1802edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 1801edo1802edo1803edo →
Prime factorization 2 × 17 × 53
Step size 0.665927¢ 
Fifth 1054\1802 (701.887¢) (→31\53)
Semitones (A1:m2) 170:136 (113.2¢ : 90.57¢)
Consistency limit 15
Distinct consistency limit 15

1802 equal divisions of the octave (abbreviated 1802edo or 1802ed2), also called 1802-tone equal temperament (1802tet) or 1802 equal temperament (1802et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1802 equal parts of about 0.666 ¢ each. Each step represents a frequency ratio of 21/1802, or the 1802nd root of 2.

1802edo is consistent in the 15-odd-limit. In the 2.3.5.11.13 subgroup, it is enfactored with the same mapping as 901edo, while correcting the 901edo's mapping for 7. It is a tuning for the hemiegads temperament in the 7-limit. Aside from this, 1802c val is the tuning for the quinmite temperament.

Prime harmonics

Approximation of prime harmonics in 1802edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.068 -0.076 +0.098 +0.069 -0.128 +0.261 +0.156 -0.305 -0.054 -0.307
Relative (%) +0.0 -10.2 -11.4 +14.6 +10.4 -19.2 +39.2 +23.5 -45.9 -8.2 -46.2
Steps
(reduced)
1802
(0)
2856
(1054)
4184
(580)
5059
(1455)
6234
(828)
6668
(1262)
7366
(158)
7655
(447)
8151
(943)
8754
(1546)
8927
(1719)