468edo

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← 467edo468edo469edo →
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 468-tone equal temperament (468tet), 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 of 468edo 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 (%) +24 +34 +16 +48 -1 +19 -42 +7 -3 +40 -3
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