# 1553edo

 ← 1552edo 1553edo 1554edo →
Prime factorization 1553 (prime)
Step size 0.772698¢
Fifth 908\1553 (701.61¢)
Semitones (A1:m2) 144:119 (111.3¢ : 91.95¢)
Dual sharp fifth 909\1553 (702.382¢)
Dual flat fifth 908\1553 (701.61¢)
Dual major 2nd 264\1553 (203.992¢)
Consistency limit 5
Distinct consistency limit 5

1553 equal divisions of the octave (abbreviated 1553edo or 1553ed2), also called 1553-tone equal temperament (1553tet) or 1553 equal temperament (1553et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1553 equal parts of about 0.773 ¢ each. Each step represents a frequency ratio of 21/1553, or the 1553rd root of 2.

## Theory

1553edo is only consistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.13 subgroup, where it notably tempers out 4096/4095 and 140625/140608.

### Odd harmonics

Approximation of odd harmonics in 1553edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.345 +0.035 +0.137 +0.082 -0.384 +0.168 -0.310 +0.132 -0.024 -0.208 -0.071
Relative (%) -44.7 +4.6 +17.8 +10.6 -49.7 +21.7 -40.1 +17.0 -3.1 -26.9 -9.2
Steps
(reduced)
2461
(908)
3606
(500)
4360
(1254)
4923
(264)
5372
(713)
5747
(1088)
6067
(1408)
6348
(136)
6597
(385)
6821
(609)
7025
(813)

### Subsets and supersets

1553edo is the 245th prime edo. 3106edo, which doubles it, provides a good correction to the harmonic 3.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [4923 -1553 [1553 4923]] -0.0130 0.0130 1.68
2.9.5 [93 -33 5, [-36 -26 51 [1553 4923 3606]] -0.0137 0.0106 1.38
2.9.5.7 [-5 5 5 -8, [2 -10 14 -1, [37 1 -4 -11 [1553 4923 3606 4360]] -0.0225 0.0178 2.31
2.9.5.7.13 4096/4095, 140625/140608, 28829034/28824005, [4 10 -9 0 -4 [1553 4923 3606 4360 5372]] -0.0271 0.0184 2.38

Francium