86400edo
86400 EDO divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.
Theory
86400 is a significantly composite number 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.
| 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 |
Tempered commas
86400edo tempers out the Kirnberger's atom, albeit inconsistently, in the 5-limit.