# 468edo

 ← 467edo 468edo 469edo →
Prime factorization 22 × 32 × 13
Step size 2.5641¢
Fifth 274\468 (702.564¢) (→137\234)
Semitones (A1:m2) 46:34 (117.9¢ : 87.18¢)
Consistency limit 13
Distinct consistency limit 13

468 equal divisions of the octave (abbreviated 468edo or 468ed2), also called 468-tone equal temperament (468tet) or 468 equal temperament (468et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 468 equal parts of about 2.56 ¢ each. Each step represents a frequency ratio of 21/468, or the 468th root of 2.

## Theory

468et tempers out 78125000/78121827, 4375/4374, 250047/250000, 2401/2400, 420175/419904, 200120949/200000000 and 40353607/40310784 in the 7-limit; 21437500/21434787, 151263/151250, 117649/117612, 514714375/514434888, 47265625/47258883, 9801/9800, 3025/3024, 1890625/1889568, 160083/160000, 41503/41472, 3294225/3294172, 43923/43904, 102487/102400 and 1771561/1769472 in the 11-limit. It provides the optimal patent val for unlit.

### Odd harmonics

Approximation of odd harmonics in 468edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.61 +0.87 +0.40 +1.22 -0.04 +0.50 -1.09 +0.17 -0.08 +1.01 -0.07
Relative (%) +23.8 +33.8 +15.8 +47.5 -1.4 +19.4 -42.5 +6.7 -3.0 +39.5 -2.7
Steps
(reduced)
742
(274)
1087
(151)
1314
(378)
1484
(80)
1619
(215)
1732
(328)
1828
(424)
1913
(41)
1988
(116)
2056
(184)
2117
(245)

### Subsets and supersets

468 factors into 22 × 32 × 13, with subset edos 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, and 234.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [371 -234 [468 742]] -0.1922 0.1921 7.49
2.3.5 2199023255552/2179240250625, 7629394531250/7625597484987 [468 742 1087]] -0.2524 0.1785 6.96
2.3.5.7 4375/4374, 2401/2400, 47141561040896/46708681640625 [468 742 1087 1314]] -0.2253 0.1615 6.30
2.3.5.7.11 3025/3024, 4375/4374, 2401/2400, 5767168/5740875 [468 742 1087 1314 1619]] -0.1782 0.1725 6.73
2.3.5.7.11.13 2080/2079, 1001/1000, 3025/3024, 1716/1715, 1982464/1974375 [468 742 1087 1314 1619 1732]] -0.1709 0.1583 6.17
2.3.5.7.11.13.17 2080/2079, 1001/1000, 3025/3024, 1716/1715, 17920/17901, 30464/30375 [468 742 1087 1314 1619 1732 1913]] -0.1526 0.1533 5.98

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)*
Cents
(reduced)*
Associated
Ratio*
Temperaments
1 179\468 458.97 125/96 Majvam
4 194\468
(40\468)
497.44
(102.56)
4/3
(35/33)
Undim
9 123\468
(19\468)
315.38
(48.72)
6/5
(36/35)
Ennealimmal
18 97\468
(7\468)
248.72
(17.95)
231/200
(99/98)
Hemiennealimmal

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct