Bird's eye view of temperaments by accuracy: Difference between revisions
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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]], 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. | 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]], 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. | ||
=== [[Orwell]] === | |||
[[#Note counts|Note count]]: 22 for {3, 5, 7, 9, 15, 21, 25, 35, 45, 75} ([[9L 13s]]) | |||
[[#Generator tunings|Generator tunings]]: 5\22, 7\31, 12\53, 19\84 | |||
Orwell is a tempermant generated by a slightly sharp subminor third representing [[7/6]], seven of which reach [[6/1]]. Its name stems from George Orwell's book 1984, as a good generator is [[84edo|19\84]]. Three subminor thirds reach 8/5, the [[5th]] subharmonic. This temperament is supported by notable edos [[22edo|22]], [[31edo|31]], and [[53edo|53]], as well as the less known though still notable [[84edo]]. This temperament represents the 7-limit with good accuracy and relatively low complexity. However, the mapping for 11 is very simple, so this temperament really comes into its own in the 11-limit (see [[#Undecimal Orwell]]). Important commas tempered out by orwell include [[225/224]], [[1728/1715]], [[2430/2401]], [[6144/6125]], [[65625/65536]], and [[2109375/2097152]]. | |||
== 11-limit focus == | == 11-limit focus == | ||