30103edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 30102edo30103edo30104edo →
Prime factorization 30103 (prime)
Step size 0.0398631¢
Fifth 17609\30103 (701.95¢)
Semitones (A1:m2) 2851:2264 (113.6¢ : 90.25¢)
Consistency limit 11
Distinct consistency limit 11

30103 equal divisions of the octave (abbreviated 30103edo or 30103ed2), also called 30103-tone equal temperament (30103tet) or 30103 equal temperament (30103et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 30103 equal parts of about 0.040 ¢ each. Each step represents a frequency ratio of 21/30103, or the 30103rd root of 2.

30103edo is consistent in the 11-odd-limit and is otherwise a strong 2.3.5.17 subgroup tuning.

As an interval size measure

Since logarithm of 2 in base 10 is equal to 0.30102999..., one step of 30103edo comes exceptionally close to being one step of an otherwise perfectly decimal tuning system, 100000ed10, similar to heptameride being one step of 301edo and savart being one step of 1000ed10. It was named jot by Augustus de Morgan in 1864.

Prime harmonics

Approximation of prime harmonics in 30103edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.0000 -0.0050 -0.0001 +0.0078 -0.0108 -0.0134 +0.0042 -0.0144 +0.0085 +0.0079 -0.0068
relative (%) +0 -13 -0 +19 -27 -34 +11 -36 +21 +20 -17
Steps
(reduced)
30103
(0)
47712
(17609)
69897
(9691)
84510
(24304)
104139
(13830)
111394
(21085)
123045
(2633)
127875
(7463)
136173
(15761)
146240
(25828)
149136
(28724)