1553edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 1552edo1553edo1554edo →
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 1553-tone equal temperament (1553tet), 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 of 1553edo 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 (%) -45 +5 +18 +11 -50 +22 -40 +17 -3 -27 -9
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

Music

Francium