253edo
253EDO is the equal division of the octave into 253 parts of 4.743083 cents each.
253 tone equal temperament
253EDO is consistent to the 17-limit, approximating the fifth by 148\253 (0.021284 cents sharper than the just 3/2), and the prime harmonics from 5 to 17 are all slightly flat. It tempers out 32805/32768 in the 5-limit; 2401/2400 in the 7-limit; 385/384, 1375/1372 and 4000/3993 in the 11-limit; 325/324, 1575/1573 and 2200/2197 in the 13-limit; 375/374 and 595/594 in the 17-limit. It provides a good tuning for higher-limit sesquiquartififths temperament.
253 tone equal modes:
63 32 63 63 32: Pentatonic
43 43 19 43 43 43 19: Pythagorean tuning
41 41 24 41 41 41 24: Meantonic tuning
35 35 35 35 35 35 35 8: Porcupine tuning
33 33 33 11 33 33 33 33 11: "The Hendecapliqued superdiatonic of the Icositriphony"
31 31 31 18 31 31 31 31 18: Superdiatonic tuning in the way of Mavila
26 26 15 26 26 26 15 26 26 26 15: Sensi tuning
20 20 20 11 20 20 20 20 11 20 20 20 20 11: Ketradektriatoh tuning
PRIME FACTORIZATION: