# 593edo

 ← 592edo 593edo 594edo →
Prime factorization 593 (prime)
Step size 2.02361¢
Fifth 347\593 (702.192¢)
Semitones (A1:m2) 57:44 (115.3¢ : 89.04¢)
Consistency limit 9
Distinct consistency limit 9

593 equal divisions of the octave (abbreviated 593edo or 593ed2), also called 593-tone equal temperament (593tet) or 593 equal temperament (593et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 593 equal parts of about 2.02 ¢ each. Each step represents a frequency ratio of 21/593, or the 593rd root of 2.

## Theory

593edo is consistent to the 9-odd-limit. The equal temperament tempers out 4375/4374, 33554432/33480783, 52734375/52706752, and 67108864/66976875 in the 7-limit. It supports vulture and squarschmidt. It is also notable in the 2.3.5.7.17 subgroup, tempering out 2500/2499.

### Prime harmonics

Approximation of prime harmonics in 593edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.237 +0.196 +0.483 -0.896 -0.730 +0.272 -0.043 -0.956 +0.440 +0.327
Relative (%) +0.0 +11.7 +9.7 +23.9 -44.3 -36.1 +13.5 -2.1 -47.2 +21.7 +16.2
Steps
(reduced)
593
(0)
940
(347)
1377
(191)
1665
(479)
2051
(272)
2194
(415)
2424
(52)
2519
(147)
2682
(310)
2881
(509)
2938
(566)

### Subsets and supersets

593edo is the 108th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [940 -593 [593 940]] -0.0748 0.0748 3.70
2.3.5 [24 -21 4, [37 25 -33 [593 940 1377]] -0.0780 0.0613 3.03
2.3.5.7 4375/4374, 33554432/33480783, 52734375/52706752 [593 940 1377 1665]] -0.1015 0.0669 3.31

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 196\593 396.63 98304/78125 Squarschmidt
1 215\593 435.08 9/7 Supermajor
1 235\593 475.55 320/243 Vulture
1 246\593 497.81 4/3 Gary
1 277\593 560.54 864/625 Whoosh

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

Francium