# 241edo

 ← 240edo 241edo 242edo →
Prime factorization 241 (prime)
Step size 4.97925¢
Fifth 141\241 (702.075¢)
Semitones (A1:m2) 23:18 (114.5¢ : 89.63¢)
Consistency limit 15
Distinct consistency limit 15

241 equal divisions of the octave (abbreviated 241edo or 241ed2), also called 241-tone equal temperament (241tet) or 241 equal temperament (241et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 241 equal parts of about 4.98 ¢ each. Each step represents a frequency ratio of 21/241, or the 241st root of 2.

## Theory

241edo is distinctly consistent in the 15-odd-limit. It has a sharp tendency, with prime harmonics 3 through 13 all tuned sharp. The equal temperament tempers out 78732/78125 in the 5-limit, 19683/19600 and 3136/3125 in the 7-limit, 540/539, 43923/43904, 65536/65219, and 151263/151250 in the 11-limit, and 351/350, 676/675, 729/728, 1001/1000 and 2080/2079 in the 13-limit. It provides the optimal patent val for subpental.

### Prime harmonics

Approximation of prime harmonics in 241edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.12 +2.07 +2.13 +1.38 +0.97 -0.39 +1.24 -0.89 +1.13 +0.19
Relative (%) +0.0 +2.4 +41.5 +42.7 +27.7 +19.4 -7.9 +24.9 -17.8 +22.7 +3.9
Steps
(reduced)
241
(0)
382
(141)
560
(78)
677
(195)
834
(111)
892
(169)
985
(21)
1024
(60)
1090
(126)
1171
(207)
1194
(230)

### Subsets and supersets

241edo is the 53rd prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal 8ve
Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [382 -241 [241 382]] -0.038 0.038 0.76
2.3.5 78732/78125, [56 -28 -5 [241 382 560]] -0.322 0.403 8.10
2.3.5.7 3136/3125, 19683/19600, 829940/823543 [241 382 560 677]] -0.431 0.397 7.97
2.3.5.7.11 540/539, 3136/3125, 8019/8000, 15488/15435 [241 382 560 677 834]] -0.425 0.355 7.14
2.3.5.7.11.13 351/350, 540/539, 676/675, 3136/3125, 10648/10647 [241 382 560 677 834 892]] -0.397 0.330 6.63

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 20\241 99.59 200/189 Quintagar / quinsandric
1 50\241 248.96 [-26 18 -1 Monzismic
1 76\241 378.42 56/45 Subpental
1 89\241 443.15 162/125 Sensipent
1 100\241 497.93 4/3 Gary

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct