224edo: Difference between revisions

'''224edo''' is the [[EDO|equal division of the octave]] into 224 parts of 5.3571 [[cent]]s each. It is a very strong [[13-limit]] system, tempering out [[32805/32768]] in the [[5-limit]]; [[4375/4374]], 16875/16807 and 65625/65536 in the [[7-limit]]; 540/539, 1375/1372, 4000/3993 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; and 625/624, 729/728, 1575/1573 and 2200/2197 in the [[13-limit]], leading to an abundance of precisely-tuned essentially tempered chords. It defines the [[optimal patent val]] for [[Ragismic_microtemperaments #Octoid|octoid temperament]] in the 7-, 11- and 13-limit, and for [[Mirkwai_family|mirkwai]], the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for [[Mirkwai_family #Indra|indra]] and [[Mirkwai_family #Shibi|shibi]] temperaments. It is the twelfth [[The_Riemann_Zeta_Function_and_Tuning #Zeta EDO lists|zeta integral edo]].