241ed49

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.

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241ed49

242ed49 →

Prime factorization	241 (prime)
Step size	27.9571 ¢
Octave	43\241ed49 (1202.15 ¢)
Twelfth	68\241ed49 (1901.08 ¢)
Consistency limit	6
Distinct consistency limit	6

241 equal divisions of the 49th harmonic (abbreviated 241ed49) is a nonoctave tuning system that divides the interval of 49/1 into 241 equal parts of about 28 ¢ each. Each step represents a frequency ratio of 49^1/241, or the 241st root of 49.

Theory

241ed49 is similar to 43edo, but the octave is stretched by 2.15 ¢. Since the 7th harmonic is exactly halfway between 120 and 121 steps, this difference is the absolute maximum amount of octave stretch 43edo can tolerate before a discrepancy for the 7th harmonic occurs.