12348edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 12347edo12348edo12349edo →
Prime factorization 22 × 32 × 73
Step size 0.0971817¢
Fifth 7223\12348 (701.944¢)
Semitones (A1:m2) 1169:929 (113.6¢ : 90.28¢)
Consistency limit 41
Distinct consistency limit 41

12348 equal divisions of the octave (abbreviated 12348edo or 12348ed2), also called 12348-tone equal temperament (12348tet) or 12348 equal temperament (12348et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 12348 equal parts of about 0.097 ¢ each. Each step represents a frequency ratio of 21/12348, or the 12348th root of 2.. It is a remarkable very high-limit equal temperament, consistent through the 41-odd-limit distinctly, tempering out 17205/17204, 25025/25024, 28861/28860, 44955/44954, 47125/47124, 52326/52325, 83657/83655, 89376/89375, 866133/866125, 1183455/1183424, 1843155/1843072, and 4629625/4629474.

Prime harmonics

Approximation of prime harmonics in 12348edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 -0.0114 -0.0163 -0.0212 -0.0060 -0.0029 +0.0009 -0.0397 +0.0055 -0.0339 -0.0404
relative (%) +0 -12 -17 -22 -6 -3 +1 -41 +6 -35 -42
Steps
(reduced)
12348
(0)
19571
(7223)
28671
(3975)
34665
(9969)
42717
(5673)
45693
(8649)
50472
(1080)
52453
(3061)
55857
(6465)
59986
(10594)
61174
(11782)