593edo: Difference between revisions

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Line 17: Line 17:
| {{monzo| 940 -593 }}
| {{monzo| 940 -593 }}
| {{mapping| 593 940 }}
| {{mapping| 593 940 }}
| -0.0748
| −0.0748
| 0.0748
| 0.0748
| 3.70
| 3.70
Line 24: Line 24:
| {{monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }}
| {{monzo| 24 -21 4 }}, {{monzo| 37 25 -33 }}
| {{mapping| 593 940 1377 }}
| {{mapping| 593 940 1377 }}
| -0.0780
| −0.0780
| 0.0613
| 0.0613
| 3.03
| 3.03
Line 31: Line 31:
| 4375/4374, 33554432/33480783, 52734375/52706752
| 4375/4374, 33554432/33480783, 52734375/52706752
| {{mapping| 593 940 1377 1665 }}
| {{mapping| 593 940 1377 1665 }}
| -0.1015
| −0.1015
| 0.0669
| 0.0669
| 3.31
| 3.31

Revision as of 01:55, 16 November 2024

← 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

Template:EDO intro

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

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 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 Template:Rank-2 end Template:Orf

Music

Francium