# 463edo

 ← 462edo 463edo 464edo →
Prime factorization 463 (prime)
Step size 2.59179¢
Fifth 271\463 (702.376¢)
Semitones (A1:m2) 45:34 (116.6¢ : 88.12¢)
Consistency limit 11
Distinct consistency limit 11

463 equal divisions of the octave (463edo), or 463-tone equal temperament (463tet), 463 equal temperament (463et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 463 equal parts of about 2.59 ¢ each.

## Theory

463et tempers out 184528125/184473632, 4096000/4084101, 703125/702464, 67108864/66976875, 95703125/95551488, 359661568/358722675 and 420175/419904 in the 7-limit; 161280/161051, 25165824/25109315, 820125/819896, 29296875/29218112, 1019215872/1019046875, 4000/3993, 759375/758912, 117649/117612, 2359296/2358125, 6250/6237, 369140625/369098752, 200704/200475, 283115520/282475249, 825000/823543, 180224/180075, 537109375/536870912, 19712/19683, 3025/3024, 199297406/199290375, 1362944/1361367, 532400/531441, 3294225/3294172 and 1771561/1771470 in the 11-limit. It supports amity, trinity and undesemi.

### Prime harmonics

Approximation of prime harmonics in 463edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 +0.42 -0.14 +0.50 +0.73 -0.79 -1.28 +0.54 -1.06 -0.64 +0.54
relative (%) +0 +16 -5 +19 +28 -30 -50 +21 -41 -25 +21
Steps
(reduced)
463
(0)
734
(271)
1075
(149)
1300
(374)
1602
(213)
1713
(324)
1892
(40)
1967
(115)
2094
(242)
2249
(397)
2294
(442)

### Subsets and supersets

463edo is the 90th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [734 -463 463 734] -0.1328 0.1327 5.12
2.3.5 1600000/1594323, [91 -12 -31 463 734 1075] -0.0689 0.1411 5.44
2.3.5.7 420175/419904, 703125/702464, 1600000/1594323 463 734 1075 1300] -0.0966 0.1313 5.07
2.3.5.7.11 3025/3024, 4000/3993, 19712/19683, 117649/117612 463 734 1075 1300 1602] -0.1197 0.1262 4.87
2.3.5.7.11.13 676/675, 1716/1715, 3025/3024, 4000/3993, 4096/4095 463 734 1075 1300 1602 1713] -0.0643 0.1691 6.52
2.3.5.7.11.13.17 442/441, 595/594, 676/675, 2500/2499, 3025/3024, 4096/4095 463 734 1075 1300 1602 1713 1892] -0.0103 0.2051 7.91

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(Reduced)
Cents
(Reduced)
Associated
Ratio
Temperaments
1 31\463 80.35 22/21 Undesemi
1 51\463 132.18 27/25 Astro
1 131\463 339.52 243/200 Amity (5-limit)
1 176\463 456.16 125/96 Qak
1 198\463 513.17 121/90 Trinity (463fg)