229ed169

← 228ed169

229ed169

230ed169 →

Prime factorization	229 (prime)
Step size	38.7819 ¢
Octave	31\229ed169 (1202.24 ¢)
Twelfth	49\229ed169 (1900.31 ¢) (semiconvergent)
Consistency limit	12
Distinct consistency limit	9

229 equal divisions of the 169th harmonic (abbreviated 229ed169) is a nonoctave tuning system that divides the interval of 169/1 into 229 equal parts of about 38.8 ¢ each. Each step represents a frequency ratio of 169^1/229, or the 229th root of 169.

Theory

229ed169 is similar to 31edo, but the octave is stretched by 2.23893 ¢. Since the 13th harmonic is exactly halfway between 114 and 115 steps, this difference is the absolute maximum amount of octave stretch 31edo can tolerate before a discrepancy for the 13th harmonic occurs.