463edo

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← 462edo463edo464edo →
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 463-tone equal temperament (463tet), 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 of 463edo 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 +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* 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)

Music

Francium