86400edo

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← 86399edo86400edo86401edo →
Prime factorization 27 × 33 × 52
Step size 0.0138889¢
Fifth 50541\86400 (701.958¢) (→16847\28800)
Semitones (A1:m2) 8187:6495 (113.7¢ : 90.21¢)
Consistency limit 5
Distinct consistency limit 5

86400 equal divisions of the octave (abbreviated 86400edo or 86400ed2), also called 86400-tone equal temperament (86400tet) or 86400 equal temperament (86400et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 86400 equal parts of about 0.014 ¢ each. Each step represents a frequency ratio of 21/86400, or the 86400th root of 2.

Theory

86400 is a number notable for being the number of seconds in a day, and as such it has a lot of divisors, factoring into 2^7 x 3^3 x 5^2. While it isn't in the ranks of highly composite and superabundant, it's abundancy index is about 2.66.

Table of selected intervals

86400edo carries an interval size measure notation proposed by Eliora in January 2022, called the clock notation. The notation involves writing interval size measures using hours, minutes, seconds derived from steps of 86400edo. The notation's purpose is to write down intervals in the small-unnoticeable range. This means that one hour is a quarter-tone, one minute is 5/6 of a cent, and one second, one step size is 1/72 of a cent.

Selected intervals in clock notation
Steps Name Clock notation Associated JI
0 Unison 00:00:00 1/1 exact
60 Minute 00:01:00
72 Cent 00:01:12
141 Schisma 00:02:21 32805/32768
1548 Syntonic comma 00:25:48 81/80
1689 Pythagorean comma 00:28:09 531441/524288
3600 Quarter-tone, Hour 01:00:00
7200 Dodecaphonic semitone 02:00:00
14682 Just whole tone 04:04:42 9/8
50400 Dodecaphonic perfect fifth 14:00:00
50541 Just perfect fifth 14:02:21 3/2
86400 Octave 24:00:00 2/1 exact