye view of temperaments by accuracy: Difference between revisions

Magic is generated by a major third of around 380 cents, five of which make a perfect twelft ([[3/1]]). This results in the magic comma, [[3125/3072]], being tempered out. Since the major third is tuned quite flat, it makes sense to equate two of them to 14/9, tempering out [[225/224]] and mapping 7/4 to +12 generators, which also tempers out [[245/243]]. While magic has slightly higher complexity and error than [[#Septimal meantone|septimal meantone]], it doesn't temper out [[81/80]] and therefore can distinguish [[9/8]] and [[10/9]], and is in fact one of the simplest temperaments capable of mapping the [[9-odd-limit]] distinctly. The canonical extension to the 11- and 13-limits tempers out 100/99 and 105/104, but that increases complexity and lowers accuracy.