# 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 (abbreviated 463edo or 463ed2), also called 463-tone equal temperament (463tet) or 463 equal temperament (463et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 463 equal parts of about 2.59 ¢ each. Each step represents a frequency ratio of 21/463, or the 463rd root of 2.

## Theory

The equal temperament tempers out the amity comma in the 5-limit; 420175/419904 and 703125/702464 in the 7-limit; 3025/3024, 4000/3993, 6250/6237, 19712/19683, and 117649/117612 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 (%) +0.0 +16.2 -5.3 +19.5 +28.3 -30.4 -49.5 +21.0 -40.9 -24.5 +20.7
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* Cents* 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)

Francium