260edo

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← 259edo260edo261edo →
Prime factorization 22 × 5 × 13
Step size 4.61538¢ 
Fifth 152\260 (701.538¢) (→38\65)
Semitones (A1:m2) 24:20 (110.8¢ : 92.31¢)
Consistency limit 9
Distinct consistency limit 9

260 equal divisions of the octave (abbreviated 260edo or 260ed2), also called 260-tone equal temperament (260tet) or 260 equal temperament (260et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 260 equal parts of about 4.62 ¢ each. Each step represents a frequency ratio of 21/260, or the 260th root of 2.

Theory

260edo is enfactored in the 7-limit, with the same tuning as 65edo in the 5-limit, and the same as 130edo in the 7-limit. The mappings for harmonics 11 and 17 differ, but 260edo's are hardly an improvement over 130edo's. 29 is the first harmonic that is offered as a sizeable improvement over 130edo, tempering out 841/840, 16820/16807, and 47096/46875.

Prime harmonics

Approximation of prime harmonics in 260edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 -0.42 +1.38 +0.40 -2.09 -0.53 +1.20 -2.13 -0.58 -0.35 -0.42
relative (%) +0 -9 +30 +9 -45 -11 +26 -46 -13 -8 -9
Steps
(reduced)
260
(0)
412
(152)
604
(84)
730
(210)
899
(119)
962
(182)
1063
(23)
1104
(64)
1176
(136)
1263
(223)
1288
(248)

Scales

  • Kartvelian Tetradecatonic: 18 18 18 18 18 18 19 19 19 19 19 19 19 19