# 190537edo

Jump to navigation
Jump to search
Prime factorization
190537 (prime)
Step size
0.00629799¢
Fifth
111457\190537 (701.955¢)

(convergent)
Semitones (A1:m2)
18051:14326 (113.7¢ : 90.22¢)
Consistency limit
11
Distinct consistency limit
11

← 190536edo | 190537edo | 190538edo → |

(convergent)

The **190537edo** divides the octave into 190537 equal parts of 0.0063 cents each. It is the denominator of the next convergent for log_{2}3 past 111202, with another such convergent not occurring until 10590737.

## Theory

190537edo has a consistency limit of 11, which is rather impressive for a convergent. However, it's strongest in the 2.3.7.17.23 subgroup. Notably, it's the first member of the log_{2}3 convergent series with a 3-2 telicity k-strength greater that 1 since 665edo and it even surpasses 665edo in telicity k-strength. However, the downside is that the step size is many times smaller than the JND. The 3-limit comma this EDO tempers out has been named the Archangelic comma.

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.00000 | +0.00000 | -0.00134 | +0.00010 | +0.00175 | +0.00200 | +0.00058 | -0.00230 | +0.00048 | -0.00079 | +0.00187 | +0.00242 |

relative (%) | +0 | +0 | -21 | +2 | +28 | +32 | +9 | -36 | +8 | -12 | +30 | +38 | |

Steps (reduced) |
190537 (0) |
301994 (111457) |
442413 (61339) |
534905 (153831) |
659150 (87539) |
705071 (133460) |
778813 (16665) |
809387 (47239) |
861906 (99758) |
925625 (163477) |
943958 (181810) |
992594 (39909) |