53edo: Difference between revisions

53edo is notable as an excellent [[5-limit]], a fact apparently first noted by Isaac Newton, notably tempering out [[Mercator's comma]] (3⁵³/2⁸⁴), the [[schisma|schisma (32805/32768)]], the [[amity comma|amity comma (1600000/1594323)]] and the [[15625/15552|kleisma (15625/15552)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], [[4375/4374|ragisma (4375/4374)]] and [[3125/3087|gariboh comma (3125/3087)]]. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[Marvel family #Athene|athene]] temperament. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit.