593edo

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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

Music

Francium