229ed169

This page presents a topic of primarily mathematical interest.

While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

← 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.